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a/_sources/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial2.ipynb b/_sources/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial2.ipynb index 4834762de..b69e95d1a 100644 --- a/_sources/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial2.ipynb +++ b/_sources/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial2.ipynb @@ -8,7 +8,7 @@ "id": "view-in-github" }, "source": [ - "\"Open   \"Open" + "\"Open   \"Open" ] }, { @@ -29,7 +29,7 @@ "\n", "__Content editors:__ Konrad Kording, Shaonan Wang\n", "\n", - "__Production editors:__ Konrad Kording, Spiros Chavlis" + "__Production editors:__ Konrad Kording, Spiros Chavlis, Konstantine Tsafatinos" ] }, { @@ -1801,11 +1801,44 @@ "source": [ "## Play around with LLMs\n", "\n", - "Try the following questions with [ChatGPT](https://openai.com/blog/chatgpt) (GPT3.5 without access to the web) and with GPTBing in creative mode (GPT4 with access to the web). Note that the latter requires installing Microsoft Edge.\n", + "1. Try using LLMs' API to do tasks, such as utilizing the GPT-2 API to extend text from a provided context. To achieve this, ensure you have a HuggingFace account and secure an API token.\n", "\n", - "Pick someone you know who is likely to have a web presence but is not super famous (not Musk or Trump). Ask GPT for a two-paragraph biography. How good is it?\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "execution": {} + }, + "outputs": [], + "source": [ + "import requests\n", + "\n", + "def query(payload, model_id, api_token):\n", + " headers = {\"Authorization\": f\"Bearer {api_token}\"}\n", + " API_URL = f\"https://api-inference.huggingface.co/models/{model_id}\"\n", + " response = requests.post(API_URL, headers=headers, json=payload)\n", + " return response.json()\n", "\n", - "Ask it something like “What is the US, UK, Germany, China, and Japan's per capita income over the past ten years? Plot the data in a single figure” (depending on when and where you run this, you will need to paste the resulting Python code into a colab notebook). Try asking it questions about the data or the definition of “per capita income” used. How good is it?" + "model_id = \"gpt2\"\n", + "api_token = \"hf_****\" # get yours at hf.co/settings/tokens\n", + "data = query(\"The goal of life is\", model_id, api_token)\n", + "print(data)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "execution": {} + }, + "source": [ + "2. Try the following questions with [ChatGPT](https://openai.com/blog/chatgpt) (GPT3.5 without access to the web) and with GPTBing in creative mode (GPT4 with access to the web). Note that the latter requires installing Microsoft Edge.\n", + "\n", + " Pick someone you know who is likely to have a web presence but is not super famous (not Musk or Trump). Ask GPT for a two-paragraph biography. How good is it?\n", + "\n", + " Ask it something like “What is the US, UK, Germany, China, and Japan's per capita income over the past ten years? Plot the data in a single figure” (depending on when and where you run this, you will need to paste the resulting Python code into a colab notebook). Try asking it questions about the data or the definition of “per capita income” used. How good is it?" ] }, { @@ -1976,7 +2009,7 @@ "name": "python3" }, "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -1990,10 +2023,10 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.3" + "version": "3.9.19" }, "toc-autonumbering": true }, "nbformat": 4, - "nbformat_minor": 0 + "nbformat_minor": 4 } \ No newline at end of file diff --git a/projects/ComputerVision/data_augmentation.html b/projects/ComputerVision/data_augmentation.html index b52e4c488..90ab553a7 100644 --- a/projects/ComputerVision/data_augmentation.html +++ b/projects/ComputerVision/data_augmentation.html @@ -1763,8 +1763,8 @@

Cutout

Mixup#

Mixup is a data augmentation technique that combines pairs of examples via a convex combination of the images and the labels. Given images \(x_i\) and \(x_j\) with labels \(y_i\) and \(y_j\), respectively, and \(\lambda \in [0, 1]\), mixup creates a new image \(\hat{x}\) with label \(\hat{y}\) the following way:

-
-(128)#\[\begin{align} +
+(128)#\[\begin{align} \hat{x} &= \lambda x_i + (1 - \lambda) x_j \\ \hat{y} &= \lambda y_i + (1 - \lambda) y_j \end{align}\]
diff --git a/projects/modelingsteps/Example_Deep_Learning_Project.html b/projects/modelingsteps/Example_Deep_Learning_Project.html index ab5c7aa7b..9d9f19ff5 100644 --- a/projects/modelingsteps/Example_Deep_Learning_Project.html +++ b/projects/modelingsteps/Example_Deep_Learning_Project.html @@ -2067,33 +2067,33 @@

Build model -
Epoch [100/500], Step [1/2], Loss: 1.5181, Accuracy: 44.57%
+
Epoch [100/500], Step [1/2], Loss: 0.8369, Accuracy: 71.51%
 ------------------------------------------
-Epoch [100/500], Step [2/2], Loss: 1.3739, Accuracy: 49.61%
+Epoch [100/500], Step [2/2], Loss: 0.9079, Accuracy: 67.83%
 ------------------------------------------
 

 

-
Epoch [200/500], Step [1/2], Loss: 1.1389, Accuracy: 59.11%
+
Epoch [200/500], Step [1/2], Loss: 0.6369, Accuracy: 77.52%
 ------------------------------------------
-Epoch [200/500], Step [2/2], Loss: 1.0898, Accuracy: 59.50%
+Epoch [200/500], Step [2/2], Loss: 0.5581, Accuracy: 81.40%
 ------------------------------------------
 

 

-
Epoch [300/500], Step [1/2], Loss: 0.9293, Accuracy: 64.53%
+
Epoch [300/500], Step [1/2], Loss: 0.5327, Accuracy: 80.23%
 ------------------------------------------
-Epoch [300/500], Step [2/2], Loss: 0.9329, Accuracy: 65.31%
+Epoch [300/500], Step [2/2], Loss: 0.4692, Accuracy: 85.08%
 ------------------------------------------
 

 

-
Epoch [400/500], Step [1/2], Loss: 0.8864, Accuracy: 69.38%
+
Epoch [400/500], Step [1/2], Loss: 0.3940, Accuracy: 87.98%
 ------------------------------------------
-Epoch [400/500], Step [2/2], Loss: 0.8522, Accuracy: 69.19%
+Epoch [400/500], Step [2/2], Loss: 0.4626, Accuracy: 82.56%
 ------------------------------------------
 

 

-
Epoch [500/500], Step [1/2], Loss: 0.7897, Accuracy: 71.90%
+
Epoch [500/500], Step [1/2], Loss: 0.3307, Accuracy: 90.50%
 ------------------------------------------
-Epoch [500/500], Step [2/2], Loss: 0.7659, Accuracy: 72.67%
+Epoch [500/500], Step [2/2], Loss: 0.3613, Accuracy: 87.60%
 ------------------------------------------
 

 

@@ -2123,7 +2123,7 @@ 
Build model
-
Test Accuracy of the model on the 172 test moves: 66.860%
+
Test Accuracy of the model on the 172 test moves: 84.302%
 

 

 

@@ -2137,7 +2137,7 @@ 
Build model
-../../_images/cba2349525942ed7116fe4ee60b69551fbe8db7877d96f2b5f73a68370265c04.png
+../../_images/78566d46f1f05e3965d54f9bb1efec22378c1d3f0317e8f5faf8b50b2220d972.png
 

 

 
The errors vary each time the model is run, but a common error seems to be that head scratching is predicted from some other movements that also involve arms a lot: throw/catch, hand clapping, phone talking, checking watch, hand waving, taking photo. If we train the model longer, these errors tend to go away as well. For some reason, crossed legged sitting is sometimes misclassified for crawling, but this doesn’t always happen.

@@ -2225,10 +2225,10 @@ 
Step 8: Modeling completion
-
71.51162790697676
+
73.83720930232558
 

 

-../../_images/b262307ae22113985561c99072e9060eec913dd4399f366e530bd1a3924d7810.png
+../../_images/3d16ae3899ad056181e31c4171b56e0d6efa3a29eb3ddf32ed9cf0fdc143a92b.png
 

 

 
That is some pretty good performance based on only 6 / 24 joints!

@@ -2274,32 +2274,32 @@ 
Step 9: Model evaluation
*** FITTING: Left Leg
 

 

-
limb performance: 79.65%
+
limb performance: 72.67%
 
 *** FITTING: Right Leg
 

 

-
limb performance: 75.00%
+
limb performance: 70.93%
 
 *** FITTING: Left Arm
 

 

-
limb performance: 55.23%
+
limb performance: 66.86%
 
 *** FITTING: Right Arm
 

 

-
limb performance: 43.60%
+
limb performance: 38.95%
 
 *** FITTING: Torso
 

 

-
limb performance: 81.98%
+
limb performance: 79.65%
 
 *** FITTING: Head
 

 

-
limb performance: 52.33%
+
limb performance: 50.00%
 

 

 

@@ -2353,44 +2353,44 @@ 
Step 9: Model evaluation
*** FITTING: limbs only
 

 

-
performance: 77.33%
+
performance: 76.16%
 

 

-
performance: 6.98%
+
performance: 68.02%
 

 

-
performance: 82.56%
+
performance: 75.58%
 

 

-
performance: 87.79%
+
performance: 73.26%
 

 

 
performance: 70.35%
 

 

-
performance: 6.98%
-median performance: 73.84%
+
performance: 85.47%
+median performance: 74.42%
 
 *** FITTING: limbs+torso+head
 

 

-
performance: 69.77%
+
performance: 81.98%
 

 

-
performance: 73.26%
+
performance: 81.98%
 

 

-
performance: 81.40%
+
performance: 86.63%
 

 

-
performance: 81.98%
+
performance: 79.07%
 

 

-
performance: 83.14%
+
performance: 79.65%
 

 

-
performance: 84.30%
-median performance: 81.69%
+
performance: 86.05%
+median performance: 81.98%
 

 

 

diff --git a/projects/modelingsteps/ModelingSteps_10_DL.html b/projects/modelingsteps/ModelingSteps_10_DL.html
index 9b34b3f1e..bf8f2a7fb 100644
--- a/projects/modelingsteps/ModelingSteps_10_DL.html
+++ b/projects/modelingsteps/ModelingSteps_10_DL.html
@@ -58,7 +58,7 @@
 const thebe_selector_output = ".output, .cell_output"
 
     
-    
+    
     
     
     
@@ -1451,7 +1451,7 @@ 
Step 10: publishing the model#

 

 

-

+

 

 
Guiding principles:

 
    
diff --git a/projects/modelingsteps/ModelingSteps_1through2_DL.html b/projects/modelingsteps/ModelingSteps_1through2_DL.html
index ac11c4e6e..953b3c187 100644
--- a/projects/modelingsteps/ModelingSteps_1through2_DL.html
+++ b/projects/modelingsteps/ModelingSteps_1through2_DL.html
@@ -58,7 +58,7 @@
 const thebe_selector_output = ".output, .cell_output"
 
     
-    
+    
     
     
     
@@ -1515,11 +1515,11 @@ 
    Objectives#
    
 
    
 
    
-
    
+
    
 

 

 

-

+

 

 
 
@@ -1746,7 +1746,7 @@ 
Disclaimer#

 

 

-

+

 

 
 
@@ -1759,7 +1759,7 @@ 
Step 1: Finding a phenomenon and a question to ask about it#

 

 

-

+

 

 
 

@@ -1843,7 +1843,7 @@ 
Example projects step 1
 
 

-

+

 

 
 

@@ -1917,7 +1917,7 @@ 
Step 2: Understanding the state of the art & background#

 

 

-

+

 

 
 

@@ -2059,7 +2059,7 @@ 
Example projects step 2
<IPython.core.display.Markdown object>
 

 

-

+

 

 
Here you will do a literature review. For the projects, do not spend too much time on this. A thorough literature review could take weeks or months depending on your prior knowledge of the field…

 
The important thing for your project here is not to exhaustively survey the literature but rather to learn the process of modeling. 1-2 days of digging into the literature should be enough!

diff --git a/projects/modelingsteps/ModelingSteps_3through4_DL.html b/projects/modelingsteps/ModelingSteps_3through4_DL.html
index da00ab69f..be6614909 100644
--- a/projects/modelingsteps/ModelingSteps_3through4_DL.html
+++ b/projects/modelingsteps/ModelingSteps_3through4_DL.html
@@ -60,7 +60,7 @@
     
     
     
-    
+    
     
     
     
@@ -1464,7 +1464,7 @@ 
Step 3: Determining the basic ingredients#

 

 

-

+

 

 
 

@@ -1731,7 +1731,7 @@ 
Example projects step 3
<IPython.core.display.Markdown object>
 

 

-

+

 

 
 

@@ -1801,7 +1801,7 @@ 
Step 4: Formulating specific, mathematically defined hypotheses#

 

 

-

+

 

 
 

@@ -1921,7 +1921,7 @@ 
Example projects step 4
<IPython.core.display.Markdown object>
 

 

-

+

 

 
 

diff --git a/projects/modelingsteps/ModelingSteps_5through6_DL.html b/projects/modelingsteps/ModelingSteps_5through6_DL.html
index c8a21316e..34dd7de13 100644
--- a/projects/modelingsteps/ModelingSteps_5through6_DL.html
+++ b/projects/modelingsteps/ModelingSteps_5through6_DL.html
@@ -58,7 +58,7 @@
 const thebe_selector_output = ".output, .cell_output"
 
     
-    
+    
     
     
     
@@ -1441,7 +1441,7 @@ 
Step 5: Selecting the toolkit#

 

 

-

+

 

 
Once you have completed Steps 1-4 to your satisfaction, you are now ready to model. You have a specific question, a goal in mind, and precise hypotheses expressed in mathematical language. All these components will empower you to chose an appropriate modeling approach.

 
In selecting the right toolkit, i.e. the right mathematics, computer science, engineering, or physics, etc approaches, you should consider the following important rules:

@@ -1511,7 +1511,7 @@ 
Step 6: Planning / drafting the model#

 

 

-

+

 

 
Planning the model involves thinking about the general outline of the model, its components and how they might fit together. You want to draw a model diagram, make some sketches and formalize necessary equations. This step will thus outline a plan of implementation. Once you have that plan, this will hugely facilitate the actual implementation of the model in computer code.

 
Your model will have:

diff --git a/projects/modelingsteps/ModelingSteps_7through9_DL.html b/projects/modelingsteps/ModelingSteps_7through9_DL.html
index 248f81fb5..5abc0e98c 100644
--- a/projects/modelingsteps/ModelingSteps_7through9_DL.html
+++ b/projects/modelingsteps/ModelingSteps_7through9_DL.html
@@ -58,7 +58,7 @@
 const thebe_selector_output = ".output, .cell_output"
 
     
-    
+    
     
     
     
@@ -1458,7 +1458,7 @@ 
Step 7: Implementing the model#

 

 

-

+

 

 
This is the step where you finally start writing code! Separately implement each box, icon, or flow relationship identified in Step 6. Test each of those model components separately! (This is called a unit test). Unit testing ensures that each model components works are expected/planned.

 
Guiding principles:

@@ -1525,7 +1525,7 @@ 
Step 8: Completing the model#

 

 

-

+

 

 
Determing what you’re done modeling is a hard question. Referring back to your original goals will be crucial. This is also where a precise question and specific hypotheses expressed in mathematical relationships come in handy.

 
Note: you can always keep improving our model, but at some point you need to decide that it is finished. Once you have a model that displays the properties of a system you are interested in, it should be possible to say something about your hypothesis and question. Keeping the model simple makes it easier to understand the phenomenon and answer the research question.

@@ -1575,7 +1575,7 @@ 
Step 9: testing and evaluating the model#

 

 

-

+

 

 
Every models needs to be evaluated quantitatively. There are many ways to achieve that and not every model should be evaluated in the same way. Ultimately, model testing depends on what your goals are and what you want to get out of the model, e.g. qualitative vs quantitative fit to data.

 
Guiding principles:

diff --git a/projects/modelingsteps/TrainIllusionDataProjectDL.html b/projects/modelingsteps/TrainIllusionDataProjectDL.html
index 3c44316a7..0d6766352 100644
--- a/projects/modelingsteps/TrainIllusionDataProjectDL.html
+++ b/projects/modelingsteps/TrainIllusionDataProjectDL.html
@@ -1772,8 +1772,8 @@ 
Question\(N\) neurons and \(M\) trials for each of 3 motion conditions: no self-motion, slowly accelerating self-motion and faster accelerating self-motion.

-

-(126)#\[\begin{align}
+

+(126)#\[\begin{align}
 N &= 40 \\
 M &= 400
 \end{align}\]

diff --git a/projects/modelingsteps/TrainIllusionModelingProjectDL.html b/projects/modelingsteps/TrainIllusionModelingProjectDL.html
index 7b5d492ab..e3143f74d 100644
--- a/projects/modelingsteps/TrainIllusionModelingProjectDL.html
+++ b/projects/modelingsteps/TrainIllusionModelingProjectDL.html
@@ -1553,8 +1553,8 @@ 
Selected toolkitDrift-Diffusion Model (DDM) because it is a well-established framework that allows us to model decision making in the case of 2 alternative choices (here: self-motion vs. other train motion).

 
For our purposes simplest equation looks something like this:

-

-(127)#\[\begin{align}
+

+(127)#\[\begin{align}
 \dot e = \frac{de}{dt}= -c \cdot e + v \, ,
 \end{align}\]

 
where \(e\) is the accumulated evidence and \(v\) is our vestibular input already containing the noise (so we don’t need to add more noise?). \(c\) is the leakage constant, i.e., \(c=0\) means perfect integration; \(c=1\) means no integration (perfect leakage).

@@ -1630,7 +1630,7 @@ 
1. Vestibular signal generator
Text(0, 0.5, 'vestibular signal (a.u.)')
 

 

-../../_images/7a6c6ae3eb2ea67795759b6dba1034c7381b0cb54d2cd77bfcede4ca357fe354.png
+../../_images/f6ab9f77e2837ddf28ee5f76c8cb41df931cd5789762da1f6effcf890edabc16.png
 

 

 
@@ -1671,7 +1671,7 @@ 
2. Integrator (DDM mechanism)
-../../_images/e87d7b08c2dc6f3986fb4495ccbc9654c5394b50dd33dd9108dabfc1f3ee8ba3.png
+../../_images/3a10e03b56d5ecdbbd326f9f6a3bfe98d118669c377b69497bff4dde15d0c0cf.png
 

 

 
@@ -1821,7 +1821,7 @@ 
Model evaluation & testing
-../../_images/18284a03f1891e727204736edfa1bc666b3f0063cdeb99b5471e269503c05923.png
+../../_images/44f2df9fa9aecdb09d84a11587e25f6add12dd7d32d158eb0853acd7ab29f906.png
 

 

 
There seems to be some parameter redundancy, i.e., we could chose different parameter combinations to make the model do something sensible…

@@ -1842,7 +1842,7 @@ 
Model evaluation & testing
-
 Motion detected for no-motion: 31.4% and motion: 61.6%
+
 Motion detected for no-motion: 31.5% and motion: 61.6%
 

 

 

@@ -1880,7 +1880,7 @@ 
Model evaluation & testing
-../../_images/7193ad58e0a35d1abada5cb4316ec93beaa66b9a913f6426e518ce1840053290.png
+../../_images/c81c8f6a77c176e76725be01bc6deec7a048dfc2f57487287143f02c94740461.png
 

 

 
Our hypothesis of linear increase of illusion strength with noise only holds true in a limited range of noise… It’s monotonic but saturating of course…

diff --git a/reports/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial1.err.log b/reports/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial1.err.log
index 0a93c9351..26d2c46a0 100644
--- a/reports/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial1.err.log
+++ b/reports/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial1.err.log
@@ -1,30 +1,30 @@
 Traceback (most recent call last):
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/nbclient/client.py", line 778, in _async_poll_for_reply
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/nbclient/client.py", line 778, in _async_poll_for_reply
     msg = await ensure_async(self.kc.shell_channel.get_msg(timeout=new_timeout))
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/jupyter_core/utils/__init__.py", line 198, in ensure_async
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/jupyter_core/utils/__init__.py", line 198, in ensure_async
     result = await obj
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/jupyter_client/channels.py", line 230, in get_msg
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/jupyter_client/channels.py", line 230, in get_msg
     res = self._recv()
 _queue.Empty
 
 During handling of the above exception, another exception occurred:
 
 Traceback (most recent call last):
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/jupyter_cache/executors/utils.py", line 58, in single_nb_execution
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/jupyter_cache/executors/utils.py", line 58, in single_nb_execution
     executenb(
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/nbclient/client.py", line 1305, in execute
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/nbclient/client.py", line 1305, in execute
     return NotebookClient(nb=nb, resources=resources, km=km, **kwargs).execute()
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/jupyter_core/utils/__init__.py", line 165, in wrapped
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/jupyter_core/utils/__init__.py", line 165, in wrapped
     return loop.run_until_complete(inner)
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/asyncio/base_events.py", line 647, in run_until_complete
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/asyncio/base_events.py", line 647, in run_until_complete
     return future.result()
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/nbclient/client.py", line 705, in async_execute
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/nbclient/client.py", line 705, in async_execute
     await self.async_execute_cell(
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/nbclient/client.py", line 1001, in async_execute_cell
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/nbclient/client.py", line 1001, in async_execute_cell
     exec_reply = await self.task_poll_for_reply
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/nbclient/client.py", line 802, in _async_poll_for_reply
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/nbclient/client.py", line 802, in _async_poll_for_reply
     error_on_timeout_execute_reply = await self._async_handle_timeout(timeout, cell)
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/nbclient/client.py", line 852, in _async_handle_timeout
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/nbclient/client.py", line 852, in _async_handle_timeout
     raise CellTimeoutError.error_from_timeout_and_cell(
 nbclient.exceptions.CellTimeoutError: A cell timed out while it was being executed, after 720 seconds.
 The message was: Cell execution timed out.
diff --git a/reports/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/W3D3_Tutorial1.err.log b/reports/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/W3D3_Tutorial1.err.log
index 99272860c..a7510f36d 100644
--- a/reports/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/W3D3_Tutorial1.err.log
+++ b/reports/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/W3D3_Tutorial1.err.log
@@ -1,30 +1,30 @@
 Traceback (most recent call last):
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/nbclient/client.py", line 778, in _async_poll_for_reply
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/nbclient/client.py", line 778, in _async_poll_for_reply
     msg = await ensure_async(self.kc.shell_channel.get_msg(timeout=new_timeout))
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/jupyter_core/utils/__init__.py", line 198, in ensure_async
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/jupyter_core/utils/__init__.py", line 198, in ensure_async
     result = await obj
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/jupyter_client/channels.py", line 230, in get_msg
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/jupyter_client/channels.py", line 230, in get_msg
     res = self._recv()
 _queue.Empty
 
 During handling of the above exception, another exception occurred:
 
 Traceback (most recent call last):
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/jupyter_cache/executors/utils.py", line 58, in single_nb_execution
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/jupyter_cache/executors/utils.py", line 58, in single_nb_execution
     executenb(
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/nbclient/client.py", line 1305, in execute
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/nbclient/client.py", line 1305, in execute
     return NotebookClient(nb=nb, resources=resources, km=km, **kwargs).execute()
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/jupyter_core/utils/__init__.py", line 165, in wrapped
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/jupyter_core/utils/__init__.py", line 165, in wrapped
     return loop.run_until_complete(inner)
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/asyncio/base_events.py", line 647, in run_until_complete
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/asyncio/base_events.py", line 647, in run_until_complete
     return future.result()
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/nbclient/client.py", line 705, in async_execute
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/nbclient/client.py", line 705, in async_execute
     await self.async_execute_cell(
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/nbclient/client.py", line 1001, in async_execute_cell
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/nbclient/client.py", line 1001, in async_execute_cell
     exec_reply = await self.task_poll_for_reply
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/nbclient/client.py", line 802, in _async_poll_for_reply
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/nbclient/client.py", line 802, in _async_poll_for_reply
     error_on_timeout_execute_reply = await self._async_handle_timeout(timeout, cell)
-  File "/opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/nbclient/client.py", line 852, in _async_handle_timeout
+  File "/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/nbclient/client.py", line 852, in _async_handle_timeout
     raise CellTimeoutError.error_from_timeout_and_cell(
 nbclient.exceptions.CellTimeoutError: A cell timed out while it was being executed, after 720 seconds.
 The message was: Cell execution timed out.
diff --git a/searchindex.js b/searchindex.js
index 9528a5f69..87bccbcf6 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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57, "vega_dataset": 57, "author": 57, "edit": 57, "author_filt": 57, "full": [57, 67, 94], "appendix": 57, "offici": 57, "document": 57, "book": 57, "yoshua": 59, "bengio": 59, "descent": [60, 67, 70], "autograd": 60, "execut": [60, 61, 62, 64, 65, 67, 69, 70, 73, 76, 77, 80, 81, 82, 84, 85, 87, 88, 89, 94, 100, 102], "set_devic": [60, 61, 62, 64, 65, 67, 69, 70, 73, 76, 77, 80, 81, 82, 84, 85, 87, 88, 89, 94, 100, 102], "steepest": 60, "ascent": 60, "analyt": [60, 61, 62], "vector": [60, 62, 77, 87], "backprop": 60, "chain": 60, "rule": [60, 87], "auto": [60, 80], "differenti": 60, "forward": [60, 87], "propag": 60, "buid": 60, "backward": 60, "modul": [60, 80, 82, 100, 102], "nn": [60, 70], "A": [61, 97, 100], "shallow": 61, "narrow": 61, "solut": [61, 62], "lnn": [61, 62], "landscap": 61, "depth": [61, 67], "effect": [61, 73, 94], "prelud": 62, "represent": [62, 73, 94], "tree": [62, 102], "sure": 62, "you": [62, 73], "enabl": [62, 81, 94], "singular": 62, "decomposit": 62, "svd": 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"solver": 97, "iter": 97, "epsilon": 97, "greedi": [97, 100], "For": [98, 100], "thinking3": 98, "amita": 99, "kapoor": 99, "futur": [99, 101], "othellogam": 100, "player": [100, 102], "compet": 100, "othello": 100, "othellonnet": 100, "valuenetwork": 100, "mse": 100, "progress": 100, "policynetwork": 100, "policybasedplay": 100, "mont": [100, 102], "carlo": [100, 102], "rollout": 100, "montecarlo": 100, "against": [100, 102], "unbeat": 100, "oppon": 100, "19": 100, "In": 101, "memori": 101, "mct": 102, "concept": 103}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 6, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinx": 56}})
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diff --git a/tutorials/Bonus_DeployModels/student/Bonus_Tutorial1.html b/tutorials/Bonus_DeployModels/student/Bonus_Tutorial1.html
index c3bde17eb..7ea47578f 100644
--- a/tutorials/Bonus_DeployModels/student/Bonus_Tutorial1.html
+++ b/tutorials/Bonus_DeployModels/student/Bonus_Tutorial1.html
@@ -48,7 +48,7 @@
 const thebe_selector_output = ".output, .cell_output"
 
 
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Tutorial Objectives
 

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Section 1: IntroductionVideo 1: Deploying Neural Networks on the Web#

 

 

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Submit your feedback
 
 

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We will start by building a simple web application in Flask, which we’ll keep extending throughout the tutorial. In the end, you will have a web app where you can upload an image and have it classified automatically by a neural network model.

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Section 2.1: Your First Flask App#

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Creating a minimal Flask app is very simple. You need to create a Flask object and define the handler for the root URL returning the HTML response. You need to provide the applications module or package, but we can use __name__ as a convenient shortcut.

We need one small trick because the app will be running in a notebook. If you just run the app, it will be accessible at http://127.0.0.1:5000. The problem is that this is a local address to the server where the notebook is running, so you can’t access it. This is where ngrok helps - it creates a tunnel from the notebook server to the outside world. Make sure you use the ngrok URL when testing your app.

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Section 2.2: Using Jinja2 Templates#

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The default template engine used by Flask is Jinja2. Jinja2 offers features that help you write clean and reusable templates such as inheritance, humanizing, and formatting data (there’s an extension for this), dividing components into sub-modules, etc.

In this section, we are going to add Jinja2 templates to the app. WIth Jinja2 you can use variables and control flow commands, like ifs and loops in your HTML code. Then you can pass data from your Python code to the template when it is rendered.

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Section 2.3: Apply the MVVM Design Pattern#

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Design patterns provide a way of writing reusable, adaptable, and extendable code. Design patterns are not libraries, but rather a set of best practices to follow when designing your software.

Model View View-Model (MVVM) is a powerful design pattern commonly used in web applications (and other GUI applications).

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Section 2.4: Creating a REST API#

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REST (Representational State Transfer) is a set of rules according to which APIs are designed to enable your service to interact with other services. If HTML pages are interfaces designed for humans, you can think about REST APIs as interfaces made for computers.

A common way to implement a REST API is for your application to respond to certain requests by returning a JSON string containing the required data.

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Section 3: Vue.js#

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We already talked about the MVVM pattern and implemented it using a back end framework - Flask. Applying the same pattern on the front end can also be beneficial when creating dynamic applications.

Vue.js is a great front end library that implements the MVVM design pattern. It is widely used for creating user interfaces and single-page applications.

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Section 4: Model Presentation#

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Now (finally) we have all the tools we need to deploy our neural network! We are going to use a pre-trained DenseNet mode. In the first step, we are going to create an API entry point that accepts an image as input and classifies it. After that, we will create a dynamic UI for easier interaction.

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Section 4.1: Image Classification API#

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First, we need to load a pre-trained DenseNet trained on ImageNet. You can use torchvision.models to quickly get a pre-trained model for many popular neural network architectures.

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Section 4.2: Create a Dynamic Application#

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We will now create a Flask app that receives an image at /predict and passes it through the model. We will also implement an interactive UI to upload the image and call the API.

The UI consists of a file upload field, a classify button, and an image displaying the uploaded file.

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Section 5: Deploy a Flask app on Heroku#

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Now you are going to deploy your application as a real web server outside of the notebook. We are going to use Heroku for this. Heroku is a PaaS (Platform-as-a-Service) that offers pre-configured environments so you can deploy an application easily and quickly. They also offer a free tier which is enough for deploying simple apps.

But first, you need to test your application locally.

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Section 5.1: Preparing Your Environment#

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You need to do all the steps from here on on your own machine and not in the notebook. You need to make sure that you have Python 3 installed and some code editor (for example VS Code). You will also be using the terminal a lot in this section.

First, you need to prepare your Python environment and install all required dependencies. You should first create an empty folder where you will store your application and do the following steps.

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Section 5.2: Create Your Application#

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You are now ready to create the files needed for your application. For now, you need just 2 files.

app.py

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Section 5.4: Preparing for Deployment on Heroku#

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Before we can deploy on Heroku there are a couple of things we need to prepare.

Create Procfile

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Section 5.5: Deploying on Heroku#

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You are now finally ready to deploy to Heroku! There are just a couple of steps needed.

1. Create a Heroku account

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Summary#

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In this tutorial you learned the basics of some modern tools for creating dynamic web applications and REST APIs. You also learned how you can deploy your neural network model as a web app.

You can now build on top of that and create more sophisticated and awesome applications and make them available to millions of people!

diff --git a/tutorials/W1D1_BasicsAndPytorch/student/W1D1_Tutorial1.html b/tutorials/W1D1_BasicsAndPytorch/student/W1D1_Tutorial1.html index 9551aec37..50961d6f3 100644 --- a/tutorials/W1D1_BasicsAndPytorch/student/W1D1_Tutorial1.html +++ b/tutorials/W1D1_BasicsAndPytorch/student/W1D1_Tutorial1.html @@ -50,7 +50,7 @@ - + @@ -1309,7 +1309,7 @@

Tutorial Objectives
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Section 1: Welcome to Neuromatch Deep learning courseVideo 1: Welcome and History#

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This will be an intensive 3 week adventure. We will all learn Deep Learning (DL) in a group. Groups need standards. Read our Code of Conduct.

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Submit your feedback
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Video 2: Why DL is cool#

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Discuss with your pod: What do you hope to get out of this course? [in about 100 words]

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Section 2.1: Creating Tensors#

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There are various ways of creating tensors, and when doing any real deep learning project, we will usually have to do so.

Construct tensors directly:

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Tensor a: tensor([[0.7889, 0.6579, 0.9194]])
-Tensor b: tensor([[ 0.2146, -0.3630, -0.4462, -0.4566],
-        [-0.9664,  0.4432, -0.3148,  0.6047],
-        [ 0.8843,  1.1931, -0.6849,  1.2385]])
+
Tensor a: tensor([[0.9728, 0.2797, 0.9038]])
+Tensor b: tensor([[ 1.3048, -2.7761,  0.0065, -1.7133],
+        [-0.8749,  0.0401, -0.0865, -0.8609],
+        [ 0.5365,  0.4012, -0.8520,  0.9674]])
 Tensor c: tensor([[0., 0., 0.]])
-Tensor d: tensor([[0.9450, 0.1686, 0.0553]])
+Tensor d: tensor([[0.7411, 0.6957, 0.3873]])
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+

@@ -1909,7 +1909,7 @@

Section 2.2: Operations in PyTorch#

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Tensor-Tensor operations

We can perform operations on tensors using methods under torch..

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Submit your feedback

Coding Exercise 2.2 : Simple tensor operations#

Below are two expressions involving operations on matrices.

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-(1)#\[\begin{equation} +
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Section 2.3 Manipulating Tensors in Pytorch#

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Indexing

Just as in numpy, elements in a tensor can be accessed by index. As in any numpy array, the first element has index 0 and ranges are specified to include the first to last_element-1. We can access elements according to their relative position to the end of the list by using negative indices. Indexing is also referred to as slicing.

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Coding Exercise 2.3: Manipulating Tensors\(A\) and \(B\) and returns the column sum of A multiplied by the sum of all the elmements of \(B\), i.e., a scalar, e.g.,

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Coding Exercise 2.3: Manipulating Tensors\(C\) and returns a 2D tensor consisting of a flattened \(C\) with the index of each element appended to this tensor in the row dimension, e.g.,

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Coding Exercise 2.3: Manipulating Tensors\(D\) and \(E\). If the dimensions allow it, this function returns the elementwise sum of \(D\)-shaped \(E\), and \(D\); else this function returns a 1D tensor that is the concatenation of the two tensors, e.g.,

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Section 2.4: GPUs#

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By default, when we create a tensor it will not live on the GPU!

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Discuss!

Try and reduce the dimensions of the tensors and increase the iterations. You can get to a point where the cpu only function is faster than the GPU function. Why might this be?

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Section 2.5: Datasets and Dataloaders#

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When training neural network models you will be working with large amounts of data. Fortunately, PyTorch offers some great tools that help you organize and manipulate your data samples.

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Video 8: Train and Test#

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Training and Test Datasets

When loading a dataset, you can specify if you want to load the training or the test samples using the train argument. We can load the training and test datasets separately. For simplicity, today we will not use both datasets separately, but this topic will be adressed in the next days.

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Dataloader

Another important concept is the Dataloader. It is a wrapper around the Dataset that splits it into minibatches (important for training the neural network) and makes the data iterable. The shuffle argument is used to shuffle the order of the samples across the minibatches.

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Section 3: Neural Networks#

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Section 3.2: Create a Simple Neural Network#

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For this example we want to have a simple neural network consisting of 3 layers:

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Section 3.3: Train Your Neural Network#

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Now it is time to train your network on your dataset. Don’t worry if you don’t fully understand everything yet - we will cover training in much more details in the next days. For now, the goal is just to see your network in action!

You will usually implement the train method directly when implementing your class NaiveNet. Here, we will implement it as a function outside of the class in order to have it in a separate cell.

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Visualize the training process#

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Video 14: XOR Widget#

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Exclusive OR (XOR) logical operation gives a true (1) output when the number of true inputs is odd. That is, a true output result if one, and only one, of the inputs to the gate is true. If both inputs are false (0) or both are true or false output results. Mathematically speaking, XOR represents the inequality function, i.e., the output is true if the inputs are not alike; otherwise, the output is false.

In case of two inputs (\(X\) and \(Y\)) the following truth table is applied:

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Interactive Demo 3.3: Solving XOR\(f(x)\) is ReLU is:

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+(8)#\[\begin{equation} y = f(x_1)+f(x_2)-f(x_1+x_2) \end{equation}\]

Try to set the weights and biases to implement this function after you played enough :)

Play with the parameters to solve XOR

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Do you think we can solve the discrete XOR (only 4 possibilities) with only 2 hidden units?

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Section 4: Ethics And Course Info#

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Video 16: Be a group#

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Video 17: Syllabus#

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Define Visualization using ALtair
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Edit the AUTHOR
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diff --git a/tutorials/W1D2_LinearDeepLearning/student/W1D2_BonusLecture.html b/tutorials/W1D2_LinearDeepLearning/student/W1D2_BonusLecture.html index 93e9dad32..b2cc0164f 100644 --- a/tutorials/W1D2_LinearDeepLearning/student/W1D2_BonusLecture.html +++ b/tutorials/W1D2_LinearDeepLearning/student/W1D2_BonusLecture.html @@ -58,7 +58,7 @@ const thebe_selector_output = ".output, .cell_output" - + @@ -1453,11 +1453,11 @@

Install and import feedback gadget#

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diff --git a/tutorials/W1D2_LinearDeepLearning/student/W1D2_Tutorial1.html b/tutorials/W1D2_LinearDeepLearning/student/W1D2_Tutorial1.html index 185a4cbad..17778fc6d 100644 --- a/tutorials/W1D2_LinearDeepLearning/student/W1D2_Tutorial1.html +++ b/tutorials/W1D2_LinearDeepLearning/student/W1D2_Tutorial1.html @@ -50,7 +50,7 @@ - + @@ -1043,7 +1043,7 @@

Tutorial Objectives
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Section 0: IntroductionVideo 0: Introduction#

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Section 1.1: Gradients & Steepest Ascent#

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Before introducing the gradient descent algorithm, let’s review a very important property of gradients. The gradient of a function always points in the direction of the steepest ascent. The following exercise will help clarify this.

Analytical Exercise 1.1: Gradient vector (Optional)#

Given the following function:

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-(9)#\[\begin{equation} +
+(9)#\[\begin{equation} z = h(x, y) = \sin(x^2 + y^2) \end{equation}\]

find the gradient vector:

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-(10)#\[\begin{equation} +
+(10)#\[\begin{equation} \begin{bmatrix} \dfrac{\partial z}{\partial x} \\ \\ \dfrac{\partial z}{\partial y} \end{bmatrix} \end{equation}\]

Hint: Use the chain rule!

Chain rule: For a composite function \(F(x) = g(h(x)) \equiv (g \circ h)(x)\):

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-(11)#\[\begin{equation} +
+(11)#\[\begin{equation} F'(x) = g'(h(x)) \cdot h'(x) \end{equation}\]

or differently denoted:

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-(12)#\[\begin{equation} +
+(12)#\[\begin{equation} \frac{dF}{dx} = \frac{dg}{dh} ~ \frac{dh}{dx} \end{equation}\]
Click here for the solution

We can rewrite the function as a composite function:

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-(13)#\[\begin{equation} +
+(13)#\[\begin{equation} z = f\left( g(x,y) \right), ~~ f(u) = \sin(u), ~~ g(x, y) = x^2 + y^2 \end{equation}\]

Using the chain rule:

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-(14)#\[\begin{align} +
+(14)#\[\begin{align} \dfrac{\partial z}{\partial x} &= \dfrac{\partial f}{\partial g} \dfrac{\partial g}{\partial x} = \cos(g(x,y)) ~ (2x) = \cos(x^2 + y^2) \cdot 2x \\ \\ \dfrac{\partial z}{\partial y} &= \dfrac{\partial f}{\partial g} \dfrac{\partial g}{\partial y} = \cos(g(x,y)) ~ (2y) = \cos(x^2 + y^2) \cdot 2y \end{align}\]
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Video 2: Gradient Descent - Discussion#

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Section 1.2: Gradient Descent Algorithm#

Let \(f(\mathbf{w}): \mathbb{R}^d \rightarrow \mathbb{R}\) be a differentiable function. Gradient Descent is an iterative algorithm for minimizing the function \(f\), starting with an initial value for variables \(\mathbf{w}\), taking steps of size \(\eta\) (learning rate) in the direction of the negative gradient at the current point to update the variables \(\mathbf{w}\).

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-(15)#\[\begin{equation} +
+(15)#\[\begin{equation} \mathbf{w}^{(t+1)} = \mathbf{w}^{(t)} - \eta \nabla f \left( \mathbf{w}^{(t)} \right) \end{equation}\]

where \(\eta > 0\) and \(\nabla f (\mathbf{w})= \left( \frac{\partial f(\mathbf{w})}{\partial w_1}, ..., \frac{\partial f(\mathbf{w})}{\partial w_d} \right)\). Since negative gradients always point locally in the direction of steepest descent, the algorithm makes small steps at each point towards the minimum.

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Section 1.2: Gradient Descent Algorithm

Hence, all we need is to calculate the gradient of the loss function with respect to the learnable parameters (i.e., weights):

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+(16)#\[\begin{equation} \dfrac{\partial Loss}{\partial \mathbf{w}} = \left[ \dfrac{\partial Loss}{\partial w_1}, \dfrac{\partial Loss}{\partial w_2} , \dots, \dfrac{\partial Loss}{\partial w_d} \right]^{\top} \end{equation}\]
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Section 1.3: Computational Graphs and Backprop#

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Exercise 1.2 is an example of how overwhelming the derivation of gradients can get, as the number of variables and nested functions increases. This function is still extraordinarily simple compared to the loss functions of modern neural networks. So how can we (as well as PyTorch and similar frameworks) approach such beasts?

Let’s look at the function again:

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-(17)#\[\begin{equation} +
+(17)#\[\begin{equation} f(x, y, z) = \tanh \left(\ln \left[1 + z \frac{2x}{sin(y)} \right] \right) \end{equation}\]

We can build a so-called computational graph (shown below) to break the original function into smaller and more approachable expressions.

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Submit your feedback\(f\), and work our way against the arrows while calculating the gradient of each expression as we go. This is called the backward pass, from which the backpropagation of errors algorithm gets its name.

Computation Graph full

By breaking the computation into simple operations on intermediate variables, we can use the chain rule to calculate any gradient:

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-(18)#\[\begin{equation} +
+(18)#\[\begin{equation} \dfrac{\partial f}{\partial x} = \dfrac{\partial f}{\partial e}~\dfrac{\partial e}{\partial d}~\dfrac{\partial d}{\partial c}~\dfrac{\partial c}{\partial a}~\dfrac{\partial a}{\partial x} = \left( 1-\tanh^2(e) \right) \cdot \frac{1}{d+1}\cdot z \cdot \frac{1}{b} \cdot 2 \end{equation}\]

Conveniently, the values for \(e\), \(b\), and \(d\) are available to us from when we did the forward pass through the graph. That is, the partial derivatives have simple expressions in terms of the intermediate variables \(a,b,c,d,e\) that we calculated and stored during the forward pass.

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Analytical Exercise 1.3: Chain Rule (Optional)\(\dfrac{\partial f}{\partial y}\) using the computational graph and chain rule.

Click here for the solution -
-(19)#\[\begin{equation} +
+(19)#\[\begin{equation} \dfrac{\partial f}{\partial y} = \dfrac{\partial f}{\partial e}~\dfrac{\partial e}{\partial d}~\dfrac{\partial d}{\partial c}~\dfrac{\partial c}{\partial b}~\dfrac{\partial b}{\partial y} = \left( 1-\tanh^2(e) \right) \cdot \frac{1}{d+1}\cdot z \cdot \frac{-a}{b^2} \cdot \cos(y) \end{equation}\]

For more: Calculus on Computational Graphs: Backpropagation

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Section 2: PyTorch AutoGrad#

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Deep learning frameworks such as PyTorch, JAX, and TensorFlow come with a very efficient and sophisticated set of algorithms, commonly known as Automatic Differentiation. AutoGrad is PyTorch’s automatic differentiation engine. Here we start by covering the essentials of AutoGrad, and you will learn more in the coming days.

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Section 2.2: Backward Propagation -
Gradient function = <AddBackward0 object at 0x72ee346e58e0>
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Section 3: PyTorch’s Neural Net module (nn module#

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PyTorch provides us with ready-to-use neural network building blocks, such as layers (e.g., linear, recurrent, etc.), different activation and loss functions, and much more, packed in the torch.nn module. If we build a neural network using torch.nn layers, the weights and biases are already in requires_grad mode and will be registered as model parameters.

For training, we need three things:

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Summary#

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diff --git a/tutorials/W1D2_LinearDeepLearning/student/W1D2_Tutorial2.html b/tutorials/W1D2_LinearDeepLearning/student/W1D2_Tutorial2.html index 2e7c52e71..bc0f456e2 100644 --- a/tutorials/W1D2_LinearDeepLearning/student/W1D2_Tutorial2.html +++ b/tutorials/W1D2_LinearDeepLearning/student/W1D2_Tutorial2.html @@ -50,7 +50,7 @@ - + @@ -1064,7 +1064,7 @@

Tutorial Objectives
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Section 1: A Shallow Narrow Linear Neural NetworkVideo 1: Shallow Narrow Linear Net#

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Coding Exercise 1.1: Implement simple narrow LNN (Optional)forward pass for our model from scratch without using PyTorch.

Also, although our model gets a single input feature and outputs a single prediction, we could calculate the loss and perform training for multiple samples at once. This is the common practice for neural networks, since computers are incredibly fast doing matrix (or tensor) operations on batches of data, rather than processing samples one at a time through for loops. Therefore, for the loss function, please implement the mean squared error (MSE), and adjust your analytical gradients accordingly when implementing the dloss_dw function.

Finally, complete the train function for the gradient descent algorithm:

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-(20)#\[\begin{equation} +
+(20)#\[\begin{equation} \mathbf{w}^{(t+1)} = \mathbf{w}^{(t)} - \eta \nabla loss (\mathbf{w}^{(t)}) \end{equation}\]
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Section 1.2: Learning landscapes#

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As you may have already asked yourself, we can analytically find \(w_1\) and \(w_2\) without using gradient descent:

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-(21)#\[\begin{equation} +
+(21)#\[\begin{equation} w_1 \cdot w_2 = \dfrac{y}{x} \end{equation}\]

In fact, we can plot the gradients, the loss function and all the possible solutions in one figure. In this example, we use the \(y = 1x\) mapping:

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Section 2.1: The effect of depth#

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Why might depth be useful? What makes a network or learning system “deep”? The reality is that shallow neural nets are often incapable of learning complex functions due to data limitations. On the other hand, depth seems like magic. Depth can change the functions a network can represent, the way a network learns, and how a network generalizes to unseen data.

So let’s look at the challenges that depth poses in training a neural network. Imagine a single input, single output linear network with 50 hidden layers and only one neuron per layer (i.e. a narrow deep neural network). The output of the network is easy to calculate:

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Interactive Demo 2.1: Depth widget - +

Video 5: Effect of Depth - Discussion#

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Section 2.2: Choosing a learning rate#

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Interactive Demo 2.2: Learning rate widget - +

Video 7: Learning Rate - Discussion#

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Section 2.3: Depth vs Learning Rate#

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Interactive Demo 2.3: Depth and Learning Rate - +

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Video 9: Depth and Learning Rate - Discussion#

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Section 2.4: Why initialization is important#

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We’ve seen, even in the simplest of cases, that depth can slow learning. Why? From the chain rule, gradients are multiplied by the current weight at each layer, so the product can vanish or explode. Therefore, weight initialization is a fundamentally important hyperparameter.

Although in practice initial values for learnable parameters are often sampled from different \(\mathcal{Uniform}\) or \(\mathcal{Normal}\) probability distribution, here we use a single value for all the parameters.

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Summary#

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Hyperparameter interaction - +

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diff --git a/tutorials/W1D2_LinearDeepLearning/student/W1D2_Tutorial3.html b/tutorials/W1D2_LinearDeepLearning/student/W1D2_Tutorial3.html index 98843e20b..6c9cfaf2c 100644 --- a/tutorials/W1D2_LinearDeepLearning/student/W1D2_Tutorial3.html +++ b/tutorials/W1D2_LinearDeepLearning/student/W1D2_Tutorial3.html @@ -50,7 +50,7 @@ - + @@ -1108,7 +1108,7 @@

Tutorial Objectives
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Section 0: Prelude

Coding Exercise 0: Re-initialization (Optional)#

Complete the function ex_initializer_, such that the weights are sampled from the following distribution:

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+(22)#\[\begin{equation} \mathcal{N}\left(\mu=0, ~~\sigma=\gamma \sqrt{\dfrac{1}{n_{in} + n_{out}}} \right) \end{equation}\]

where \(\gamma\) is the initialization scale, \(n_{in}\) and \(n_{out}\) are respectively input and output dimensions of the layer. the Underscore (“_”) in ex_initializer_ and other functions, denotes “in-place” operation.

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Section 1: Deep Linear Neural Nets#

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So far, depth just seems to slow down the learning. And we know that a single nonlinear hidden layer (given enough number of neurons and infinite training samples) has the potential to approximate any function. So it seems fair to ask: What is depth good for?

One reason can be that shallow nonlinear neural networks hardly meet their true potential in practice. In the contrast, deep neural nets are often surprisingly powerful in learning complex functions without sacrificing generalization. A core intuition behind deep learning is that deep nets derive their power through learning internal representations. How does this work? To address representation learning, we have to go beyond the 1D chain.

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Section 2: Singular Value Decomposition (SVD)#

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In this section, we intend to study the learning (training) dynamics we just saw. First, we should know that a linear neural network is performing sequential matrix multiplications, which can be simplified to:

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-(23)#\[\begin{align} +
+(23)#\[\begin{align} \mathbf{y} &= \mathbf{W}_{L}~\mathbf{W}_{L-1}~\dots~\mathbf{W}_{1} ~ \mathbf{x} \\ &= \left(\prod_{i=1}^{L}{\mathbf{W}_{i}}\right) ~ \mathbf{x} \\ &= \mathbf{W}_{tot} ~ \mathbf{x} @@ -2398,8 +2398,8 @@

Submit your feedback\(A\) (yes, ANY) can be decomposed (factorized) to 3 matrices:

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-(24)#\[\begin{equation} +
+(24)#\[\begin{equation} \mathbf{A} = \mathbf{U} \mathbf{Σ} \mathbf{V}^{\top} \end{equation}\]

where \(U\) is an orthogonal matrix, \(\Sigma\) is a diagonal matrix, and \(V\) is again an orthogonal matrix. The diagonal elements of \(\Sigma\) are called singular values.

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Make sure you execute this cell to train the network and plot#

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Video 3: SVD - Discussion#

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Section 3: Representational Similarity Analysis (RSA)Video 4: RSA#

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The previous section ended with an interesting remark. SVD helped to break our deep “wide” linear neural net into 8 deep “narrow” linear neural nets.

The first narrow net (highest singular value) converges fastest, while the last four narrow nets, converge almost simultaneously and have the smallest singular values. Can it be that the narrow net with larger mode is learning the difference between “living things” and “objects”, while another narrow net with smaller mode is learning the difference between Fish and Birds? how could we check this hypothesis?

Representational Similarity Analysis (RSA) is an approach that could help us understand the internal representation of our network. The main idea is that the activity of hidden units (neurons) in the network must be similar when the network is presented with similar input. For our dataset (hierarchically structured data), we expect the activity of neurons in the hidden layer to be more similar for Tuna and Canary, and less similar for Tuna and Oak.

For similarity measure, we can use the good old dot (scalar) product, which is also called cosine similarity. For calculating the dot product between multiple vectors (which would be our case), we can simply use matrix multiplication. Therefore the Representational Similarity Matrix for multiple-input (batch) activity could be calculated as follow:

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-(25)#\[\begin{equation} +
+(25)#\[\begin{equation} RSM = \mathbf{H} \mathbf{H}^{\top} \end{equation}\]

where \(\mathbf{H} = \mathbf{X} \mathbf{W_1}\) is the activity of hidden neurons for a given batch \(\mathbf{X}\).

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Let’s take a moment to analyze this more. A deep neural net is learning the representations, rather than a naive mapping (look-up table). This is thought to be the reason for deep neural nets supreme generalization and transfer learning ability. Unsurprisingly, neural nets with no hidden layer are incapable of representation learning, even with extremely small initialization.

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Video 5: RSA - Discussion#

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Section 4: Illusory Correlations#

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Let’s recall the training loss curves. There was often a long plateau (where the weights are stuck at a saddle point), followed by a sudden drop. For very deep complex neural nets, such plateaus can take hours of training, and we are often tempted to stop the training, because we believe it is “as good as it gets”! Another side effect of “immature interruption” of training is the network finding (learning) illusory correlations.

To better understand this, let’s do the next demonstration and exercise.

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Video 7: Illusory Correlations - Discussion#

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Summary#

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Bonus#

Video 9: Linear Regression#

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Section 5.1: Linear Regression\(\mathbf{x} \in \mathbb{R}^M\), where \(M\) denotes the number of independent variables, while the dependent variables are collected in vector \(\mathbf{y} \in \mathbb{R}^N\), where \(N\) denotes the number of dependent variables. And the mapping between them is represented by the weight matrix \(\mathbf{W} \in \mathbb{R}^{N \times M}\) and a bias vector \(\mathbf{b} \in \mathbb{R}^{N}\) (generalizing to affine mappings).

The multivariate regression model can be written as:

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-(26)#\[\begin{equation} +
+(26)#\[\begin{equation} \mathbf{y} = \mathbf{W} ~ \mathbf{x} + \mathbf{b} \end{equation}\]

or it can be written in matrix format as:

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-(27)#\[\begin{equation} +
+(27)#\[\begin{equation} \begin{bmatrix} y_{1} \\ y_{2} \\ \vdots \\ y_{N} \\ \end{bmatrix} = \begin{bmatrix} w_{1,1} & w_{1,2} & \dots & w_{1,M} \\ w_{2,1} & w_{2,2} & \dots & w_{2,M} \\ \vdots & \ddots & \ddots & \vdots \\ w_{N,1} & w_{N,2} & \dots & w_{N,M} \end{bmatrix} \begin{bmatrix} x_{1} \\ x_{2} \\ \vdots \\ x_{M} \\ \end{bmatrix} + \begin{bmatrix} b_{1} \\ b_{2} \\ \vdots \\b_{N} \\ \end{bmatrix} \end{equation}\]

Section 5.2: Vectorized regression#

Linear regression can be simply extended to multi-samples (\(D\)) input-output mapping, which we can collect in a matrix \(\mathbf{X} \in \mathbb{R}^{M \times D}\), sometimes called the design matrix. The sample dimension also shows up in the output matrix \(\mathbf{Y} \in \mathbb{R}^{N \times D}\). Thus, linear regression takes the following form:

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-(28)#\[\begin{equation} +
+(28)#\[\begin{equation} \mathbf{Y} = \mathbf{W} ~ \mathbf{X} + \mathbf{b} \end{equation}\]

where matrix \(\mathbf{W} \in \mathbb{R}^{N \times M}\) and the vector \(\mathbf{b} \in \mathbb{R}^{N}\) (broadcasted over sample dimension) are the desired parameters to find.

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Section 5.2: Vectorized regression#

Linear regression is a relatively simple optimization problem. Unlike most other models that we will see in this course, linear regression for mean squared loss can be solved analytically.

For \(D\) samples (batch size), \(\mathbf{X} \in \mathbb{R}^{M \times D}\), and \(\mathbf{Y} \in \mathbb{R}^{N \times D}\), the goal of linear regression is to find \(\mathbf{W} \in \mathbb{R}^{N \times M}\) such that:

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-(29)#\[\begin{equation} +
+(29)#\[\begin{equation} \mathbf{Y} = \mathbf{W} ~ \mathbf{X} \end{equation}\]

Given the Squared Error loss function, we have:

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-(30)#\[\begin{equation} +
+(30)#\[\begin{equation} Loss(\mathbf{W}) = ||\mathbf{Y} - \mathbf{W} ~ \mathbf{X}||^2 \end{equation}\]

So, using matrix notation, the optimization problem is given by:

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-(31)#\[\begin{align} +
+(31)#\[\begin{align} \mathbf{W^{*}} &= \underset{\mathbf{W}}{\mathrm{argmin}} \left( Loss (\mathbf{W}) \right) \\ &= \underset{\mathbf{W}}{\mathrm{argmin}} \left( ||\mathbf{Y} - \mathbf{W} ~ \mathbf{X}||^2 \right) \\ &= \underset{\mathbf{W}}{\mathrm{argmin}} \left( \left( \mathbf{Y} - \mathbf{W} ~ \mathbf{X}\right)^{\top} \left( \mathbf{Y} - \mathbf{W} ~ \mathbf{X}\right) \right) \end{align}\]

To solve the minimization problem, we can simply set the derivative of the loss with respect to \(\mathbf{W}\) to zero.

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-(32)#\[\begin{equation} +
+(32)#\[\begin{equation} \dfrac{\partial Loss}{\partial \mathbf{W}} = 0 \end{equation}\]

Assuming that \(\mathbf{X}\mathbf{X}^{\top}\) is full-rank, and thus it is invertible, we can write:

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-(33)#\[\begin{equation} +
+(33)#\[\begin{equation} \mathbf{W}^{\mathbf{*}} = \mathbf{Y} \mathbf{X}^{\top} \left( \mathbf{X} \mathbf{X}^{\top} \right) ^{-1} \end{equation}\]

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Demonstration: Linear Regression vs. DLNN#

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diff --git a/tutorials/W1D3_MultiLayerPerceptrons/student/W1D3_Tutorial1.html b/tutorials/W1D3_MultiLayerPerceptrons/student/W1D3_Tutorial1.html index 755be5483..2f9b77b56 100644 --- a/tutorials/W1D3_MultiLayerPerceptrons/student/W1D3_Tutorial1.html +++ b/tutorials/W1D3_MultiLayerPerceptrons/student/W1D3_Tutorial1.html @@ -50,7 +50,7 @@ - + @@ -1040,7 +1040,7 @@

Tutorial objectives
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Section 0: Introduction to MLPs#

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Section 1: The Need for MLPs#

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Coding Exercise 1: Function approximation with ReLU

These are the points we will use to learn how to approximate the function. We have 10 training data points so we will have 9 ReLUs (we don’t need a ReLU for the last data point as we don’t have anything to the right of it to model).

We first need to figure out the bias term for each ReLU and compute the activation of each ReLU where:

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-(34)#\[\begin{equation} +
+(34)#\[\begin{equation} y(x) = \text{max}(0, x+b) \end{equation}\]

We then need to figure out the correct weights on each ReLU so the linear combination approximates the desired function.

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Section 2: MLPs in PyTorch#

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In the previous segment, we implemented a function to approximate any smooth function using MLPs. We saw that using Lipschitz continuity; We can prove that our approximation is mathematically correct. MLPs are fascinating, but before we get into the details on designing them, let’s familiarize ourselves with some basic terminology of MLPs - layer, neuron, depth, width, weight, bias, and activation function. Armed with these ideas, we can now design an MLP given its input, hidden layers, and output size.

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Coding Exercise 2: Implement a general-purpose MLP in PytorchLeaky ReLU) in all hidden layers

Leaky ReLU is described by the following mathematical formula:

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-(35)#\[\begin{align} +
+(35)#\[\begin{align} \text{LeakyReLU}(x) &= \text{max}(0,x) + \text{negative_slope} \cdot \text{min}(0, x) \\ &= \left\{ @@ -1664,7 +1664,7 @@

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Section 2.1: Classification with MLPs#

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The main loss function we could use out of the box for multi-class classification for N samples and C number of classes is:

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    Submit your feedbackx with shape (N, C) and class index in the range \([0, C-1]\) as the target (label) for each N samples, hence a batch of labels with shape (N, ). There are other optional parameters like class weights and class ignores. Feel free to check the PyTorch documentation here for more detail. Additionally, here you can learn where is appropriate to use the CrossEntropyLoss.

To get CrossEntropyLoss of a sample \(i\), we could first calculate \(-\log(\text{softmax}(x))\) and then take the element corresponding to \(\text {labels}_i\) as the loss. However, due to numerical stability, we implement this more stable equivalent form,

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-(36)#\[\begin{equation} +
+(36)#\[\begin{equation} \operatorname{loss}(x_i, \text {labels}_i)=-\log \left(\frac{\exp (x[\text {labels}_i])}{\sum_{j} \exp (x[j])}\right)=-x_i[\text {labels}_i]+\log \left(\sum_{j=1}^C \exp (x_i[j])\right) \end{equation}\]

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Coding Exercise 2.1: Implement Batch Cross Entropy Loss

A batch of labels with shape (N, ) that ranges from 0 to C-1

Returns the average loss \(L\) calculated according to:

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-(37)#\[\begin{align} +
+(37)#\[\begin{align} \text{loss}(x_i, \text {labels}_i) &= -x_i[\text {labels}_i]+\log \left(\sum_{j=1}^C \exp (x_i[j])\right) \\ L &= \frac{1}{N} \sum_{i=1}^{N}{\text{loss}(x_i, \text {labels}_i)} \end{align}\]
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Before we could start optimizing these loss functions, we need a dataset!

Let’s turn this fancy-looking equation into a classification dataset

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-(38)#\[\begin{equation} +
+(38)#\[\begin{equation} \begin{array}{c} X_{k}(t)=t\left(\begin{array}{c} \sin \left[\frac{2 \pi}{K}\left(2 t+k-1\right)\right]+\mathcal{N}\left(0, \sigma\right) \\ @@ -1874,7 +1874,7 @@

Section 2.3: Training and Evaluation#

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And we need to make a Pytorch data loader out of it. Data loading in PyTorch can be separated in 2 parts:

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    Now let’s put everything together and train your first deep-ish model!

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Bonus: Neuron Physiology and Motivation to Deep Learning#

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Leaky Integrate-and-fire (LIF) neuronal model#

The basic idea of LIF neuron was proposed in 1907 by Louis Édouard Lapicque, long before we understood the electrophysiology of a neuron (see a translation of Lapicque’s paper ). More details of the model can be found in the book Theoretical neuroscience by Peter Dayan and Laurence F. Abbott.

The model dynamics is defined with the following formula,

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-(39)#\[\begin{equation} +
+(39)#\[\begin{equation} \frac{d V_m}{d t}=\left\{\begin{array}{cc} \frac{1}{C_m}\left(-\frac{V_m}{R_m} + I \right) & t>t_{rest} \\ 0 & \text { otherwise } \end{array}\right. \end{equation}\]

Note that \(V_{m}\), \(C_{m}\), and \(R_{m}\) are the membrane voltage, capacitance, and resitance of the neuron, respectively, so the \(-\frac{V_{m}}{R_{m}}\) denotes the leakage current. When \(I\) is sufficiently strong such that \(V_{m}\) reaches a certain threshold value \(V_{\rm th}\), it momentarily spikes and then \(V_{m}\) is reset to \(V_{\rm reset}< V_{\rm th}\), and voltage stays at \(V_{\rm reset}\) for \(\tau_{\rm ref}\) ms, mimicking the refractoriness of the neuron during an action potential (note that \(V_{\rm reset}\) and \(\tau_{\rm ref}\) is assumed to be zero in the lecture):

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-(40)#\[\begin{eqnarray} +
+(40)#\[\begin{eqnarray} V_{m}(t)=V_{\rm reset} \text{ for } t\in(t_{\text{sp}}, t_{\text{sp}} + \tau_{\text{ref}}] \end{eqnarray}\]

where \(t_{\rm sp}\) is the spike time when \(V_{m}(t)\) just exceeded \(V_{\rm th}\).

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Leaky Integrate-and-fire (LIF) neuronal model#

In the cell below is given a function for LIF neuron model with it’s arguments described.

Note that we will use Euler’s method to make a numerical approximation to a derivative. Hence we will use the following implementation of the model dynamics,

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-(41)#\[\begin{equation} +
+(41)#\[\begin{equation} V_m^{[n]}=\left\{\begin{array}{cc} V_m^{[n-1]} + \frac{1}{C_m}\left(-\frac{V_m^{[n-1]}}{R_m}+I \right) \Delta t & t>t_{r e s t} \\ 0 & \text { otherwise } @@ -2471,7 +2471,7 @@

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Submit your feedback - + diff --git a/tutorials/W1D3_MultiLayerPerceptrons/student/W1D3_Tutorial2.html b/tutorials/W1D3_MultiLayerPerceptrons/student/W1D3_Tutorial2.html index e16902860..a9ee86bc7 100644 --- a/tutorials/W1D3_MultiLayerPerceptrons/student/W1D3_Tutorial2.html +++ b/tutorials/W1D3_MultiLayerPerceptrons/student/W1D3_Tutorial2.html @@ -50,7 +50,7 @@ - + @@ -989,7 +989,7 @@

Tutorial Objectives
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Section 1: Wider vs deeper networks#

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Submit your feedback#

Let’s use the same spiral dataset generated before with two features. And then add more polynomial features (which makes the first layer wider). And finally, train a single linear layer. We could use the same MLP network with no hidden layers (though it would not be called an MLP anymore!).

Note that we will add polynomial terms upto \(P=50\) which means that for every \(x_1^n x_2^m\) term, \(n+m\leq P\). Now it’s fun math exercise to prove why the total number of polynomial features upto \(P\) becomes:

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-(42)#\[\begin{equation} +
+(42)#\[\begin{equation} \text{# of terms} = \frac{(P+1)(P+2)}{2} \end{equation}\]

Also, we don’t need the polynomial term with degree zero (which is the constatnt term) since nn.Linear layers have bias terms. Therefore we will have one fewer polynomial feature.

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Section 1.1: Where Wide Fails
Random seed 2021 has been set.

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Accuracy on the 3200 training samples: 69.88
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Accuracy on the 3200 training samples: 69.88
 Accuracy on the 800 testing samples: 72.62
 

 

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Section 2: Deeper MLPsVideo 2: Case study#

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Section 3: Ethical aspects#

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Summary#

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Bonus: The need for good initialization#

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Xavier initialization#

Let us look at the scale distribution of an output (e.g., a hidden variable) \(o_i\) for some fully-connected layer without nonlinearities. With \(n_{in}\) inputs (\(x_j\)) and their associated weights \(w_{ij}\) for this layer. Then an output is given by,

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-(43)#\[\begin{equation} +
+(43)#\[\begin{equation} o_{i} = \sum_{j=1}^{n_\mathrm{in}} w_{ij} x_j \end{equation}\]

The weights \(w_{ij}\) are all drawn independently from the same distribution. Furthermore, let us assume that this distribution has zero mean and variance \(\sigma^2\). Note that this does not mean that the distribution has to be Gaussian, just that the mean and variance need to exist. For now, let us assume that the inputs to the layer \(x_j\) also have zero mean and variance \(\gamma^2\) and that they are independent of \(w_{ij}\) and independent of each other. In this case, we can compute the mean and variance of \(o_i\) as follows:

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-(44)#\[\begin{align} +
+(44)#\[\begin{align} E[o_i] &= \sum_{j=1}^{n_\mathrm{in}} E[w_{ij} x_j] \\ \\ &= \sum_{j=1}^{n_\mathrm{in}} E[w_{ij}] E[x_j] = 0, \\ \\ \\ \mathrm{Var}[o_i] &= E[o_i^2] - (E[o_i])^2 \\ \\ @@ -2265,20 +2265,20 @@

Xavier initialization

One way to keep the variance fixed is to set \(n_{in}\sigma^2=1\) . Now consider backpropagation. There we face a similar problem, albeit with gradients being propagated from the layers closer to the output. Using the same reasoning as for forward propagation, we see that the gradients’ variance can blow up unless \(n_{out}\sigma^2=1\) , where \(n_{out}\) is the number of outputs of this layer. This leaves us in a dilemma: we cannot possibly satisfy both conditions simultaneously. Instead, we simply try to satisfy:

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-(45)#\[\begin{align} +
+(45)#\[\begin{align} \frac{1}{2} (n_\mathrm{in} + n_\mathrm{out}) \sigma^2 = 1 \text{ or equivalently } \sigma = \sqrt{\frac{2}{n_\mathrm{in} + n_\mathrm{out}}} \end{align}\]

This is the reasoning underlying the now-standard and practically beneficial Xavier initialization, named after the first author of its creators Glorot and Bengio, 2010. Typically, the Xavier initialization samples weights from a Gaussian distribution with zero mean and variance \(\sigma^2=\frac{2}{(n_{in}+n_{out})}\),

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-(46)#\[\begin{equation} +
+(46)#\[\begin{equation} w_{ij} \sim \mathcal{N} \left (\mu=0, \sigma=\sqrt{\frac{2}{(n_{in}+n_{out})}} \right) \end{equation}\]

We can also adapt Xavier’s intuition to choose the variance when sampling weights from a uniform distribution. Note that the uniform distribution \(\mathcal{U}(−a,a)\) has variance \(\frac{a^2}{3}\). Plugging this into our condition on \(\sigma^2\) yields the suggestion to initialize according to

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-(47)#\[\begin{equation} +
+(47)#\[\begin{equation} w_{ij} \sim \mathcal{U} \left(-\sqrt{\frac{6}{n_\mathrm{in} + n_\mathrm{out}}}, \sqrt{\frac{6}{n_\mathrm{in} + n_\mathrm{out}}}\right) \end{equation}\]

This explanation is mainly taken from here.

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Xavier initializationInitialization with transfer function#

Let’s derive the optimal gain for LeakyReLU following similar steps.

LeakyReLU is described mathematically:

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-(48)#\[\begin{equation} +
+(48)#\[\begin{equation} f(x)=\left\{ \begin{array}{ll} \alpha \cdot x & \text { for } x<0 \\ @@ -2298,15 +2298,15 @@

Initialization with transfer function\(\alpha\) controls the angle of the negative slope.

Considering a single layer with this activation function gives,

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-(49)#\[\begin{align} +
+(49)#\[\begin{align} o_{i} &= \sum_{j=1}^{n_\mathrm{in}} w_{ij} x_j\\ z_{i} &= f\left( o_{i} \right) \end{align}\]

where \(z_i\) denotes the activation of node \(i\).

The expectation of the output is still zero, i.e., \(\mathbb{E}[f(o_i)=0]\), but the variance changes, and assuming that the probability \(P(x < 0) = 0.5\), we have that:

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-(50)#\[\begin{align} +
+(50)#\[\begin{align} \mathrm{Var}[f(o_i)] &= \mathbb{E}[f(o_i)^2] - \left( \mathbb{E}[f(o_i)] \right)^{2} \\ \\ &= \frac{\mathrm{Var}[o_i] + \alpha^2 \mathrm{Var}[o_i]}{2} \\ \\ &= \frac{1+\alpha^2}{2}n_\mathrm{in} \sigma^2 \gamma^2 @@ -2314,8 +2314,8 @@

Initialization with transfer function\(\gamma\) is the variance of the distribution of the inputs \(x_j\) and \(\sigma\) is the variance of the distribution of weights \(w_{ij}\), as before.

Therefore, following the rest of derivation as before,


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-(51)#\[\begin{equation} +
+(51)#\[\begin{equation} \sigma = gain\sqrt{\frac{2}{n_\mathrm{in} + n_\mathrm{out}}}, \, \text{where} \,\, gain = \sqrt{\frac{2}{1+\alpha^2}} \end{equation}\]

As we can see from the derived formula of \(\sigma\), the transfer function we choose is related with the variance of the distribution of the weights. As the negative slope of the LeakyReLU \(\alpha\) becomes larger, the \(gain\) becomes smaller and thus, the distribution of the weights is narrower. On the other hand, as \(\alpha\) becomes smaller and smaller, the distribution of the weights is wider. Recall that, we initialize our weights, for example, by sampling from a normal distribution with zero mean and variance \(\sigma^2\).

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Best gain for Xavier Initialization with Leaky ReLU 4 # Calculate the theoretical gain 5 theoretical_gain = np.sqrt(2.0 / (1 + negative_slope ** 2)) -File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/numpy/core/fromnumeric.py:1229, in argmax(a, axis, out, keepdims) +File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/numpy/core/fromnumeric.py:1229, in argmax(a, axis, out, keepdims) 1142 """ 1143 Returns the indices of the maximum values along an axis. 1144 @@ -2408,14 +2408,14 @@

Best gain for Xavier Initialization with Leaky ReLU 1228 kwds = {'keepdims': keepdims} if keepdims is not np._NoValue else {} -> 1229 return _wrapfunc(a, 'argmax', axis=axis, out=out, **kwds) -File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/numpy/core/fromnumeric.py:56, in _wrapfunc(obj, method, *args, **kwds) +File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/numpy/core/fromnumeric.py:56, in _wrapfunc(obj, method, *args, **kwds) 54 bound = getattr(obj, method, None) 55 if bound is None: ---> 56 return _wrapit(obj, method, *args, **kwds) 58 try: 59 return bound(*args, **kwds) -File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/numpy/core/fromnumeric.py:45, in _wrapit(obj, method, *args, **kwds) +File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/numpy/core/fromnumeric.py:45, in _wrapit(obj, method, *args, **kwds) 43 except AttributeError: 44 wrap = None ---> 45 result = getattr(asarray(obj), method)(*args, **kwds) diff --git a/tutorials/W1D5_Optimization/student/W1D5_Tutorial1.html b/tutorials/W1D5_Optimization/student/W1D5_Tutorial1.html index 2a0b0bdd4..13668f763 100644 --- a/tutorials/W1D5_Optimization/student/W1D5_Tutorial1.html +++ b/tutorials/W1D5_Optimization/student/W1D5_Tutorial1.html @@ -50,7 +50,7 @@ - + @@ -1246,7 +1246,7 @@

Tutorial Objectives
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Section 1. IntroductionVideo 1: Introduction#

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Section 2: Case study: successfully training an MLP for image classification

Video 2: Case Study - MLP Classification#

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Section 3: High dimensional search#

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Section 4: Poor conditioning#

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We illustrate this issue in a 2-dimensional setting. We freeze all but two parameters of the network: one of them is an element of the weight matrix (filter) for class 0, while the other is the bias for class 7. These results in an optimization with two decision variables.

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Coding Exercise 4: Implement momentum#

In this exercise you will implement the momentum update given by:

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-(52)#\[\begin{equation} +
+(52)#\[\begin{equation} w_{t+1} = w_t - \eta \nabla J(w_t) + \beta (w_t - w_{t-1}) \end{equation}\]

It is convenient to re-express this update rule in terms of a recursion. For that, we define ‘velocity’ as the quantity:

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-(53)#\[\begin{equation} +
+(53)#\[\begin{equation} v_{t-1} := w_{t} - w_{t-1} \end{equation}\]

which leads to the two-step update rule:

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-(54)#\[\begin{equation} +
+(54)#\[\begin{equation} v_t = - \eta \nabla J(w_t) + \beta (\underbrace{w_t - w_{t-1}}_{v_{t-1}}) \end{equation}\]
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+(55)#\[\begin{equation} w_{t+1} \leftarrow w_t + v_{t} \end{equation}\]

Pay attention to the positive sign of the update in the last equation, given the definition of \(v_t\), above.

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Interactive Demo 4: Momentum vs. GD
Random seed 2021 has been set.

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Section 5: Non-convexity#

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Take a couple of minutes to play with a more complex 3D visualization of the loss landscape of a neural network on a non-convex problem. Visit https://losslandscape.com/explorer.

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    Interactive Demo 5: Overparameterization to the rescue!
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Section 6: Full gradients are expensive#

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Interactive Demo 6.1: Cost of computation - +

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Interactive Demo 6.2: Compare different minibatch sizes - +

Remarks: SGD works! We have an algorithm that can be applied (with due precautions) to learn datasets of arbitrary size.

However, note the difference in the vertical scale across the plots above. When using a larger minibatch, we can perform fewer parameter updates as the forward and backward passes are more expensive.

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Section 7: Adaptive methods#

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Coding Exercise 7: Implement RMSprop#

In this exercise you will implement the update of the RMSprop optimizer:

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-(56)#\[\begin{align} +
+(56)#\[\begin{align} v_{t} &= \alpha v_{t-1} + (1 - \alpha) \nabla J(w_t)^2 \\ \\ w_{t+1} &= w_t - \eta \frac{\nabla J(w_t)}{\sqrt{v_t + \epsilon}} \end{align}\]
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Interactive Demo 7: Compare optimizers - +

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Remarks: Note that RMSprop allows us to use a ‘per-dimension’ learning rate without having to tune one learning rate for each dimension ourselves. The method uses information collected about the variance of the gradients throughout training to adapt the step size for each of the parameters automatically. The savings in tuning efforts of RMSprop over SGD or ‘plain’ momentum are undisputed on this task.

Moreover, adaptive optimization methods are currently a highly active research domain, with many related algorithms like Adam, AMSgrad, Adagrad being used in practical application and theoretically investigated.

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Section 8: Ethical concerns#

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Bonus: Putting it all together#

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Exercise Bonus: Train your own model
Random seed 2021 has been set.
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[VALID] Epoch 1 - Batch 200 - Loss: 2.235 - Acc: 38.193%
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[VALID] Epoch 1 - Batch 200 - Loss: 2.235 - Acc: 38.193%
 [TRAIN] Epoch 1 - Batch 200 - Loss: 2.274 - Acc: 30.930%
 

 

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diff --git a/tutorials/W2D1_Regularization/student/W2D1_Tutorial1.html b/tutorials/W2D1_Regularization/student/W2D1_Tutorial1.html index 0d58a413f..4cd58a7e8 100644 --- a/tutorials/W2D1_Regularization/student/W2D1_Tutorial1.html +++ b/tutorials/W2D1_Regularization/student/W2D1_Tutorial1.html @@ -50,7 +50,7 @@ - + @@ -1005,7 +1005,7 @@

Tutorial Objectives
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Section 1: Regularization is Shrinkage#

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A key idea of neural nets is that they use models that are “too complex” - complex enough to fit all the noise in the data. One then needs to “regularize” them to make the models fit complex enough, but not too complex. The more complex the model, the better it fits the training data, but if it is too complex, it generalizes less well; it memorizes the training data but is less accurate on future test data.

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Submit your feedbackVideo 2: Regularization as Shrinkage#

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One way to think about Regularization is to think in terms of the magnitude of the overall weights of the model. A model with big weights can fit more data perfectly, whereas a model with smaller weights tends to underperform on the train set but can surprisingly do very well on the test set. Having the weights too small can also be an issue as it can then underfit the model.

In these tutorials, we use the sum of the Frobenius norm of all the tensors in the model as a measure of the “size of the model”.

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Submit your feedback#

Before we start, let’s define the Frobenius norm, sometimes also called the Euclidean norm of an \(m×n\) matrix \(A\) as the square root of the sum of the absolute squares of its elements.


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-(57)#\[\begin{equation} +
+(57)#\[\begin{equation} ||A||_F= \sqrt{\sum_{i=1}^m\sum_{j=1}^n|a_{ij}|^2} \end{equation}\]

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Apart from calculating the weight size for an entire model, we could also determine the weight size in every layer. For this, we can modify our calculate_frobenius_norm function as shown below.

Have a look how it works!!

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Section 2: OverfittingVideo 3: Overparameterization and Overfitting#

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Section 2.1: Visualizing Overfitting
Random seed 2021 has been set.
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Now that we have finished training, let’s see how the model has evolved over the training process.

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Animation (Run Me!) 54 plt.close() 56 import IPython -File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/matplotlib/animation.py:1285, in Animation.to_html5_video(self, embed_limit) +File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/matplotlib/animation.py:1285, in Animation.to_html5_video(self, embed_limit) 1282 path = Path(tmpdir, "temp.m4v") 1283 # We create a writer manually so that we can get the 1284 # appropriate size for the tag @@ -2111,7 +2111,7 @@

Animation (Run Me!) 1288 fps=1000. / self._interval) 1289 self.save(str(path), writer=writer) -File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/matplotlib/animation.py:148, in MovieWriterRegistry.__getitem__(self, name) +File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/matplotlib/animation.py:148, in MovieWriterRegistry.__getitem__(self, name) 146 if self.is_available(name): 147 return self._registered[name] --> 148 raise RuntimeError(f"Requested MovieWriter ({name}) not available") @@ -2174,7 +2174,7 @@

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Now let’s visualize the Frobenious norm of the model as we trained. You should see that the value of weights increases over the epochs.

Frobenious norm of the model

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Section 3: Memorization
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Time to memorize the dataset: 228.84848880767822
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Time to memorize the dataset: 241.6447606086731
 

 

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Data Visualizer
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-../../../_images/e2bbfa7fcba2c15582af5f938bb59bfd0604fbbcd2a43c8c054346d49a7ad0b6.png +../../../_images/e2bbfa7fcba2c15582af5f938bb59bfd0604fbbcd2a43c8c054346d49a7ad0b6.png

Isn’t it surprising to see that the ANN was able to achieve 100% training accuracy on randomly shuffled labels? This is one of the reasons why training accuracy is not a good indicator of model performance.

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Section 4: Early Stopping#

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Now that we have established that the validation accuracy reaches the peak well before the model overfits, we want to stop the training somehow early. You should have also observed from the above plots that the train/test loss on real data is not very smooth, and hence you might guess that the choice of the epoch can play a crucial role in the validation/test accuracy.

Early stopping stops training when the validation accuracies stop increasing.

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Bonus: Train with randomized labels
Random seed 2021 has been set.
-../../../_images/95f88f7e75611a5dfb12461c69670991eb7a9f23c58d715c1ed41a11777107d3.png +../../../_images/95f88f7e75611a5dfb12461c69670991eb7a9f23c58d715c1ed41a11777107d3.png
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Also, it is interesting to note that sometimes the model trained on slightly shuffled data does slightly better than the one trained on pure data. Shuffling some of the data is a form of regularization, i.e., one of many ways of adding noise to the training data.

diff --git a/tutorials/W2D1_Regularization/student/W2D1_Tutorial2.html b/tutorials/W2D1_Regularization/student/W2D1_Tutorial2.html index 43fa69ac3..16978d4fb 100644 --- a/tutorials/W2D1_Regularization/student/W2D1_Tutorial2.html +++ b/tutorials/W2D1_Regularization/student/W2D1_Tutorial2.html @@ -50,7 +50,7 @@ - + @@ -1098,7 +1098,7 @@

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Section 1: L1 and L2 Regularization#

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Some of you might have already come across L1 and L2 regularization before in other courses. L1 and L2 are the most common types of regularization. These update the general cost function by adding another term known as the regularization term.


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-(58)#\[\begin{equation} +
+(58)#\[\begin{equation} \text{Cost function} = Loss(\text{e.g., binary cross entropy}) + \text{Regularization term} \end{equation}\]

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Dataloaders for Regularization
Random seed 2021 has been set.

-../../../_images/b9ae3a198b7e9657cfcd1bb3e387ab53c26153ea18f0437e4d25ce65a1b1658e.png +../../../_images/b9ae3a198b7e9657cfcd1bb3e387ab53c26153ea18f0437e4d25ce65a1b1658e.png 
Maximum Validation Accuracy reached: 51.0
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Dataloaders for Regularization

Section 1.2: L1 Regularization#

L1 Regularization (or LASSO\(^{\ddagger}\)) uses a penalty which is the sum of the absolute value of all the weights in the Deep Learning architecture, resulting in the following loss function (\(L\) is the usual Cross-Entropy loss):

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-(59)#\[\begin{equation} +
+(59)#\[\begin{equation} L_R = L + \lambda \sum \left| w^{(r)}_{ij} \right| \end{equation}\]

where \(r\) denotes the layer, and \(ij\) the specific weight in that layer.

At a high level, L1 Regularization is similar to L2 Regularization since it leads to smaller weights (you will see the analogy in the next subsection). It results in the following weight update equation when using Stochastic Gradient Descent:

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-(60)#\[\begin{equation} +
+(60)#\[\begin{equation} w^{(r)}_{ij}←w^{(r)}_{ij} − \eta \cdot \lambda \cdot \text{sgn}\left(w^{(r)}_{ij}\right)−\eta \frac{\partial L}{\partial w_{ij}^{(r)}} \end{equation}\]

where \(\text{sgn}(\cdot)\) is the sign function, such that

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+(61)#\[\begin{equation} \text{sgn}(w) = \left\{ \begin{array}{ll} @@ -2191,7 +2191,7 @@

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Now, let’s train a classifier that uses L1 regularization. Tune the hyperparameter lambda1 such that the validation accuracy is higher than that of the unregularized model.

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Section 1.3: L2 / Ridge Regularization#

L2 Regularization (or Ridge), also referred to as “Weight Decay”, is widely used. It works by adding a quadratic penalty term to the Cross-Entropy Loss Function \(L\), which results in a new Loss Function \(L_R\) given by:

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-(62)#\[\begin{equation} +
+(62)#\[\begin{equation} L_R = L + \lambda \sum \left( w^{(r)}_{ij} \right)^2 \end{equation}\]

where, again, \(r\) superscript denotes the layer, and \(ij\) the specific weight in that layer.

To get further insight into L2 Regularization, we investigate its effect on the Gradient Descent based update equations for the weight and bias parameters. Taking the derivative on both sides of the above equation, we obtain

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-(63)#\[\begin{equation} +
+(63)#\[\begin{equation} \frac{\partial L_R}{\partial w^{(r)}_{ij}}=\frac{\partial L}{\partial w^{(r)}_{ij}} + 2\lambda w^{(r)}_{ij} \end{equation}\]

Thus the weight update rule becomes:

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-(64)#\[\begin{equation} +
+(64)#\[\begin{equation} w^{(r)}_{ij}←w^{(r)}_{ij}−η\frac{\partial L}{\partial w^{(r)}_{ij}}−2 \eta \lambda w^{(r)}_{ij}=(1−2 \eta \lambda)w^{(r)}_{ij} − \eta \frac{\partial L}{\partial w^{(r)}_{ij}} \end{equation}\]

where \(\eta\) is the learning rate.

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Now we’ll train a classifier that uses L2 regularization. Tune the hyperparameter lambda2 such that the validation accuracy is higher than that of the unregularized model.

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Now, let’s run a model with both L1 and L2 regularization terms.

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Section 2: Dropout#

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With Dropout, we literally drop out (zero out) some neurons during training. Throughout the training, the standard dropout zeros out some fraction (usually 50%) of the nodes in each layer, and on each iteration, before calculating the subsequent layer. Randomly selecting different subsets to drop out introduces noise into the process and reduces overfitting.


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Run to train the default network
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Run to train the default network
Random seed 2021 has been set.

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Now that we have finished the training, let’s see how the model has evolved over the training process.

Animation! (Run Me!)

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Run to train the default network 23 plt.close() 24 display(html_anim) -File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/matplotlib/animation.py:1285, in Animation.to_html5_video(self, embed_limit) +File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/matplotlib/animation.py:1285, in Animation.to_html5_video(self, embed_limit) 1282 path = Path(tmpdir, "temp.m4v") 1283 # We create a writer manually so that we can get the 1284 # appropriate size for the tag @@ -2785,7 +2785,7 @@

Run to train the default network 1288 fps=1000. / self._interval) 1289 self.save(str(path), writer=writer) -File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/matplotlib/animation.py:148, in MovieWriterRegistry.__getitem__(self, name) +File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/matplotlib/animation.py:148, in MovieWriterRegistry.__getitem__(self, name) 146 if self.is_available(name): 147 return self._registered[name] --> 148 raise RuntimeError(f"Requested MovieWriter ({name}) not available") @@ -2895,7 +2895,7 @@

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Section 2.1: Dropout Implementation Caveats
Random seed 2021 has been set.
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Random seed 2021 has been set.
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Random seed 2021 has been set.
 

 

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Section 3: Data Augmentation#

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Data augmentation is often used to increase the number of training samples. Now we will explore the effects of data augmentation on regularization. Here regularization is achieved by adding noise into training data after every epoch.

PyTorch’s torchvision module provides a few built-in data augmentation techniques, which we can use on image datasets. Some of the techniques we most frequently use are:

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Data Loader without Data Augmentation
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Random seed 2021 has been set.
 

 

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Section 4: Stochastic Gradient Descent#

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Generating Data Loaders
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Random seed 2021 has been set.
 

 

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Plot Train and Validation accuracy (Run me)

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Section 5: Hyperparameter Tuning#

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Hyperparameter tuning is often tricky and time-consuming, and it is a vital part of training any Deep Learning model to give good generalization. There are a few techniques that we can use to guide us during the search.

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Bonus: Adversarial Attacks#

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Designing perturbations to the input data to trick a machine learning model is called an “adversarial attack”. These attacks are an inevitable consequence of learning in high dimensional space using complex decision boundaries. Depending on the application, these attacks can be very dangerous.


diff --git a/tutorials/W2D2_ConvnetsAndDlThinking/student/W2D2_BonusLecture.html b/tutorials/W2D2_ConvnetsAndDlThinking/student/W2D2_BonusLecture.html index 3e533ba23..b9f7a4936 100644 --- a/tutorials/W2D2_ConvnetsAndDlThinking/student/W2D2_BonusLecture.html +++ b/tutorials/W2D2_ConvnetsAndDlThinking/student/W2D2_BonusLecture.html @@ -58,7 +58,7 @@ const thebe_selector_output = ".output, .cell_output" - + @@ -1453,11 +1453,11 @@

Install and import feedback gadget#

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diff --git a/tutorials/W2D2_ConvnetsAndDlThinking/student/W2D2_Tutorial1.html b/tutorials/W2D2_ConvnetsAndDlThinking/student/W2D2_Tutorial1.html index f4fbdb335..b8175d084 100644 --- a/tutorials/W2D2_ConvnetsAndDlThinking/student/W2D2_Tutorial1.html +++ b/tutorials/W2D2_ConvnetsAndDlThinking/student/W2D2_Tutorial1.html @@ -50,7 +50,7 @@ - + @@ -1343,7 +1343,7 @@

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Section 0: Recap the Experience from Last Week#

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Coming Up

The rest of these lectures focus on another way to reduce parameters: weight-sharing. Weight-sharing is based on the idea that some sets of weights can be used at multiple points in a network. We will focus primarily on CNNs today, where the weight-sharing is across the 2D space of an image. This weight-sharing technique (across space) can reduce the number of parameters and increase a network’s ability to generalize. For completeness, a similar approach is the Recurrent Neural Networks (RNNs), which share parameters across time, but we will not dive into this in this tutorial.

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Section 1: Neuroscience motivation, General CNN structure#

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Section 2: Convolutions and Edge Detection#

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Before jumping into coding exercises, take a moment to look at this animation that steps through the process of convolution.

Recall from the video that convolution involves sliding the kernel across the image, taking the element-wise product, and adding those products together.

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Definitional Note

Coding Exercise 2.1: Convolution of a Simple Kernel#

At its core, convolution is just repeatedly multiplying a matrix, known as a kernel or filter, with some other, larger matrix (in our case the pixels of an image). Consider the below image and kernel:

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Think! 2.2.1: Edge Detection#

One of the simpler tasks performed by a convolutional layer is edge detection; that is, finding a place in the image where there is a large and abrupt change in color. Edge-detecting filters are usually learned by the first layers in a CNN. Observe the following simple kernel and discuss whether this will detect vertical edges (where the trace of the edge is vertical; i.e. there is a boundary between left and right), or whether it will detect horizontal edges (where the trace of the edge is horizontal; i.e., there is a boundary between top and bottom).

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Consider the image below, which has a black vertical stripe with white on the side. This is like a very zoomed-in vertical edge within an image!

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Section 3.1: Multiple Filters -
<matplotlib.image.AxesImage at 0x764deac8f4f0>
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<matplotlib.image.AxesImage at 0x7f79ab6816d0>
 

 

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We apply the filters to the images.

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Section 3.3: PoolingVideo 4: Pooling#

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Like convolutional layers, pooling layers have fixed-shape windows (pooling windows) that are systematically applied to the input. As with filters, we can change the shape of the window and the size of the stride. And, just like with filters, every time we apply a pooling operation we produce a single output.

Pooling performs a kind of information compression that provides summary statistics for a neighborhood of the input.

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Section 4: Putting it all together#

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Interactive Demo 4.1: Number of Parameters - +

The difference in parameters is huge, and it continues to increase as the input image size increases. Larger images require that the linear layer use a matrix that can be directly multiplied with the input pixels.


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Video 6: Implement your own CNN#

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Note: We are using a softmax function here which converts a real value to a value between 0 and 1, which can be interpreted as a probability.

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Bonus 1: Write your own training loop revisited#

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Bonus 1.1: Understand the Dataset#

The dataset we are going to use for this task is called Fashion-MNIST. It consists of a training set of 60,000 examples and a test set of 10,000 examples. We further divide the test set into a validation set and a test set (8,000 and 2,000, respectively). Each example is a \(28 \times 28\) gray scale image, associated with a label from 10 classes. Following are the labels of the dataset:


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Loading Fashion-MNIST Data#

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Load a sample dataset (EMNIST) -
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Interactive Demo Bonus 2.1: Dropout exploration - +

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Submit your feedback - + diff --git a/tutorials/W2D2_ConvnetsAndDlThinking/student/W2D2_Tutorial2.html b/tutorials/W2D2_ConvnetsAndDlThinking/student/W2D2_Tutorial2.html index 81f56e28d..3b9494977 100644 --- a/tutorials/W2D2_ConvnetsAndDlThinking/student/W2D2_Tutorial2.html +++ b/tutorials/W2D2_ConvnetsAndDlThinking/student/W2D2_Tutorial2.html @@ -50,7 +50,7 @@ - + @@ -976,7 +976,7 @@

Tutorial Objectives
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Section 1: Intro to Deep Learning Thinking#

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This tutorial is a bit different from others - there will be no coding! Instead you will watch a series of vignettes about various scenarios where you want to use a neural network. This tutorial will focus on cost functions, a tutorial you will see later in the course will be similar but focused on designing architectures.

Each section below will start with a vignette where either Lyle or Konrad is trying to figure out how to set up a neural network for a specific problem. Try to think of questions you want to ask them as you watch, then pay attention to what questions Lyle and Konrad are asking. Were they what you would have asked? How do their questions help quickly clarify the situation?

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Section 2: Cost function for neurons#

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Video 3: Spiking Neuron Predictions Set-up#

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Konrad, a neuroscientist, wants to predict what neurons in someone’s motor cortex are doing while they are riding a motorcycle.

Upon discussion with Lyle, it emerges that we have data on 12 parameters of motorcycle riding, including acceleration, angle, braking, degrees of leaning. These inputs are fairly smooth over time, the angle of the motorcycle typically does not change much in 100 ms for example.

We also have recorded data on the timing of spikes of \(N\) neurons in motor cortex. The underlying firing rate is smooth but every millisecond spikes are random and independent. This means we can assume that the number of spikes in a short interval can be modeled using a Poisson distribution with an underlying firing rate for that interval \(\lambda\).

For neuron \(i\), the probability of seeing \(k_{i}\) spikes in some interval given an underlying firing rate \(\lambda_{i}\) is:

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+(68)#\[\begin{equation} \mathcal{f(k_{i}:λ_{i})} = \mathcal{Pr(X=k_{i})} = \frac {\lambda_{i}^{k_{i}}e^{-\lambda_{i}}}{k_{i}!} \end{equation}\]

So this poisson distribution may be relevant if we want to, in a way, have a good model for the spiking of neurons.

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Think! 1: Designing a cost function to predict neural activitiesClick here for the solution

First, we will convert our spike timing data to the number of spikes per time bin for time bins of size 50 ms. This gives us \(k_{i,t}\) for every neuron \(i\) and time bin \(t\).

We are assuming a Poisson distribution for our spiking. That means that we get the probability of seeing spike count \(k_{i, t}\) given underlying firing rate \(\lambda_{i, t}\) using this equation:

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-(69)#\[\begin{equation} +
+(69)#\[\begin{equation} \mathcal{f(k_{i,t}:\lambda_{i,t})} = \mathcal{Pr}(X=k_{i,t}) = \frac {\lambda_{i,t}^{k_{i,t}}e^{-\lambda_{i,t}}}{k_{i,t}!} \end{equation}\]

That seems a pretty good thing to optimize to make our predictions as good as possible! We want a high probability of seeing the actual spike count we recorded given the neural network prediction of the underlying firing rate.

We will make this negative later so we have an equation that we want to minimize rather than maximize, so we can use all our normal tricks for minimization (instead of maximization). First though, let’s scale up to include all our neurons and time bins.

We can treat each time bin as independent because, while the underlying probability of firing changes slowly, every milisecond spiking is random and independent. From probability, we know that we can compute the probability of a set of independent events (all the spike counts) by multiplying the probabilities of each event. So the probability of seeing all of our data given the neural network predictions is all of our probabilities of \(k_{i,t}\) multiplied together:

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+(70)#\[\begin{align} \mathcal{Pr}(\text{all_data}) &= \prod_{i=1}^{N}\prod_{t=1}^\top \mathcal{Pr}(X=k_{i,t})\\ &= \prod_{i=1}^{N}\prod_{t=1}^\top \frac {\lambda_{i,t}^{k_{i,t}}e^{-\lambda_{i,t}}}{k_{i,t}!} \end{align}\]

This is also known as our likelihood!

We usually use the log likelihood instead of the likelihood when minimizing or maximizing for numerical computation reasons. W We can convert the above equation to log likelihood:

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+(71)#\[\begin{align} \text{log likelihood} &= \sum_{i=1}^N\sum_{t=1}^\top \text{log}(\mathcal{Pr}(X=k_{i,t}) \\ &= \sum_{i=1}^N\sum_{t=1}^\top k_{i,t} \text{log}(\lambda_{i,t}) - \lambda_{i,t} - \text{log}(k_{i,t}!) \end{align}\]

And last but not least, we want to make it negative so we can minimize instead of maximize:

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+(72)#\[\begin{equation} \text{negative log likelihood} = \sum_{i=1}^N\sum_{t=1}^\top - k_{i,t} \text{log}(\lambda_{i,t}) + \lambda_{i,t} + \text{log}(k_{i,t}!) \end{equation}\]
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Video 4: Spiking Neurons Wrap-up#

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Check out the papers mentioned in the above video:

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Section 3: How can an ANN know its uncertainty#

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Video 6: ANN Uncertainty Set-up#

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Lyle wants to build an artificial neural network that has a measure of its own uncertainty about it’s predictions. He wants the neural network to give a prediction/estimate and an uncertainty, or standard deviation, measurement on it.

Let’s say Lyle wants to estimate the location of an atom in a chemical molecule based on various inputs. He wants to have the estimate of the location and an estimate of the variance. We don’t train neural networks on one data point at a time though - he wants a cost function that takes in N data points (input and atom location pairings).

We think we may be able to use a Gaussian distribution to help Lyle here:

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-(73)#\[\begin{equation} +
+(73)#\[\begin{equation} g(x) = \frac{1}{\sigma\sqrt{2\pi}} \text{exp} \left( -\frac{1}{2}\frac{(x-\mu)^2}{\sigma^2} \right) \end{equation}\]

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Think! 2: Designing a cost function so we measure uncertainty\(i\), the neural network predicts the mean (\(\mu_i\)) and standard deviation (\(\sigma_i\)) of the location given the inputs. We can then compute the probability of seeing the actual recorded location (\(x_i\)) given these predictions:

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-(74)#\[\begin{equation} +
+(74)#\[\begin{equation} g(x) = \frac{1}{\sigma\sqrt{2\pi}} \text{exp}\left( -\frac{1}{2}\frac{(x_i-\mu_i)^2}{\sigma_i^2} \right) \end{equation}\]

The location of the atom is independent in each data point so we can get the overall likelihood by multiplying the probabilities for the individual data points.

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+(75)#\[\begin{equation} \text{likelihood} = \prod_{i=1}^N\frac{1}{\sigma\sqrt{2\pi}} \text{exp}\left( -\frac{1}{2}\frac{(x_i-\mu_i)^2}{\sigma_i^2} \right) \end{equation}\]

And, as before, we want to take the log of this for numerical reasons and convert to negative log likelihood:

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+(76)#\[\begin{equation} \text{negative log likelihood} = \sum_{i=1}^N \text{log} \left( \frac{1}{\sigma\sqrt{2\pi}} \text{exp}\left( -\frac{1}{2}\frac{(x_i-\mu_i)^2}{\sigma_i^2} \right) \right) \end{equation}\]

Changing the parameters of the neural network so it predicts \(\mu_i\) and \(\sigma_i\) that minimize this equation will give us (hopefully fairly accurate) predictions of the location and the network uncertainty about the location!

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Video 7: ANN Uncertainty Wrap-up#

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Check out the papers mentioned in the above video:

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Section 4: Embedding faces#

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Video 9: Embedding Faces Set-up#

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Konrad needs help recognizing faces. He wants to build a network that embeds photos of faces so that photos of the same person are nearby in the embedding space and photos of different people are far in the embedding space. We can’t just use pixel space because the pixels will be very different between a photo of someone straight on vs. from their side!

We will use a neural network to go from the pixels of each image to an embedding space. Let’s say you have a convolutional neural network with m units in the last layer. If you feed a face photo \(i\) through the CNN, the activities of the units in the last layer form an \(m\) dimensional vector \(\bar{y}_i\) - this is an embedding of that face photo in \(m\) dimensional space.

We think we might be able to incorporate Euclidean distance to help us here. The Euclidean distance between two vectors is:

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+(77)#\[\begin{equation} d(\bar{y}_i, \bar{y}_j) = \sqrt{\sum_{c=1}^m(\bar{y}_{i_c} - \bar{y}_{j_c})^2} \end{equation}\]

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Think! 3: Designing a cost function for face embedding Click here for the solution

We want the same faces to have similar embeddings. Let’s say we have one photo of Lyle \(a\) and another photo of Lyle \(p\). We want the embeddings of those photos to be very similar: we want the Euclidean distance between \(\bar{y}_a\) and \(\bar{y}_p\) (the activitys of the last layer of the CNN when photo \(a\) and \(p\) are fed through) to be small.

So one possible cost function is:

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-(78)#\[\begin{equation} +
+(78)#\[\begin{equation} \text{Cost function} = d(\bar{y}_a, \bar{y}_p) \end{equation}\]

Imagine if we just feed in pairs of the same face and minimize that though. There would be no motivation to ever have different embeddings, we would be only minimizing the distance between embeddings. If the CNN was smart, it would just have the same embedding for every single photo - then the cost function would equal 0!

This is clearly not what we want. We want to motivate the CNN to have similar embeddings only when the faces are the same. This means we need to also train it to maximize distance when the faces are different.

We could choose another two photos of different people and maximize that distance but then there’s no relation to the embeddings we’ve already established of the two photos of Lyle. Instead, we will add one more photo to the mix: a photo of Konrad \(n\). We want the distance of this photo to be far from our original photos of Lyle \(a\) and \(p\). So we want the distance between \(a\) and \(p\) to be small and the distance between \(a\) and \(n\) for example to be large:

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-(79)#\[\begin{equation} +
+(79)#\[\begin{equation} \text{Cost function} = d(\bar{y}_a, \bar{y}_p) - d(\bar{y}_a, \bar{y}_n) \end{equation}\]

We could compare \(n\) to both \(a\) and \(p\):

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-(80)#\[\begin{equation} +
+(80)#\[\begin{equation} \text{Cost function} = d(\bar{y}_a, \bar{y}_p) - d(\bar{y}_a, \bar{y}_n) - d(\bar{y}_p, \bar{y}_n) \end{equation}\]

But then the cost function is a bit unbalanced, there are two dissimiliarty terms and they might dominate (so achieving the similarity is less important). So let’s go with just including one dissimilarity term.

This is an established cost function - triplet loss! We chose the subscripts \(a\), \(p\), and \(n\) for a reason: we have an anchor image, a positive image (the same person’s face as the anchor) and a negative image (a different person’s face as the anchor). We can then sum over N data points where each data point is a set of three images:

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-(81)#\[\begin{equation} +
+(81)#\[\begin{equation} \text{Cost function} = \sum_{i=1}^N [d(\bar{y}_{a, i}, \bar{y}_{p, i}) - d(\bar{y}_{a, i}, \bar{y}_{n, i})] \end{equation}\]

There’s one little addition in triplet loss. Instead of just using the above cost function, researchers add a constant \(\alpha\) and then make the cost function 0 if it becomes negative. Why do you think they do this?

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-(82)#\[\begin{equation} +
+(82)#\[\begin{equation} \text{Cost function} = \text{max} \left( \sum_{i=1}^N \left[ d(\bar{y}_{a, i}, \bar{y}_{p, i}) - d(\bar{y}_{a, i}, \bar{y}_{n, i}) + \alpha \right], 0 \right) \end{equation}\]
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Video 10: Embedding Faces Wrap-up#

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Check out the papers mentioned in the above video:

    diff --git a/tutorials/W2D3_ModernConvnets/student/W2D3_Tutorial1.html b/tutorials/W2D3_ModernConvnets/student/W2D3_Tutorial1.html index 944a2ea32..8a5f9a55c 100644 --- a/tutorials/W2D3_ModernConvnets/student/W2D3_Tutorial1.html +++ b/tutorials/W2D3_ModernConvnets/student/W2D3_Tutorial1.html @@ -50,7 +50,7 @@ - + @@ -1352,7 +1352,7 @@

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Section 1: Modern CNNs and Transfer Learning#

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Images are high dimensional. That is to say that image_length * image_width * image_channels is a big number, and multiplying that big number by a normal sized fully-connected layer leads to a ton of parameters to learn. Yesterday, we learned about convolutional neural networks, one way of working around high dimensionality in images and other domains.

The widget below (i.e., Interactive Demo 1) calculates the parameters required for a single convolutional or fully connected layer that operates on an image of a certain height and width.

Recall that, the number of parameters of a convolutional layer \(l\) are calculated as:

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+(83)#\[\begin{equation} \text{num_of_params}_l = \left[ \left( H \times W \times K_{l-1} \right) + 1 \right] \times K_l \end{equation}\]

where \(H\) denotes the shape of the height of the filter, \(W\) the shape of the width of the filter, and \(K_l\) denotes the number of the filters in the \(l\)-th layer. The added \(1\) is because of the bias term for each filter.

While a fully connected layer contains:

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+(84)#\[\begin{equation} \text{num_of_params}_l = \left[ \left( N_{l-1} \times N_l \right) + 1 \times N_l \right] \end{equation}\]

where \(N_l\) denotes the number of nodes in the \(l\)-th layer.

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Parameter Calculator
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Section 2: The History of Convnets#

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Section 3: Big and Deep Convnets#

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Interactive Demo 3.2: What does AlexNet see? - +

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Section 4: Convnets After AlexNet#

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In this section we’ll be working with a state of the art CNN model called ResNet. ResNet has two particularly interesting features. First, it uses skip connections to avoid the vanishing gradient problem. Second, each block (collection of layers) in a ResNet can be treated as learning a residual function.

Mathematically, a neural network can be thought of as a series of operations that maps an input (like an image of a dog) to an output (like the label “dog”). In math-speak a mapping from an input to an output is called a function. Neural networks are a flexible way of expressing that function.

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Section 5: Inception + ResNeXt#

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Parameter Calculator - +

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Now we want to look at the number of parameters.

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    Section 6: Depthwise separable convolutions#

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    Section 7: Transfer Learning#

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    The most common way large image models are trained in practice is via transfer learning. One first pretrains a network on a large classification dataset like ImageNet, then uses the weights of this network as initialization for training (“fine-tuning”) that network on your task of choice.

    While training a network twice sounds like a strange thing to do, the model ends up training faster on the target dataset and often outperforms training “from scratch”. There are also other benefits such as robustness to noise that are the subject of active research.

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    Summary#

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    Bonus: Speed-Accuracy Trade-Off / Different BackbonesVideo 9: Speed-accuracy trade-off#

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    As the models got larger and the number of connections increased so did the computational costs involved. In the modern era of image processing, there is a tradeoff between model performance and computational cost. Models can reach extremely high performance on many problems, but achieving state of the art results requires huge amounts of compute power.

    https://raw.githubusercontent.com/NeuromatchAcademy/course-content-dl/main/tutorials/W2D3_ModernConvnets/static/compute_vs_performance.png @@ -4863,7 +4863,7 @@

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    diff --git a/tutorials/W2D3_ModernConvnets/student/W2D3_Tutorial2.html b/tutorials/W2D3_ModernConvnets/student/W2D3_Tutorial2.html index e5ad263f0..bd08bb79f 100644 --- a/tutorials/W2D3_ModernConvnets/student/W2D3_Tutorial2.html +++ b/tutorials/W2D3_ModernConvnets/student/W2D3_Tutorial2.html @@ -50,7 +50,7 @@ - + @@ -962,7 +962,7 @@

    Tutorial Objectives
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    These are the slides for the videos in this tutorial. If you want to download locally the slides, click here.

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    Download Faces Data#

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    One application of large CNNs is facial recognition. The problem formulation in facial recognition is a little different from the image classification we’ve seen so far. In facial recognition, we don’t want to have a fixed number of individuals that the model can learn. If that were the case then to learn a new person it would be necessary to modify the output portion of the architecture and retrain to account for the new person.

    Instead, we train a model to learn an embedding where images from the same individual are close to each other in an embedded space, and images corresponding to different people are far apart. When the model is trained, it takes as input an image and outputs an embedding vector corresponding to the image.

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    Section 1.3: Embedding with a pretrained network - +
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    We cannot show 512-dimensional vectors visually, but using Principal Component Analysis (PCA) we can project the 512 dimensions onto a 2-dimensional space while preserving the maximum amount of data variation possible. This is just a visual aid for us to understand the concept. Note that if you would like to do any calculation, like distances between two images, this would be done with the whole 512-dimensional embedding vectors.

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    Section 2: Ethics – bias/discrimination due to pre-training datasetsVideo 2: Ethical aspects#

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    Lastly, to show the importance of the dataset which you use to pretrain your model, look at how much space white men and women take in different embeddings. FairFace is a dataset which is specifically created with completely balanced classes. The blue dots in all visualizations are white male and white female.

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    Section 3: Within Sum of Squares\(x\) of each group \(S_i\) are from the centroid \(\mu_i\). This concept is known as Within Sum of Squares (WSS) from cluster analysis.

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    +(85)#\[\begin{equation} \text{WSS} = \sum_{x\in S_i} ||x - \mu_i||^2 \end{equation}\]

    where \(|| \cdot ||\) is the Euclidean norm.

    diff --git a/tutorials/W2D4_GenerativeModels/student/W2D4_BonusLecture.html b/tutorials/W2D4_GenerativeModels/student/W2D4_BonusLecture.html index 32d3cde0a..5ecc093ea 100644 --- a/tutorials/W2D4_GenerativeModels/student/W2D4_BonusLecture.html +++ b/tutorials/W2D4_GenerativeModels/student/W2D4_BonusLecture.html @@ -58,7 +58,7 @@ const thebe_selector_output = ".output, .cell_output" - + @@ -1453,11 +1453,11 @@

    Install and import feedback gadget#

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    diff --git a/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial1.html b/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial1.html index f77f9bb24..1a4151de8 100644 --- a/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial1.html +++ b/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial1.html @@ -1100,7 +1100,7 @@

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    Section 1: Generative models#

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    Download BigGAN (a generative model) and a few standard image datasets

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    Interactive Demo 1.1: BigGAN Generator -

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    Interactive Demo 1.2: BigGAN Interpolation - +

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    Section 2: Latent Variable Models#

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    In the video, the concept of a latent variable model was introduced. We saw how PCA (principal component analysis) can be extended into a generative model with latent variables called probabilistic PCA (pPCA). For pPCA the latent variables (z in the video) are the projections onto the principal component axes.

    The dimensionality of the principal components is typically set to be substantially lower-dimensional than the original data. Thus, the latent variables (the projection onto the principal component axes) are a lower-dimensional representation of the original data (dimensionality reduction!). With pPCA we can estimate the original distribution of the high dimensional data. This allows us to generate data with a distribution that “looks” more like the original data than if we were to only use PCA to generate data from the latent variables. Let’s see how that might look with a simple example.

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    (Bonus) Coding Exercise 2: pPCA -(86)#\[\begin{equation} +
    +(86)#\[\begin{equation} x = \mu + W z + \epsilon, \,\text{where}\,~~ \epsilon \sim \mathcal{N}(0,~\sigma^2 \mathbf{I}) \end{equation}\]
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    Section 3: AutoencodersVideo 3: Autoencoders#

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    Download MNIST and CIFAR10 datasets

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    Select a dataset

    Section 3.1: Conceptual introduction to AutoEncoders#

    Now we’ll create our first autoencoder. It will reduce images down to \(K\) dimensions. The architecture will be quite simple: the input will be linearly mapped to a single hidden (or latent) layer \(\mathbf{h}\) with \(K\) units, which will then be linearly mapped back to an output that is the same size as the input:

    -
    -(87)#\[\begin{equation} +
    +(87)#\[\begin{equation} \mathbf{x} \longrightarrow \mathbf{h} \longrightarrow \mathbf{x'} \end{equation}\]

    The loss function we’ll use will simply be mean squared error (MSE) quantifying how well the reconstruction (\(\mathbf{x'}\)) matches the original image (\(\mathbf{x}\)):

    -
    -(88)#\[\begin{equation} +
    +(88)#\[\begin{equation} \text{MSE Loss} = \sum_{i=1}^{N} ||\mathbf{x}_i - \mathbf{x'}_i||^2_2 \end{equation}\]

    If all goes well, then the AutoEncoder will learn, end to end, a good “encoding” or “compression” of inputs to a latent representation (\(\mathbf{x \longrightarrow h}\)) as well as a good “decoding” of that latent representation to a reconstruction of the original input (\(\mathbf{h \longrightarrow x'}\)).

    @@ -2794,7 +2794,7 @@

    Submit your feedback -

    +

    @@ -2824,7 +2824,7 @@

    Comparison to PCA - +

    Let’s visualize some of the reconstructions (\(\mathbf{x'}\)) side-by-side with the input images (\(\mathbf{x}\)).

    Visualize the reconstructions \(\mathbf{x}'\), run this code a few times to see different examples.

    @@ -2893,7 +2893,7 @@

    Submit your feedback - + @@ -3188,7 +3188,7 @@

    Submit your feedback - + @@ -3203,7 +3203,7 @@

    Section 4: Variational Auto-Encoders (VAEs)#

    -
    +
    @@ -3222,7 +3222,7 @@

    Submit your feedback - +

    Train a VAE for MNIST while watching the video. (Note: this VAE has a 2D latent space. If you are feeling ambitious, edit the code and modify the latent space dimensionality and see what happens.)

    @@ -3496,7 +3496,7 @@

    Submit your feedback -
    ---------------------------------------------------------------------------
+
    ---------------------------------------------------------------------------
 KeyboardInterrupt                         Traceback (most recent call last)
 Cell In[46], line 247
     243   return elbo_vals
@@ -3508,39 +3508,58 @@ 
    Submit your feedback    253 # ELBO is the loss function used to train VAEs
     254 # (see lecture!)
 
-Cell In[46], line 237, in train_vae(vae, dataset, epochs, n_samples)
+Cell In[46], line 236, in train_vae(vae, dataset, epochs, n_samples)
+    234 im = im.to(DEVICE)
     235 opt.zero_grad()
-    236 loss = -vae.elbo(im)
---> 237 loss.backward()
+--> 236 loss = -vae.elbo(im)
+    237 loss.backward()
     238 opt.step()
-    240 elbo_vals.append(-loss.item())
-
-File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/torch/_tensor.py:522, in Tensor.backward(self, gradient, retain_graph, create_graph, inputs)
-    512 if has_torch_function_unary(self):
-    513     return handle_torch_function(
-    514         Tensor.backward,
-    515         (self,),
-   (...)
-    520         inputs=inputs,
-    521     )
---> 522 torch.autograd.backward(
-    523     self, gradient, retain_graph, create_graph, inputs=inputs
-    524 )
-
-File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/torch/autograd/__init__.py:266, in backward(tensors, grad_tensors, retain_graph, create_graph, grad_variables, inputs)
-    261     retain_graph = create_graph
-    263 # The reason we repeat the same comment below is that
-    264 # some Python versions print out the first line of a multi-line function
-    265 # calls in the traceback and some print out the last line
---> 266 Variable._execution_engine.run_backward(  # Calls into the C++ engine to run the backward pass
-    267     tensors,
-    268     grad_tensors_,
-    269     retain_graph,
-    270     create_graph,
-    271     inputs,
-    272     allow_unreachable=True,
-    273     accumulate_grad=True,
-    274 )
+
+Cell In[46], line 160, in ConvVAE.elbo(self, x, n)
+    145 def elbo(self, x, n=1):
+    146   """
+    147   Run input end to end through the VAE
+    148   and compute the ELBO using n
+   (...)
+    158     Difference between true and estimated KL divergence
+    159   """
+--> 160   phi = self.infer(x)
+    161   zs = rsample(phi, n)
+    162   mu_xs = self.generate(zs)
+
+Cell In[46], line 82, in ConvVAE.infer(self, x)
+     80 s = self.q_bias(x)
+     81 s = F.relu(self.q_conv_1(s))
+---> 82 s = F.relu(self.q_conv_2(s))
+     83 flat_s = s.view(s.size()[0], -1)
+     84 phi = self.q_fc_phi(flat_s)
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/nn/modules/module.py:1511, in Module._wrapped_call_impl(self, *args, **kwargs)
+   1509     return self._compiled_call_impl(*args, **kwargs)  # type: ignore[misc]
+   1510 else:
+-> 1511     return self._call_impl(*args, **kwargs)
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/nn/modules/module.py:1520, in Module._call_impl(self, *args, **kwargs)
+   1515 # If we don't have any hooks, we want to skip the rest of the logic in
+   1516 # this function, and just call forward.
+   1517 if not (self._backward_hooks or self._backward_pre_hooks or self._forward_hooks or self._forward_pre_hooks
+   1518         or _global_backward_pre_hooks or _global_backward_hooks
+   1519         or _global_forward_hooks or _global_forward_pre_hooks):
+-> 1520     return forward_call(*args, **kwargs)
+   1522 try:
+   1523     result = None
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/nn/modules/conv.py:460, in Conv2d.forward(self, input)
+    459 def forward(self, input: Tensor) -> Tensor:
+--> 460     return self._conv_forward(input, self.weight, self.bias)
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/nn/modules/conv.py:456, in Conv2d._conv_forward(self, input, weight, bias)
+    452 if self.padding_mode != 'zeros':
+    453     return F.conv2d(F.pad(input, self._reversed_padding_repeated_twice, mode=self.padding_mode),
+    454                     weight, bias, self.stride,
+    455                     _pair(0), self.dilation, self.groups)
+--> 456 return F.conv2d(input, weight, bias, self.stride,
+    457                 self.padding, self.dilation, self.groups)
 
 KeyboardInterrupt: 
 
    
@@ -3554,25 +3573,25 @@ 
    Section 4.1: Components of a VAE
-(89)#\[\begin{equation}
+
    
+(89)#\[\begin{equation}
 \mathbf{x} \overset{\text{AE}}{\longrightarrow} \mathbf{h} \, ,
 \end{equation}\]
    
 
    in a VAE we would say that a recognition model maps from inputs to entire distributions over hidden vectors,
    
-
    
-(90)#\[\begin{equation}
+
    
+(90)#\[\begin{equation}
 \mathbf{x} \overset{\text{VAE}}{\longrightarrow} q_{\mathbf{w_e}}(\mathbf{z}) \, ,
 \end{equation}\]
    
 
    which we will then sample from. Here \(\mathbf{w_e}\) refers to the weights of the recognition model, which parametarize our distribution generating network. We’ll say more in a moment about what kind of distribution \(q_{\mathbf{w_e}}(\mathbf{z})\) is.
 Part of what makes VAEs work is that the loss function will require good reconstructions of the input not just for a single \(\mathbf{z}\), but on average from samples of \(\mathbf{z} \sim q_{\mathbf{w_e}}(\mathbf{z})\).
    
 
    In the classic autoencoder, we had a decoder which maps from hidden vectors to reconstructions of the input:
    
-
    
-(91)#\[\begin{equation}
+
    
+(91)#\[\begin{equation}
 \mathbf{h} \overset{\text{AE}}{\longrightarrow} \mathbf{x'} \, .
 \end{equation}\]
    
 
    In a density network, reconstructions are expressed in terms of a distribution:
    
-
    
-(92)#\[\begin{equation}
+
    
+(92)#\[\begin{equation}
 \mathbf{z} \overset{\text{VAE}}{\longrightarrow} p_{\mathbf{w_d}}(\mathbf{x}|\mathbf{z})
 \end{equation}\]
    
 
    where, as above, \(p_{\mathbf{w_d}}(\mathbf{x}|\mathbf{z})\) is defined by mapping \(\mathbf{z}\) through a density network then treating the resulting \(f(\mathbf{z};\mathbf{w_d})\) as the mean of a (Gaussian) distribution over \(\mathbf{x}\). Similarly, our reconstruction distribution is parametarized by the weights of the density network.
    
@@ -3580,13 +3599,13 @@ 
    Section 4.1: Components of a VAE
 
    Section 4.2: Generating novel images from the decoder#
    
 
    If we isolate the decoder part of the AutoEncoder, what we have is a neural network that takes as input a vector of size \(K\) and produces as output an image that looks something like our training data. Recall that in our earlier notation, we had an input \(\mathbf{x}\) that was mapped to a low-dimensional hidden representation \(\mathbf{h}\) which was then decoded into a reconstruction of the input, \(\mathbf{x'}\):
    
-
    
-(93)#\[\begin{equation}
+
    
+(93)#\[\begin{equation}
 \mathbf{x} \overset{\text{encode}}{\longrightarrow} \mathbf{h} \overset{\text{decode}}{\longrightarrow} \mathbf{x'}\, .
 \end{equation}\]
    
 
    Partly as a matter of convention, and partly to distinguish where we are going next from the previous section, we’re going to introduce a new variable, \(\mathbf{z} \in \mathbb{R}^K\), which will take the place of \(\mathbf{h}\). The key difference is that while \(\mathbf{h}\) is produced by the encoder for a particular \(\mathbf{x}\), \(\mathbf{z}\) will be drawn out of thin air from a prior of our choosing:
    
-
    
-(94)#\[\begin{equation}
+
    
+(94)#\[\begin{equation}
 \mathbf{z} \sim p(\mathbf{z})\\ \mathbf{z} \overset{\text{decode}}{\longrightarrow} \mathbf{x}\, .
 \end{equation}\]
    
 
    (Note that it is also common convention to drop the “prime” on \(\mathbf{x}\) when it is no longer being thought of as a “reconstruction”).
    
diff --git a/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial2.html b/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial2.html
index 82351c7c2..a27390457 100644
--- a/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial2.html
+++ b/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial2.html
@@ -50,7 +50,7 @@
 
 
 
-
+
 
 
 
@@ -1017,7 +1017,7 @@ 
    Tutorial Objectives
 
    
-
    
+

    @@ -1337,7 +1337,7 @@

    Notes: score-based model vs. diffusion model#

    -
    +
    @@ -1356,14 +1356,14 @@

    Submit your feedback
    -
    +

    Video 2: Math Behind Diffusion#

    -
    +
    @@ -1382,7 +1382,7 @@

    Submit your feedback - +

    @@ -1390,29 +1390,29 @@

    Submit your feedback#

    In this section, we’d like to understand the forward diffusion process, and gain intuition about how diffusion turns data into “noise”.

    In this tutorial, we will use the process also known as Variance Exploding SDE (VPSDE) in diffusion literature.

    -
    -(95)#\[\begin{equation} +
    +(95)#\[\begin{equation} d\mathbf x=g(t)d\mathbf w \end{equation}\]

    \(d\mathbf w\) is the differential of the Wiener process, which is like the Gaussian random noise; \(g(t)\) is the diffusion coefficient at time \(t\). In our code, we can discretize it as:

    -
    -(96)#\[\begin{equation} +
    +(96)#\[\begin{equation} \mathbf{x}_{t+\Delta t} = \mathbf{x}_{t}+g(t) \sqrt{\Delta t} z_t \end{equation}\]

    where \(z_t\sim \mathcal{N} (0,I)\) are independent and identically distributed (i.i.d.) normal random variable.

    Given an initial state \(\mathbf{x}_0\) the conditional distribution of \(\mathbf{x}_t\) is a Gaussian around \(\mathbf x_0\):

    -
    -(97)#\[\begin{equation} +
    +(97)#\[\begin{equation} p(\mathbf{x}_t\mid \mathbf{x}_0) = \mathcal N(\mathbf{x}_t;\mathbf{x}_0,\sigma_t^2 I) \end{equation}\]

    The key quantity to note is the \(\sigma_t\) which is the integrated noise scale at time \(t\). \(I\) denotes the identity matrix.

    -
    -(98)#\[\begin{equation} +
    +(98)#\[\begin{equation} \sigma_t^2=∫_0^t g^2(\tau)d\tau \end{equation}\]

    Marginalizing over all the initial states, the distribution of \(\mathbf x_t\) is \(p_t(x_t)\), i.e., convolving a Gaussian over the initial data distribution \(p_0(\mathbf x_0)\) which blurs the data up.

    -
    -(99)#\[\begin{equation} +
    +(99)#\[\begin{equation} p_t(\mathbf{x}_t) = \int_{\mathbf x_0} p_0(\mathbf x_0)\mathcal N(\mathbf{x}_t;\mathbf{x}_0,\sigma_t^2 I) \end{equation}\]
    @@ -1454,7 +1454,7 @@

    1D diffusion process
    -
    +

    @@ -1513,7 +1513,7 @@

    2D diffusion process 33 plt.close() # Prevents displaying the initial static plot ---> 34 HTML(animation.to_html5_video()) # to_jshtml -File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/matplotlib/animation.py:1285, in Animation.to_html5_video(self, embed_limit) +File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/matplotlib/animation.py:1285, in Animation.to_html5_video(self, embed_limit) 1282 path = Path(tmpdir, "temp.m4v") 1283 # We create a writer manually so that we can get the 1284 # appropriate size for the tag @@ -1523,7 +1523,7 @@

    2D diffusion process 1288 fps=1000. / self._interval) 1289 self.save(str(path), writer=writer) -File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/matplotlib/animation.py:148, in MovieWriterRegistry.__getitem__(self, name) +File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/matplotlib/animation.py:148, in MovieWriterRegistry.__getitem__(self, name) 146 if self.is_available(name): 147 return self._registered[name] --> 148 raise RuntimeError(f"Requested MovieWriter ({name}) not available") @@ -1550,7 +1550,7 @@

    Submit your feedback -

    +
    @@ -1559,8 +1559,8 @@

    Submit your feedback#

    The big idea of diffusion model is to use the “score” function to reverse the diffusion process. So what is score, what’s the intuition to it?

    The Score is the gradient of the log data distribution, so it tells us which direction to go to increase the probability of data.

    -
    -(100)#\[\begin{equation} +
    +(100)#\[\begin{equation} \mathbf{s}(\mathbf{x})=\nabla \log p(\mathbf{x}) \end{equation}\]
    @@ -1872,7 +1872,7 @@

    Submit your feedback -

    + @@ -1881,13 +1881,13 @@

    Submit your feedback#

    After getting some intuition about the score function, we are now well-equipped to reverse the diffusion process!

    There is a result in stochastic process literature that if we have the forward process

    -
    -(101)#\[\begin{equation} +
    +(101)#\[\begin{equation} d\mathbf{x} = g(t)d \mathbf{w} \end{equation}\]

    Then the following process (reverse SDE) will be its time reversal:

    -
    -(102)#\[\begin{equation} +
    +(102)#\[\begin{equation} d\mathbf{x} = -g^2(t) \nabla_\mathbf{x} \log p_t(\mathbf{x}) dt + g(t) d \mathbf{w}. \end{equation}\]

    where time \(t\) runs backward.

    @@ -1901,8 +1901,8 @@

    Section 1.3: Reverse Diffusion#

    Here let’s put our knowledge into action and see that the score function indeed enables the reverse diffusion and the recovery of the initial distribution.

    In the following cell, you are going to implement the discretization of the reverse diffusion equation:

    -
    -(103)#\[\begin{equation} +
    +(103)#\[\begin{equation} \mathbf{x}_{t-\Delta t} = \mathbf{x}_t + g(t)^2 s(\mathbf{x}_t, t)\Delta t + g(t)\sqrt{\Delta t} \mathbf{z}_t \end{equation}\]

    where \(\mathbf{z}_t \sim \mathcal{N}(\mathbf{0}, I)\) and \(g(t)=\lambda^t\).

    @@ -2036,7 +2036,7 @@

    Submit your feedback -

    +
    @@ -2048,25 +2048,25 @@

    Section 2: Learning the score by denoising\(\{x_i\}\) from it. The way we estimate the score is called denoising score matching.

    It can be shown that optimizing the upper objective, i.e., denoising score matching (DSM), is equivalent to optimizing the lower objective, i.e., explicit score matching, which minimizes the mean squared error (MSE) between the score model and the true time-dependent score.

    -
    -(104)#\[\begin{equation} +
    +(104)#\[\begin{equation} J_{DSM}(\theta)=\mathbb E_{x\sim p_0(x)\\\tilde x\sim p_t(\tilde x\mid x)}\|s_\theta(\tilde x)-\nabla_\tilde x\log p_t(\tilde x\mid x)\|^2\\ J_{ESM}(\theta)=\mathbb E_{\tilde x\sim p_t(\tilde x)}\|s_\theta(\tilde x)-\nabla_\tilde x\log p_t(\tilde x)\|^2 \end{equation}\]

    In both cases, the optimal \(s_\theta(x)\) will be the same as the true score \(\nabla_\tilde x\log p_t(\tilde x)\). Both objectives are equivalent in terms of their optimum.

    Using the fact that the forward process has Gaussian conditional distribution \(p_t(\tilde x\mid x)= \mathcal N(x,\sigma^2_t I)\), the objective can be simplified even further!

    -
    -(105)#\[\begin{equation} +
    +(105)#\[\begin{equation} \mathbb E_{x\sim p_0(x)}\mathbb E_{z\sim \mathcal N(0,I)}\|s_\theta(x+\sigma_t z)+\frac{1}{\sigma_t}z\|^2 \end{equation}\]

    To train the score model for all \(t\) or noise levels, the objective is integrated over all time \(t\in[\epsilon,1]\), with particular weighting \(\gamma_t\) of different times:

    -
    -(106)#\[\begin{equation} +
    +(106)#\[\begin{equation} \int_\epsilon^1dt \gamma_t\mathbb E_{x\sim p_0(x)}\mathbb E_{z\sim \mathcal N(0,I)}\|s_\theta(x+\sigma_t z, t)+\frac{1}{\sigma_t}z\|^2 \end{equation}\]

    Here as a naive example, we choose weight \(\gamma_t=\sigma_t^2\), which emphasizes the high noise period (\(t\sim 1\)) more than the low noise period (\(t\sim 0\)):

    -
    -(107)#\[\begin{equation} +
    +(107)#\[\begin{equation} \int_\epsilon^1dt \mathbb E_{x\sim p_0(x)}\mathbb E_{z\sim \mathcal N(0,I)}\|\sigma_t s_\theta(x+\sigma_t z, t)+z\|^2 \end{equation}\]

    To put it in plain language, this objective is simply doing the following steps:

    @@ -2114,7 +2114,7 @@

    Submit your feedback -

    +
    @@ -2193,7 +2193,7 @@

    Submit your feedback -

    +
    @@ -2432,18 +2432,18 @@

    Summary -(108)#\[\begin{equation} +
    +(108)#\[\begin{equation} d\mathbf{x} = \mathbf{f}(\mathbf{x}, t)dt + g(t)d \mathbf{w} \end{equation}\]

    There exists a reverse time stochastic process (reverse SDE)

    -
    -(109)#\[\begin{equation} +
    +(109)#\[\begin{equation} d\mathbf{x} = \bigg[\mathbf{f}(\mathbf{x}, t) - g^2(t) \nabla_\mathbf{x} \log p_t(\mathbf{x}) \bigg]dt + g(t) d \mathbf{w}. \end{equation}\]

    and a probability flow Ordinary Differential Equation (ODE)

    -
    -(110)#\[\begin{equation} +
    +(110)#\[\begin{equation} d\mathbf{x} = \bigg[\mathbf{f}(\mathbf{x}, t) - \frac{1}{2}g^2(t) \nabla_\mathbf{x} \log p_t(\mathbf{x})\bigg] dt. \end{equation}\]

    such that solving the reverse SDE or the probability flow ODE amounts to the time reversal of the solution to the forward SDE.

    @@ -2459,31 +2459,31 @@

    Summary#

    How to fit the score based on the samples, when we have no access to the exact scores?

    This objective is called denoising score matching. Mathematically, it utilized this equivalence relationship of the following objectives.

    -
    -(111)#\[\begin{align} +
    +(111)#\[\begin{align} J_{DSM}(\theta) &=\mathbb E_{\tilde x,x\sim p_t(\tilde x,x)} \|s_\theta(\tilde x)-\nabla_\tilde x\log p_t(\tilde x\mid x)\|^2\\ J_{ESM}(\theta) &=\mathbb E_{\tilde x\sim p_t(\tilde x)} \|s_\theta(\tilde x)-\nabla_\tilde x\log p_t(\tilde x)\|^2 \end{align}\]

    In practise, it’s to sample \(x\) from data distribution, add noise with \(\sigma\) and denoise it. Since we have at time \(t\), \(p_t(\tilde x\mid x)= \mathcal N(\tilde x;x,\sigma^2_t I)\), then \(\tilde x=x+\sigma_t z,z\sim \mathcal N(0,I)\). Then

    -
    -(112)#\[\begin{equation} +
    +(112)#\[\begin{equation} \nabla_\tilde x\log p_t(\tilde x|x)=-\frac{1}{\sigma_t^2}(x+\sigma_t z -x)=-\frac{1}{\sigma_t}z \end{equation}\]

    The objective simplifies into

    -
    -(113)#\[\begin{equation} +
    +(113)#\[\begin{equation} \mathbb E_{x\sim p_0(x)}\mathbb E_{z\sim \mathcal N(0,I)} \|s_\theta(x+\sigma_t z)+\frac{1}{\sigma_t}z\|^2 \end{equation}\]

    Finally, in the time dependent score model \(s(x,t)\), to learn this for any time \(t\in [\epsilon,1]\), we integrate over all \(t\) with a certain weighting function \(\gamma_t\) to emphasize certain part.

    -
    -(114)#\[\begin{equation} +
    +(114)#\[\begin{equation} \int_\epsilon^1dt \gamma_t\mathbb E_{x\sim p_0(x)}\mathbb E_{z\sim \mathcal N(0,I)} \|s_\theta(x+\sigma_t z, t)+\frac{1}{\sigma_t}z\|^2 \end{equation}\]

    (the \(\epsilon\) is set to ensure numerical stability, as \(t\to 0,\sigma_t\to 0\)) Now all the expectations could be easily evaluated by sampling.

    A commonly used weighting is the following:

    -
    -(115)#\[\begin{equation} +
    +(115)#\[\begin{equation} \int_\epsilon^1dt \mathbb E_{x\sim p_0(x)}\mathbb E_{z\sim \mathcal N(0,I)} \|\sigma_t s_\theta(x+\sigma_t z, t)+z\|^2 \end{equation}\]

    diff --git a/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial3.html b/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial3.html index 888ab0ec8..31dc0251d 100644 --- a/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial3.html +++ b/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial3.html @@ -50,7 +50,7 @@ - + @@ -1029,7 +1029,7 @@

    Tutorial Objectives
    -
    +

    @@ -1273,7 +1273,7 @@

    Neural Network Architecture#

    -
    +
    @@ -1292,7 +1292,7 @@

    Submit your feedback
    -
    +

    @@ -1306,14 +1306,14 @@

    Coding Exercise 1: Train Diffusion for MNIST -(116)#\[\begin{equation} +
    +(116)#\[\begin{equation} d\mathbf x=g(t)d\mathbf w \end{equation}\]

    and we let the diffusion coefficient \(g(t)=\lambda^t\), with \(\lambda > 1\).

    If so, the marginal distribution of state \(\mathbf x_t\) at time t given an initial state \(\mathbf x_0\) will be a Gaussian \(\mathcal N(\mathbf x_t|\mathbf x_0,\sigma_t^2 I)\). The variance is the integration of the squared diffusion coefficient.

    -
    -(117)#\[\begin{equation} +
    +(117)#\[\begin{equation} \sigma_t^2 =\int_0^tg(\tau)^2d\tau=\frac{\lambda^{2t}-1}{2\log\lambda} \end{equation}\]
    @@ -1374,7 +1374,7 @@

    Submit your feedback -

    +

    @@ -1551,7 +1551,7 @@

    Submit your feedback - +

    @@ -1559,8 +1559,8 @@

    Submit your feedback

    Coding Exercise 2: Defining the loss function#

    In the next cell, you will implement the denoising score matching (DSM) objective as we used in the last tutorial.

    -
    -(118)#\[\begin{equation} +
    +(118)#\[\begin{equation} \mathcal L=\int_\epsilon^1dt \mathbb E_{x\sim p_0(x)}\mathbb E_{z\sim \mathcal N(0,I)}\|\sigma_t s_\theta(x+\sigma_t z, t)+z\|^2 \end{equation}\]

    where the time weighting is chosen as \(\gamma_t=\sigma_t^2\), which emphasizes the high noise period (\(t\sim 1\)) more than the low noise period (\(t\sim 0\)).

    @@ -1648,7 +1648,7 @@

    Submit your feedback -

    + @@ -1826,7 +1826,7 @@

    Sampling 31 uncond_score_model.to(DEVICE) 32 save_samples_uncond(uncond_score_model, suffix="", device=DEVICE) -File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/torch/serialization.py:998, in load(f, map_location, pickle_module, weights_only, mmap, **pickle_load_args) +File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/serialization.py:998, in load(f, map_location, pickle_module, weights_only, mmap, **pickle_load_args) 995 if 'encoding' not in pickle_load_args.keys(): 996 pickle_load_args['encoding'] = 'utf-8' --> 998 with _open_file_like(f, 'rb') as opened_file: @@ -1836,14 +1836,14 @@

    Sampling 1002 # reset back to the original position. 1003 orig_position = opened_file.tell() -File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/torch/serialization.py:445, in _open_file_like(name_or_buffer, mode) +File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/serialization.py:445, in _open_file_like(name_or_buffer, mode) 443 def _open_file_like(name_or_buffer, mode): 444 if _is_path(name_or_buffer): --> 445 return _open_file(name_or_buffer, mode) 446 else: 447 if 'w' in mode: -File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/torch/serialization.py:426, in _open_file.__init__(self, name, mode) +File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/serialization.py:426, in _open_file.__init__(self, name, mode) 425 def __init__(self, name, mode): --> 426 super().__init__(open(name, mode)) @@ -1870,7 +1870,7 @@

    Section 2: Conditional Diffusion Model#

    -
    +
    @@ -1889,7 +1889,7 @@

    Submit your feedback - +

    In formulation, the conditional diffusion is highly similar to the unconditional diffusion.

    If you are curious about how to build and train a conditional diffusion model, you are welcome to look at the Bonus exercise at the end.

    @@ -1898,7 +1898,7 @@

    Submit your feedback#

    -
    +

    @@ -1917,7 +1917,7 @@

    Submit your feedback - +

    Interactive Demo 2: Stable Diffusion#

    @@ -1946,7 +1946,7 @@

    Download the Stable Diffusion models - +

    Now you can let loose your imagination and create artworks from text!

    Example prompts:

    @@ -1985,7 +1985,7 @@

    Submit your feedback - +

    @@ -2121,7 +2121,7 @@

    Submit your feedback - + @@ -2134,7 +2134,7 @@

    Section 3: Ethical Considerations#

    -
    +
    @@ -2153,7 +2153,7 @@

    Submit your feedback - +

    @@ -2179,7 +2179,7 @@

    Submit your feedback - +

    diff --git a/tutorials/W2D5_AttentionAndTransformers/student/W2D5_Tutorial1.html b/tutorials/W2D5_AttentionAndTransformers/student/W2D5_Tutorial1.html index 0972c51c3..96a57eaa9 100644 --- a/tutorials/W2D5_AttentionAndTransformers/student/W2D5_Tutorial1.html +++ b/tutorials/W2D5_AttentionAndTransformers/student/W2D5_Tutorial1.html @@ -50,7 +50,7 @@ - + @@ -1232,7 +1232,7 @@

    Tutorial Objectives
    -
    +
    @@ -1855,7 +1855,7 @@

    Section 1: Attention overview#

    -
    +
    @@ -1874,7 +1874,7 @@

    Submit your feedback
    -
    +

    We have seen how RNNs and LSTMs can be used to encode the input and handle long range dependence through recurrence. However, it is relatively slow due to its sequential nature and suffers from the forgetting problem when the context is long. Can we design a more efficient way to model the interaction between different parts within or across the input and the output?

    Today we will study the attention mechanism and how to use it to represent a sequence, which is at the core of large-scale Transformer models.

    @@ -1900,7 +1900,7 @@

    Submit your feedback - +

    @@ -1914,7 +1914,7 @@

    Section 2: Queries, keys, and values#

    -
    +
    @@ -1933,7 +1933,7 @@

    Submit your feedback - +

    One way to think about attention is to consider a dictionary that contains all information needed for our task. Each entry in the dictionary contains some value and the corresponding key to retrieve it. For a specific prediction, we would like to retrieve relevant information from the dictionary. Therefore, we issue a query, match it to keys in the dictionary, and return the corresponding values.

    @@ -2064,7 +2064,7 @@

    Submit your feedback - +

    @@ -2088,15 +2088,15 @@

    Submit your feedback - +

    Coding Exercise 2: Dot product attention#

    In this exercise, let’s compute the scaled dot product attention using its matrix form.

    -
    -(119)#\[\begin{equation} +
    +(119)#\[\begin{equation} \mathrm{softmax} \left( \frac{Q K^\text{T}}{\sqrt{d}} \right) V \end{equation}\]

    where \(Q\) denotes the query or values of the embeddings (in other words the hidden states), \(K\) the key, and \(k\) denotes the dimension of the query key vector.

    @@ -2245,7 +2245,7 @@

    Submit your feedback -

    +
    @@ -2259,7 +2259,7 @@

    Section 3: Multihead attention#

    -
    +
    @@ -2278,7 +2278,7 @@

    Submit your feedback - +

    One powerful idea in Transformer is multi-head attention, which is used to capture different aspects of the dependence among words (e.g., syntactical vs semantic). For more info see here.

    @@ -2368,7 +2368,7 @@

    Submit your feedback - +

    @@ -2382,7 +2382,7 @@

    Section 4: Transformer overview I#

    -
    +
    @@ -2401,7 +2401,7 @@

    Submit your feedback - +

    Coding Exercise 4: Transformer encoder#

    @@ -2497,7 +2497,7 @@

    Submit your feedback - +

    @@ -2511,7 +2511,7 @@

    Section 5: Transformer overview II#

    -
    +
    @@ -2530,7 +2530,7 @@

    Submit your feedback - +

    Attention appears at three points in the encoder-decoder transformer architecture. First, the self-attention among words in the input sequence. Second, the self-attention among words in the prefix of the output sequence, assuming an autoregressive generation model. Third, the attention between input words and output prefix words.

    @@ -2557,7 +2557,7 @@

    Submit your feedback - +

    @@ -2571,7 +2571,7 @@

    Section 6: Positional encoding#

    -
    +
    @@ -2590,13 +2590,13 @@

    Submit your feedback - +

    Self-attention is concerned with relationship between words and is not sensitive to positions or word orderings. Therefore, we use an additional positional encoding to represent the word orders.

    There are multiple ways to encode the position. For our purpose to have continuous values of the positions based on binary encoding, let’s use the following implementation of deterministic (as opposed to learned) position encoding using sinusoidal functions.

    -
    -(120)#\[\begin{equation} +
    +(120)#\[\begin{equation} PE_{(pos,2i)} = sin(pos/10000^{2i/d_{model}})\\ PE_{(pos,2i+1)}=cos(pos/10000^{2i/d_{model}}) \end{equation}\]
    @@ -2780,7 +2780,7 @@

    Submit your feedback -

    +

    @@ -2928,7 +2928,7 @@

    Section 8: Ethics in language models#

    -
    +
    @@ -2947,7 +2947,7 @@

    Submit your feedback - +

    Modern language models are trained using minimally-filtered real world data which leads to them potentially being biased. Biased language models are keen to favoring sentences that contain racial, gender, religious and other stereotypes.

    The goal of this section is to verify whether BERT is biased or not.

    @@ -3065,7 +3065,7 @@

    Submit your feedback - +

    @@ -3102,7 +3102,7 @@

    Submit your feedback - + @@ -3128,7 +3128,7 @@

    Submit your feedback - + diff --git a/tutorials/W2D5_AttentionAndTransformers/student/W2D5_Tutorial2.html b/tutorials/W2D5_AttentionAndTransformers/student/W2D5_Tutorial2.html index f2a36245e..67e62d14e 100644 --- a/tutorials/W2D5_AttentionAndTransformers/student/W2D5_Tutorial2.html +++ b/tutorials/W2D5_AttentionAndTransformers/student/W2D5_Tutorial2.html @@ -48,7 +48,7 @@ const thebe_selector_output = ".output, .cell_output" - + @@ -948,7 +948,7 @@

    Tutorial Objectives
    -
    +
    @@ -1218,7 +1218,7 @@

    Bonus 1: Language modeling as pre-training#

    -
    +
    @@ -1237,7 +1237,7 @@

    Submit your feedback
    -
    +

    Bonus Interactive Demo 1: GPT-2 for sentiment classification#

    @@ -1512,7 +1512,7 @@

    Bonus 2: Light-weight fine-tuning#

    -
    +
    @@ -1531,7 +1531,7 @@

    Submit your feedback - +

    Fine-tuning these large pre-trained models with billions of parameters tends to be very slow. In this section, we will explore the effect of fine-tuning a few layers (while fixing the others) to save training time.

    The HuggingFace python library provides a simplified API for training and fine-tuning transformer language models. In this exercise we will fine-tune a pre-trained language model for sentiment classification.

    @@ -1712,7 +1712,7 @@

    Bonus 3: Model robustness#

    -
    +

    @@ -1731,7 +1731,7 @@

    Submit your feedback - +

    Given the previously trained model for sentiment classification, it is possible to deceive it using various text perturbations. The text perturbations can act as previously unseen noise to the model, which might persuade it to impart wrong values of sentiment!

    @@ -1798,7 +1798,7 @@

    Submit your feedback - +

    We can apply various text perturbations to the selected review using the textattack python library. This will help us augment the original text to break the model!

    Important: Locally or on colab (with !) you can simple

    @@ -4115,7 +4115,134 @@

    Helper functions to avoid - +
    +
    ---------------------------------------------------------------------------
+ImportError                               Traceback (most recent call last)
+Cell In[33], line 4
+      1 # @title Helper functions to avoid `textattack` issue
+      2 get_ipython().system('pip install flair --quiet')
+----> 4 import flair
+      5 from collections import OrderedDict
+      6 from flair.data import Sentence
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/flair/__init__.py:42
+     39 # global variable: arrow symbol
+     40 _arrow = " → "
+---> 42 from . import (  # noqa: E402 import after setting device
+     43     data,
+     44     models,
+     45     nn,
+     46     trainers,
+     47     visual,
+     48 )
+     50 logging.config.dictConfig(
+     51     {
+     52         "version": 1,
+   (...)
+     64     }
+     65 )
+     67 logger = logging.getLogger("flair")
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/flair/models/__init__.py:1
+----> 1 from .clustering import ClusteringModel
+      2 from .entity_linker_model import SpanClassifier
+      3 from .language_model import LanguageModel
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/flair/models/clustering.py:14
+     12 from flair.data import Corpus, _iter_dataset
+     13 from flair.datasets import DataLoader
+---> 14 from flair.embeddings import DocumentEmbeddings
+     16 log = logging.getLogger("flair")
+     19 class ClusteringModel:
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/flair/embeddings/__init__.py:13
+     10 from .base import Embeddings, ScalarMix
+     12 # Expose document embedding classes
+---> 13 from .document import (
+     14     DocumentCNNEmbeddings,
+     15     DocumentEmbeddings,
+     16     DocumentLMEmbeddings,
+     17     DocumentPoolEmbeddings,
+     18     DocumentRNNEmbeddings,
+     19     DocumentTFIDFEmbeddings,
+     20     SentenceTransformerDocumentEmbeddings,
+     21     TransformerDocumentEmbeddings,
+     22 )
+     24 # Expose image embedding classes
+     25 from .image import (
+     26     ConvTransformNetworkImageEmbeddings,
+     27     IdentityImageEmbeddings,
+   (...)
+     30     PrecomputedImageEmbeddings,
+     31 )
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/flair/embeddings/document.py:16
+     10 from flair.data import Sentence
+     11 from flair.embeddings.base import (
+     12     DocumentEmbeddings,
+     13     load_embeddings,
+     14     register_embeddings,
+     15 )
+---> 16 from flair.embeddings.token import FlairEmbeddings, StackedEmbeddings, TokenEmbeddings
+     17 from flair.embeddings.transformer import (
+     18     TransformerEmbeddings,
+     19     TransformerOnnxDocumentEmbeddings,
+     20 )
+     21 from flair.nn import LockedDropout, WordDropout
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/flair/embeddings/token.py:10
+      7 from pathlib import Path
+      8 from typing import Any, Dict, List, Optional, Union
+---> 10 import gensim
+     11 import numpy as np
+     12 import torch
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/gensim/__init__.py:11
+      7 __version__ = '4.3.2'
+      9 import logging
+---> 11 from gensim import parsing, corpora, matutils, interfaces, models, similarities, utils  # noqa:F401
+     14 logger = logging.getLogger('gensim')
+     15 if not logger.handlers:  # To ensure reload() doesn't add another one
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/gensim/corpora/__init__.py:6
+      1 """
+      2 This package contains implementations of various streaming corpus I/O format.
+      3 """
+      5 # bring corpus classes directly into package namespace, to save some typing
+----> 6 from .indexedcorpus import IndexedCorpus  # noqa:F401 must appear before the other classes
+      8 from .mmcorpus import MmCorpus  # noqa:F401
+      9 from .bleicorpus import BleiCorpus  # noqa:F401
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/gensim/corpora/indexedcorpus.py:14
+     10 import logging
+     12 import numpy
+---> 14 from gensim import interfaces, utils
+     16 logger = logging.getLogger(__name__)
+     19 class IndexedCorpus(interfaces.CorpusABC):
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/gensim/interfaces.py:19
+      7 """Basic interfaces used across the whole Gensim package.
+      8 
+      9 These interfaces are used for building corpora, model transformation and similarity queries.
+   (...)
+     14 
+     15 """
+     17 import logging
+---> 19 from gensim import utils, matutils
+     22 logger = logging.getLogger(__name__)
+     25 class CorpusABC(utils.SaveLoad):
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/gensim/matutils.py:20
+     18 import scipy.sparse
+     19 from scipy.stats import entropy
+---> 20 from scipy.linalg import get_blas_funcs, triu
+     21 from scipy.linalg.lapack import get_lapack_funcs
+     22 from scipy.special import psi  # gamma function utils
+
+ImportError: cannot import name 'triu' from 'scipy.linalg' (/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/scipy/linalg/__init__.py)
+
    +
    +

    @@ -4244,7 +4371,7 @@

    Submit your feedback - +

    diff --git a/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial1.html b/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial1.html index bd4f0e56a..af75d17c7 100644 --- a/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial1.html +++ b/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial1.html @@ -48,7 +48,7 @@ const thebe_selector_output = ".output, .cell_output" - + @@ -995,7 +995,7 @@

    Tutorial objectives
    -
    +
    @@ -1141,6 +1141,62 @@

    Install fastText +
    ---------------------------------------------------------------------------
+ImportError                               Traceback (most recent call last)
+Cell In[5], line 11
+      9 from nltk.corpus import brown
+     10 from nltk.tokenize import word_tokenize
+---> 11 from gensim.models import Word2Vec
+     13 import torch.nn as nn
+     14 from torch.nn import functional as F
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/gensim/__init__.py:11
+      7 __version__ = '4.3.2'
+      9 import logging
+---> 11 from gensim import parsing, corpora, matutils, interfaces, models, similarities, utils  # noqa:F401
+     14 logger = logging.getLogger('gensim')
+     15 if not logger.handlers:  # To ensure reload() doesn't add another one
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/gensim/corpora/__init__.py:6
+      1 """
+      2 This package contains implementations of various streaming corpus I/O format.
+      3 """
+      5 # bring corpus classes directly into package namespace, to save some typing
+----> 6 from .indexedcorpus import IndexedCorpus  # noqa:F401 must appear before the other classes
+      8 from .mmcorpus import MmCorpus  # noqa:F401
+      9 from .bleicorpus import BleiCorpus  # noqa:F401
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/gensim/corpora/indexedcorpus.py:14
+     10 import logging
+     12 import numpy
+---> 14 from gensim import interfaces, utils
+     16 logger = logging.getLogger(__name__)
+     19 class IndexedCorpus(interfaces.CorpusABC):
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/gensim/interfaces.py:19
+      7 """Basic interfaces used across the whole Gensim package.
+      8 
+      9 These interfaces are used for building corpora, model transformation and similarity queries.
+   (...)
+     14 
+     15 """
+     17 import logging
+---> 19 from gensim import utils, matutils
+     22 logger = logging.getLogger(__name__)
+     25 class CorpusABC(utils.SaveLoad):
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/gensim/matutils.py:20
+     18 import scipy.sparse
+     19 from scipy.stats import entropy
+---> 20 from scipy.linalg import get_blas_funcs, triu
+     21 from scipy.linalg.lapack import get_lapack_funcs
+     22 from scipy.special import psi  # gamma function utils
+
+ImportError: cannot import name 'triu' from 'scipy.linalg' (/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/scipy/linalg/__init__.py)
+
    +
    +
    @@ -1375,7 +1431,7 @@

    Section 1: Intro: What time series are there?#

    -
    +
    @@ -1394,14 +1450,14 @@

    Submit your feedback
    -
    +

    Video 2: What is NLP?#

    -
    +
    @@ -1420,7 +1476,7 @@

    Submit your feedback - +

    @@ -1432,7 +1488,7 @@

    Section 2: EmbeddingsVideo 3: NLP Tokenization#

    -
    +
    @@ -1451,7 +1507,7 @@

    Submit your feedback - +

    @@ -1526,6 +1582,7 @@

    Creating Word Embeddings @@ -1540,19 +1597,7 @@

    Creating Word Embeddings -
    Embedding of "company" is [ 0.23635082 -0.14757146 -0.00128662  0.1517792  -0.26336694  0.19548376
-  0.3248975   0.06998292  0.06557198 -0.03440798  0.15586787  0.14049861
-  0.12518767  0.0020447  -0.34335127  0.10796688  0.31969354  0.03538975
-  0.01583967 -0.1471612   0.2405943  -0.12975995  0.1916085  -0.1395368
- -0.0279079   0.2866217  -0.31615633  0.03445482 -0.2831301  -0.00316796
-  0.19220795 -0.07129102  0.51387644  0.01845836  0.01809897 -0.0383398
-  0.37205502  0.24731402  0.32878748 -0.39879128  0.18217117  0.08973505
- -0.45490304 -0.06776157  0.40727717  0.02118984  0.15573873 -0.13689192
-  0.1931406   0.36442065]
-
    -
    - +

    @@ -1652,9 +1697,7 @@

    Visualizing Word Embeddings -../../../_images/f5d5a9200b33b99a470f200ecf6693bd13737a9e652ea3e3712147f8b9cdd4d3.png - +

    @@ -1680,7 +1723,7 @@

    Submit your feedback - +

    @@ -1691,7 +1734,7 @@

    Section 2.2: Embedding exploration#

    -
    +
    @@ -1710,14 +1753,14 @@

    Submit your feedback - +

    Video 5: Distributional Similarity and Vector Embeddings#

    -
    +
    @@ -1736,7 +1779,7 @@

    Submit your feedback - +

    Words or subword units such as morphemes are the basic units we use to express meaning in language. The technique of mapping words to vectors of real numbers is known as word embedding.

    In this section, we will use pretrained fastText embeddings, a context-oblivious embedding similar to word2vec.

    @@ -1956,7 +1999,7 @@

    Submit your feedback - +

    @@ -2044,7 +2087,9 @@

    Word Analogies 
    [(0.615874171257019, 'affliction')]
-[(0.5437814593315125, 'bull')]
+
    +
    +
    [(0.5437814593315125, 'bull')]
    @@ -2065,7 +2110,7 @@

    Submit your feedback - + @@ -2076,7 +2121,7 @@

    Section 2.3: Neural Net with word embeddings#

    -
    +
    @@ -2095,7 +2140,7 @@

    Submit your feedback - +

    Training context-oblivious word embeddings is relatively cheap, but most people still use pre-trained word embeddings. After we cover context-sensitive word embeddings, we’ll see how to “fine tune” embeddings (adjust them to the task at hand).

    Let’s use the pretrained FastText embeddings to train a neural network on the IMDB dataset.

    @@ -2181,6 +2226,7 @@

    Coding Exercise 1: Simple feed forward netClick for solution

    @@ -2199,7 +2245,7 @@

    Submit your feedback - +
    @@ -2355,8 +2401,7 @@

    Submit your feedback -

    +
    @@ -2369,6 +2414,7 @@

    Submit your feedback
    @@ -2431,71 +2477,7 @@

    Submit your feedback -
    ---------------------------------------------------------------------------
-ValueError                                Traceback (most recent call last)
-Cell In[50], line 1
-----> 1 plot_train_val(np.arange(EPOCHS), train_acc, val_acc,
-      2                'training_accuracy', 'validation_accuracy',
-      3                'Neural Net on AG_NEWS text classification', 'accuracy')
-      4 plot_train_val(np.arange(EPOCHS), [x.detach().cpu().numpy() for x in train_loss],
-      5                [x.detach().cpu().numpy() for x in val_loss],
-      6                'training_loss', 'validation_loss',
-      7                'Neural Net on AG_NEWS text classification', 'loss')
-
-Cell In[45], line 107, in plot_train_val(x, train, val, train_label, val_label, title, ylabel)
-    106 def plot_train_val(x, train, val, train_label, val_label, title, ylabel):
---> 107   plt.plot(x, train, label=train_label)
-    108   plt.plot(x, val, label=val_label)
-    109   plt.legend()
-
-File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/matplotlib/pyplot.py:3590, in plot(scalex, scaley, data, *args, **kwargs)
-   3582 @_copy_docstring_and_deprecators(Axes.plot)
-   3583 def plot(
-   3584     *args: float | ArrayLike | str,
-   (...)
-   3588     **kwargs,
-   3589 ) -> list[Line2D]:
--> 3590     return gca().plot(
-   3591         *args,
-   3592         scalex=scalex,
-   3593         scaley=scaley,
-   3594         **({"data": data} if data is not None else {}),
-   3595         **kwargs,
-   3596     )
-
-File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/matplotlib/axes/_axes.py:1724, in Axes.plot(self, scalex, scaley, data, *args, **kwargs)
-   1481 """
-   1482 Plot y versus x as lines and/or markers.
-   1483 
-   (...)
-   1721 (``'green'``) or hex strings (``'#008000'``).
-   1722 """
-   1723 kwargs = cbook.normalize_kwargs(kwargs, mlines.Line2D)
--> 1724 lines = [*self._get_lines(self, *args, data=data, **kwargs)]
-   1725 for line in lines:
-   1726     self.add_line(line)
-
-File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/matplotlib/axes/_base.py:303, in _process_plot_var_args.__call__(self, axes, data, *args, **kwargs)
-    301     this += args[0],
-    302     args = args[1:]
---> 303 yield from self._plot_args(
-    304     axes, this, kwargs, ambiguous_fmt_datakey=ambiguous_fmt_datakey)
-
-File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/matplotlib/axes/_base.py:499, in _process_plot_var_args._plot_args(self, axes, tup, kwargs, return_kwargs, ambiguous_fmt_datakey)
-    496     axes.yaxis.update_units(y)
-    498 if x.shape[0] != y.shape[0]:
---> 499     raise ValueError(f"x and y must have same first dimension, but "
-    500                      f"have shapes {x.shape} and {y.shape}")
-    501 if x.ndim > 2 or y.ndim > 2:
-    502     raise ValueError(f"x and y can be no greater than 2D, but have "
-    503                      f"shapes {x.shape} and {y.shape}")
-
-ValueError: x and y must have same first dimension, but have shapes (10,) and (0,)
-
    -
    -../../../_images/c0a6b1dc0db3d99024cb6f13d5aa1a9714fdb11ebf8efbac3aa83ed064cd6209.png -

    +

    diff --git a/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial2.html b/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial2.html index c0a694fa9..78d94c604 100644 --- a/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial2.html +++ b/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial2.html @@ -50,7 +50,7 @@ - + @@ -1032,7 +1032,7 @@

    Contents

    -

    Open In Colab   Open in Kaggle

    +

    Open In Colab   Open in Kaggle

    Tutorial 2: Natural Language Processing and LLMs#

    Week 3, Day 1: Time Series and Natural Language Processing

    @@ -1040,7 +1040,7 @@

    Tutorial 2: Natural Language Processing and LLMs
    @@ -1048,7 +1048,7 @@

    Tutorial Objectives
    -
    +

    @@ -1235,7 +1235,7 @@

    Section 1: NLP architectures#

    -
    +

    A core principle of Natural Language Processing is embedding words as vectors. In the relevant vector space, words with similar meanings are close to one another.

    In classical transformer systems, a core principle is encoding and decoding. We can encode an input sequence as a vector (that implicitly codes what we just read). And we can then take this vector and decode it, e.g., as a new sentence. So a sequence-to-sequence (e.g., sentence translation) system may read a sentence (made out of words embedded in a relevant space) and encode it as an overall vector. It then takes the resulting encoding of the sentence and decodes it into a translated sentence.

    @@ -1257,7 +1257,7 @@

    Submit your feedback
    -
    +

    @@ -1269,7 +1269,7 @@

    Section 2: The NLP pipeline#

    -
    +
    @@ -1288,7 +1288,7 @@

    Submit your feedback - +

    @@ -1316,7 +1316,7 @@

    Generating a dataset
    -
    +
    @@ -1474,7 +1474,7 @@

    Tokenizer Features 
    Hello, world!
-('hell', 9140) ('##o', 2277) (',', 16) ('world', 4375) ('!', 5)
+('hell', 9140) ('##o', 2273) (',', 16) ('world', 4375) ('!', 5)
 ['these', 'to', '##aster', '##so', '##ck', '##s', 'are', 'so', 'gro', '##omm', '##p', '##y', '!']
    @@ -1508,7 +1508,7 @@

    Submit your feedback -

    +

    @@ -1533,7 +1533,7 @@

    Submit your feedback - + @@ -1558,7 +1558,7 @@

    Submit your feedback - + @@ -1580,7 +1580,7 @@

    Learning Goals#

    -
    +
    @@ -1599,7 +1599,7 @@

    Submit your feedback - +

    @@ -1616,7 +1616,7 @@

    Learning goals#

    -
    +
    @@ -1635,7 +1635,7 @@

    Submit your feedback - +

    @@ -1659,7 +1659,7 @@

    Using state-of-the-art (SOTA) Models - +

    Think 4.1! Tokenizers#

    @@ -1681,7 +1681,7 @@

    Submit your feedback - +

    Next, we’ll download a pre-built model architecture. CodeParrot (the model) is a GPT-2 model, which is a transformer-based language model. You can see some of the options here. But you can choose (or build!) another!

    Note that codeparrot/codeparrot (https://huggingface.co/codeparrot/codeparrot) is about 7GB to download (so it may take a while, or it may be too large for your runtime if you’re on a free Colab). Instead, we will use a smaller model, codeparrot/codeparrot-small (https://huggingface.co/codeparrot/codeparrot-small), which is only ~500MB.

    @@ -1701,7 +1701,7 @@

    Submit your feedback - +
    @@ -1760,16 +1760,16 @@

    Submit your feedback

    @@ -1785,15 +1785,32 @@

    Submit your feedback 
    class SimpleAdder {
-    public:
-        class SimpleAdder(Adder):
-            def __init__(self, *args, **kwargs):
-                super().__init__(*args, **kwargs)
-                self.name = 'SimpleAdder'
-                self.adder = self.adder_class()
-                self.adder.name = 'SimpleAdder'
-                self.adder.adder_class = self.adder_class()
-                self.adder.
+    private:
+        type: "SimpleAdder"
+    }
+}
+
+class SimpleAdder {
+    private:
+        type: "SimpleAdder"
+    }
+}
+
+class SimpleAdder {
+    private:
+        type: "SimpleAdder"
+    }
+}
+
+class SimpleAdder {
+    private:
+        type: "SimpleAdder"
+    }
+}
+
+class SimpleAdder {
+    private:
+        type: "
    @@ -1843,7 +1860,7 @@

    Submit your feedback - +

    @@ -1871,7 +1888,7 @@

    Fine-Tuning -
    {'code': <class 'str'>, 'repo_name': <class 'str'>, 'path': <class 'str'>, 'language': <class 'str'>, 'license': <class 'str'>, 'size': <class 'int'>}
+
    {'code': <class 'str'>, 'repo_name': <class 'str'>, 'path': <class 'str'>, 'language': <class 'str'>, 'license': <class 'str'>, 'size': <class 'int'>}
    @@ -1927,7 +1944,7 @@

    Coding Exercise 4.1: Implement the code to fine-tune the model -

    +
    @@ -1972,20 +1989,19 @@

    Coding Exercise 4.1: Implement the code to fine-tune the model 
    class SimpleAdder {
     public:
-        def __init__(self, *args, **kwargs):
-            super(SimpleAdder, self).__init__(*args, **kwargs)
-            self.name = 'SimpleAdder'
+        class SimpleAdder(object):
+            def __init__(self, name):
+                self.name = name
 
-    def get_name(self):
-        return self.name
+            def __call__(self, *args, **kwargs):
+                return self.name
 
-    def get_description(self):
-        return 'SimpleAdder'
+        class SimpleAdder2(SimpleAdder):
+            def __init__(self, name):
+                SimpleAdder.__init__(self, name)
 
-    def get_icon(self):
-        return'simple-adder'
-
-    def get_icon_url(self):
+        class SimpleAdder3(SimpleAdder):
+            def __init__(self, name):

    @@ -2017,7 +2033,7 @@

    Submit your feedback -

    + @@ -2042,7 +2058,7 @@

    Submit your feedback - + @@ -2056,7 +2072,7 @@

    Section 5: GPT Today and Tomorrow#

    -
    +
    @@ -2075,12 +2091,40 @@

    Submit your feedback - +

    Play around with LLMs#

    -

    Try the following questions with ChatGPT (GPT3.5 without access to the web) and with GPTBing in creative mode (GPT4 with access to the web). Note that the latter requires installing Microsoft Edge.

    +
      +

    1. Try using LLMs’ API to do tasks, such as utilizing the GPT-2 API to extend text from a provided context. To achieve this, ensure you have a HuggingFace account and secure an API token.

      2. +
    +
    +
    +
    import requests
+
+def query(payload, model_id, api_token):
+    headers = {"Authorization": f"Bearer {api_token}"}
+    API_URL = f"https://api-inference.huggingface.co/models/{model_id}"
+    response = requests.post(API_URL, headers=headers, json=payload)
+    return response.json()
+
+model_id = "gpt2"
+api_token = "hf_****" # get yours at hf.co/settings/tokens
+data = query("The goal of life is", model_id, api_token)
+print(data)
+
    +
    +
    +
    +
    {'error': 'Authorization header is correct, but the token seems invalid'}
+
    +
    +
    +
    +
      +

    1. Try the following questions with ChatGPT (GPT3.5 without access to the web) and with GPTBing in creative mode (GPT4 with access to the web). Note that the latter requires installing Microsoft Edge.

      2. +

    Pick someone you know who is likely to have a web presence but is not super famous (not Musk or Trump). Ask GPT for a two-paragraph biography. How good is it?

    Ask it something like “What is the US, UK, Germany, China, and Japan’s per capita income over the past ten years? Plot the data in a single figure” (depending on when and where you run this, you will need to paste the resulting Python code into a colab notebook). Try asking it questions about the data or the definition of “per capita income” used. How good is it?

    @@ -2099,7 +2143,7 @@

    Submit your feedback - +

    @@ -2123,7 +2167,7 @@

    Bonus Section: Using Large Language Models (LLMs)Video 6: Using GPT#

    -
    +
    @@ -2142,7 +2186,7 @@

    Submit your feedback - +

    diff --git a/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial3.html b/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial3.html index 4b34d738d..3b3369d95 100644 --- a/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial3.html +++ b/tutorials/W3D1_TimeSeriesAndNaturalLanguageProcessing/student/W3D1_Tutorial3.html @@ -50,7 +50,7 @@ - + @@ -828,7 +828,7 @@

    Tutorial objectives
    -
    +
    @@ -1137,8 +1137,8 @@

    Section 1 : Multilingual Embeddings#

    We first train separate embeddings for each language using fastText and a combination of data from Facebook and Wikipedia. Then, we find a dictionary of common words between the two languages. The dictionaries are automatically induced from parallel data - datasets consisting of a pair of sentences in two languages with the same meaning.

    Then, we find a matrix that projects the embeddings into a common space between the given languages. The matrix is designed to minimize the distance between a word \(x_i\) and its projection \(y_i\). If our dictionary consists of pairs \((x_i, y_i)\), our projector \(M\) would be:

    -
    -(121)#\[\begin{equation} +
    +(121)#\[\begin{equation} M = \underset{W}{\operatorname{argmax}} \sum_i ||x_i - Wy_i||^2 \end{equation}\]

    Also, the projector matrix \(W\) is constrained to e orthogonal, so actual distances between word embedding vectors are preserved. Multilingual models are trained by using our multilingual word embeddings as the base representations in DeepText and “freezing” them or leaving them unchanged during the training process.

    @@ -1380,7 +1380,7 @@

    Training multilingual embeddings 
    Cosine Similarity between HI and HELLO: 0.7028388977050781
-Cosine Similarity between BONJOUR and HELLO: 0.5818601846694946
+Cosine Similarity between BONJOUR and HELLO: 0.5818599462509155

    @@ -1398,8 +1398,8 @@

    Training multilingual embeddings -
    Cosine Similarity between cat and chatte: 0.43272870779037476
-Cosine Similarity between cat and chat: 0.6866634488105774
+
    Cosine Similarity between cat and chatte: 0.4327273964881897
+Cosine Similarity between cat and chat: 0.6866635084152222
 Cosine Similarity between chatte and chat: 0.6003133654594421
 
    
 
    
@@ -1422,7 +1422,7 @@ 
    Submit your feedback
 
 
    
-
    
+
    diff --git a/tutorials/W3D2_DlThinking2/student/W3D2_Tutorial1.html b/tutorials/W3D2_DlThinking2/student/W3D2_Tutorial1.html index b741bfe4a..690f660d7 100644 --- a/tutorials/W3D2_DlThinking2/student/W3D2_Tutorial1.html +++ b/tutorials/W3D2_DlThinking2/student/W3D2_Tutorial1.html @@ -50,7 +50,7 @@ - + @@ -987,7 +987,7 @@

    Tutorial Objectives
    -
    +
    @@ -1035,7 +1035,7 @@

    Section 1: Intro Deep Learning Thinking 2#

    -
    +
    @@ -1054,7 +1054,7 @@

    Submit your feedback
    -
    +

    Like Deep Learning thinking 1 last week, this tutorial is a bit different from others - there will be no coding! Instead, you will watch a series of vignettes about various scenarios where you want to use a neural network. This tutorial will focus on various architectures and multimodal thinking.

    Each section below will start with a vignette where either Lyle or Konrad is trying to figure out how to set up a neural network for a specific problem. Try to think of questions you want to ask them as you watch, then pay attention to what questions Lyle and Konrad are asking. Were they what you would have asked? How do their questions help quickly clarify the situation?

    @@ -1068,7 +1068,7 @@

    Section 2: Getting More Data#

    -
    +

    @@ -1087,7 +1087,7 @@

    Submit your feedback - +

    Konrad wants to build a neural network that classifies images based on the objects contained within them. He needs more data to help him train an accurate network, but buying more images is costly. He needs a different solution.

    @@ -1128,7 +1128,7 @@

    Submit your feedback - + @@ -1138,7 +1138,7 @@

    Wrap-up#

    -
    +
    @@ -1157,7 +1157,7 @@

    Submit your feedback - +

    Check out the paper mentioned in the above video:

      @@ -1184,7 +1184,7 @@

      Submit your feedback - +

    @@ -1197,7 +1197,7 @@

    Section 3: Detecting Tumors - What to do if there still isn’t enough data<

    Video 4: Detecting Tumors Vignette#

    -
    +
    @@ -1216,14 +1216,14 @@

    Submit your feedback - +

    Video 5: Detecting Tumors Set-up#

    -
    +
    @@ -1242,7 +1242,7 @@

    Submit your feedback - +

    Konrad works for a hospital and wants to train a neural network to detect tumors in brain scans automatically. This type of tumor is pretty rare, which is great for humanity but means we only have a few thousand training examples for our neural network. This isn’t enough.

    Even with adding in images of other types of tumors, we don’t have enough data. We have a lot of images of other things in ImageNet, like cats and dogs, though! Maybe we can use that?

    @@ -1288,7 +1288,7 @@

    Submit your feedback - +

    @@ -1298,7 +1298,7 @@

    Wrap-up#

    Video 6: Detecting Tumors Wrap-up#

    -
    +
    @@ -1317,7 +1317,7 @@

    Submit your feedback - +

    Check out the paper mentioned in the above video:

      @@ -1334,7 +1334,7 @@

      Section 4: Brains on Forrest Gump#

      -
      +

    @@ -1353,14 +1353,14 @@

    Submit your feedback - +

    Video 8: Brains on Forrest Gump Set-up#

    -
    +
    @@ -1379,7 +1379,7 @@

    Submit your feedback - +

    Konrad has a great dataset - he has someone watching all of the movie Forrest Gump and MRI data (brain imaging) over the whole time the person is watching the movie. So, basically, he has the video stream over time and the brain data over time. He wants to figure out what those two data streams have in common. In other words, he wants to pull the shared information from two data modalities.

    @@ -1409,8 +1409,8 @@

    Think! 3: Designing a strategy for pulling shared info about brain data and

    The key is to realize that if both embeddings contain the same information, they should be correlated.

    Looking at the formula for Pearson correlation:


    -
    -(122)#\[\begin{equation} +
    +(122)#\[\begin{equation} \rho = \frac{\text{cov}(X_1, X_2)}{\text{var}(X_1) \cdot \text{var}(X_2)} \end{equation}\]

    @@ -1434,7 +1434,7 @@

    Submit your feedback -

    + @@ -1444,7 +1444,7 @@

    Wrap-up

    Video 9: Brains on Forrest Gump Wrap-up#

    -
    +
    @@ -1463,7 +1463,7 @@

    Submit your feedback - +

    Check out the paper mentioned in the above video:

      @@ -1480,7 +1480,7 @@

      Summary#

      -
      +

    @@ -1499,7 +1499,7 @@

    Submit your feedback - +

    In this tutorial, we saw several tricks on how to do well when there is very limited data we saw:

      diff --git a/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/W3D3_BonusLecture.html b/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/W3D3_BonusLecture.html index d83daee9e..5bcfe73f8 100644 --- a/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/W3D3_BonusLecture.html +++ b/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/W3D3_BonusLecture.html @@ -58,7 +58,7 @@ const thebe_selector_output = ".output, .cell_output" - + @@ -1453,11 +1453,11 @@

      Install and import feedback gadget#

      -
      +
      -
      +

    @@ -1476,7 +1476,7 @@

    Submit your feedback
    -
    +

    diff --git a/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/W3D3_Tutorial1.html b/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/W3D3_Tutorial1.html index fd786c40d..98a164fdb 100644 --- a/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/W3D3_Tutorial1.html +++ b/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/W3D3_Tutorial1.html @@ -1454,7 +1454,7 @@

    Tutorial Objectives
    -
    +
    @@ -1924,7 +1924,7 @@

    Section 0: IntroductionVideo 0: Introduction#

    -
    +
    @@ -1943,7 +1943,7 @@

    Submit your feedback
    -
    +

    @@ -1955,7 +1955,7 @@

    Section 1: Representations are important#

    -
    +
    @@ -1974,7 +1974,7 @@

    Submit your feedback - +

    @@ -2124,7 +2124,7 @@

    Submit your feedback - +
    @@ -2153,7 +2153,7 @@

    Submit your feedback{"version_major": 2, "version_minor": 0, "model_id": "bc077cf53b344bd0be402207263efa1f"}
    Network performance after 25 classifier training epochs (chance: 33.33%):
+
    Network performance after 25 classifier training epochs (chance: 33.33%):
     Training accuracy: 51.81%
     Testing accuracy: 39.55%
 
    
@@ -2275,7 +2275,7 @@ 
    Submit your feedback
-
    
+

    When the classifier is trained with an encoder network, however, it achieves very high classification accuracy (~98.70%) on the test set, after only 10 training epochs.

    Shape classification results using different feature encoders:

    @@ -2307,7 +2307,7 @@

    Section 2: Supervised learning induces invariant representations#

    -
    +

    @@ -2326,7 +2326,7 @@

    Submit your feedback - +

    @@ -2443,7 +2443,7 @@

    Submit your feedback - +

    @@ -2488,7 +2488,7 @@

    Submit your feedback - + @@ -2535,7 +2535,7 @@

    Submit your feedback - + @@ -2549,7 +2549,7 @@

    Section 3: Random projections don’t work as wellVideo 3: Random Representations#

    -
    +
    @@ -2568,7 +2568,7 @@

    Submit your feedback - +

    @@ -2657,7 +2657,7 @@

    Submit your feedback - +

    @@ -2702,7 +2702,7 @@

    Submit your feedback - + @@ -2798,7 +2798,7 @@

    Submit your feedback - +

    The network loss training is fairly stable by 25 epochs, at which point the classifier performs at 44.67% accuracy on the test dataset.

    Shape classification results using different feature encoders:

    @@ -2844,7 +2844,7 @@

    Submit your feedback - + @@ -2858,7 +2858,7 @@

    Section 4: Generative approaches to representation learning can failVideo 4: Generative models#

    -
    +
    @@ -2877,7 +2877,7 @@

    Submit your feedback - +

    @@ -2946,7 +2946,7 @@

    Submit your feedback - +

    @@ -2972,7 +2972,7 @@

    Submit your feedback - + @@ -3018,7 +3018,7 @@

    Submit your feedback - + @@ -3066,7 +3066,7 @@

    Submit your feedback - + @@ -3172,7 +3172,7 @@

    Submit your feedback - +

    The network loss training is fairly stable by 25 epochs, at which point the classifier performs at 45.75% accuracy on the test dataset.

    Shape classification results using different feature encoders:

    @@ -3208,7 +3208,7 @@

    Section 5: The modern approach to self-supervised training for invarianceVideo 5: Modern Approach in Self-supervised Learning#

    -
    +
    @@ -3227,7 +3227,7 @@

    Submit your feedback - +

    @@ -3297,7 +3297,7 @@

    Submit your feedback - +

    @@ -3311,7 +3311,7 @@

    Section 6: How to train for invariance to transformations with a target netw

    Video 6: Data Transformations#

    -
    +
    @@ -3330,7 +3330,7 @@

    Submit your feedback - +

    @@ -3469,7 +3469,7 @@

    Submit your feedback - +

    We can now train the SimCLR encoder with the custom contrastive loss for a few epochs.

    @@ -3560,7 +3560,7 @@

    Interactive Demo 6.1.1: Evaluating the classification performance of a logis Training a classifier on the pre-trained SimCLR encoder representations...

    -
    Network performance after 10 classifier training epochs (chance: 33.33%):
+
    Network performance after 10 classifier training epochs (chance: 33.33%):
     Training accuracy: 97.83%
     Testing accuracy: 97.53%
 
    
@@ -3589,7 +3589,7 @@ 
    Submit your feedback
-
    
+

    The network (using the transforms proposed above) performs at 97.53% accuracy on the test dataset, after 15 classifier training epochs.

    Shape classification results using different feature encoders:

    @@ -3626,7 +3626,7 @@

    Section 7: Ethical considerations for self-supervised learning from biased d

    Video 7: Un/Self-Supervised Learning#

    -
    +

    @@ -3645,7 +3645,7 @@

    Submit your feedback - +

    @@ -3847,10 +3847,10 @@

    Section 7.1: The consequences of training models on biased datasets -
    Random encoder: training classifiers...
+
    Random encoder: training classifiers...
 
    
 
    
-
    ---------------------------------------------------------------------------
+
    ---------------------------------------------------------------------------
 KeyboardInterrupt                         Traceback (most recent call last)
 Cell In[72], line 6
       3 set_seed(SEED)
@@ -3920,12 +3920,12 @@ 
    Section 7.1: The consequences of training models on biased datasets    166         feats_flat = torch.flatten(feats_extr, 1)
     167         feats_proj = self.linear_projections(feats_flat)
 
-File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/torch/nn/modules/module.py:1511, in Module._wrapped_call_impl(self, *args, **kwargs)
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/nn/modules/module.py:1511, in Module._wrapped_call_impl(self, *args, **kwargs)
    1509     return self._compiled_call_impl(*args, **kwargs)  # type: ignore[misc]
    1510 else:
 -> 1511     return self._call_impl(*args, **kwargs)
 
-File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/torch/nn/modules/module.py:1520, in Module._call_impl(self, *args, **kwargs)
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/nn/modules/module.py:1520, in Module._call_impl(self, *args, **kwargs)
    1515 # If we don't have any hooks, we want to skip the rest of the logic in
    1516 # this function, and just call forward.
    1517 if not (self._backward_hooks or self._backward_pre_hooks or self._forward_hooks or self._forward_pre_hooks
@@ -3935,18 +3935,18 @@ 
    Section 7.1: The consequences of training models on biased datasets   1522 try:
    1523     result = None
 
-File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/torch/nn/modules/container.py:217, in Sequential.forward(self, input)
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/nn/modules/container.py:217, in Sequential.forward(self, input)
     215 def forward(self, input):
     216     for module in self:
 --> 217         input = module(input)
     218     return input
 
-File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/torch/nn/modules/module.py:1511, in Module._wrapped_call_impl(self, *args, **kwargs)
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/nn/modules/module.py:1511, in Module._wrapped_call_impl(self, *args, **kwargs)
    1509     return self._compiled_call_impl(*args, **kwargs)  # type: ignore[misc]
    1510 else:
 -> 1511     return self._call_impl(*args, **kwargs)
 
-File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/torch/nn/modules/module.py:1520, in Module._call_impl(self, *args, **kwargs)
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/nn/modules/module.py:1520, in Module._call_impl(self, *args, **kwargs)
    1515 # If we don't have any hooks, we want to skip the rest of the logic in
    1516 # this function, and just call forward.
    1517 if not (self._backward_hooks or self._backward_pre_hooks or self._forward_hooks or self._forward_pre_hooks
@@ -3956,17 +3956,33 @@ 
    Section 7.1: The consequences of training models on biased datasets   1522 try:
    1523     result = None
 
-File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/torch/nn/modules/conv.py:460, in Conv2d.forward(self, input)
-    459 def forward(self, input: Tensor) -> Tensor:
---> 460     return self._conv_forward(input, self.weight, self.bias)
-
-File /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/torch/nn/modules/conv.py:456, in Conv2d._conv_forward(self, input, weight, bias)
-    452 if self.padding_mode != 'zeros':
-    453     return F.conv2d(F.pad(input, self._reversed_padding_repeated_twice, mode=self.padding_mode),
-    454                     weight, bias, self.stride,
-    455                     _pair(0), self.dilation, self.groups)
---> 456 return F.conv2d(input, weight, bias, self.stride,
-    457                 self.padding, self.dilation, self.groups)
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/nn/modules/batchnorm.py:175, in _BatchNorm.forward(self, input)
+    168     bn_training = (self.running_mean is None) and (self.running_var is None)
+    170 r"""
+    171 Buffers are only updated if they are to be tracked and we are in training mode. Thus they only need to be
+    172 passed when the update should occur (i.e. in training mode when they are tracked), or when buffer stats are
+    173 used for normalization (i.e. in eval mode when buffers are not None).
+    174 """
+--> 175 return F.batch_norm(
+    176     input,
+    177     # If buffers are not to be tracked, ensure that they won't be updated
+    178     self.running_mean
+    179     if not self.training or self.track_running_stats
+    180     else None,
+    181     self.running_var if not self.training or self.track_running_stats else None,
+    182     self.weight,
+    183     self.bias,
+    184     bn_training,
+    185     exponential_average_factor,
+    186     self.eps,
+    187 )
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/nn/functional.py:2482, in batch_norm(input, running_mean, running_var, weight, bias, training, momentum, eps)
+   2479 if training:
+   2480     _verify_batch_size(input.size())
+-> 2482 return torch.batch_norm(
+   2483     input, weight, bias, running_mean, running_var, training, momentum, eps, torch.backends.cudnn.enabled
+   2484 )
 
 KeyboardInterrupt: 
 
    
diff --git a/tutorials/W3D4_BasicReinforcementLearning/student/W3D4_BonusLecture.html b/tutorials/W3D4_BasicReinforcementLearning/student/W3D4_BonusLecture.html
index 29c6f6735..8bb2775fb 100644
--- a/tutorials/W3D4_BasicReinforcementLearning/student/W3D4_BonusLecture.html
+++ b/tutorials/W3D4_BasicReinforcementLearning/student/W3D4_BonusLecture.html
@@ -58,7 +58,7 @@
 const thebe_selector_output = ".output, .cell_output"
 
     
-    
+    
     
     
     
@@ -1453,11 +1453,11 @@ 
    Install and import feedback gadget#
    
 
    
 
    
-
    
+
    
 
    
 
    
 
    
-
    
+

    @@ -1476,7 +1476,7 @@

    Submit your feedback
    -
    +

    diff --git a/tutorials/W3D4_BasicReinforcementLearning/student/W3D4_Tutorial1.html b/tutorials/W3D4_BasicReinforcementLearning/student/W3D4_Tutorial1.html index 2bd48b3bb..f816c515b 100644 --- a/tutorials/W3D4_BasicReinforcementLearning/student/W3D4_Tutorial1.html +++ b/tutorials/W3D4_BasicReinforcementLearning/student/W3D4_Tutorial1.html @@ -50,7 +50,7 @@ - + @@ -1040,7 +1040,7 @@

    Tutorial Objectives
    -
    +
    @@ -1099,7 +1099,7 @@

    Section 1: A history of RL#

    -
    +
    @@ -1118,7 +1118,7 @@

    Submit your feedback
    -
    +

    @@ -1137,7 +1137,7 @@

    Section 2.1: Grid WorldVideo 2: Grid World#

    -
    +
    @@ -1156,7 +1156,7 @@

    Submit your feedback - +

    @@ -1298,10 +1298,10 @@

    Create the GridWorldPlanner object (defaults to simple example) @@ -1445,7 +1445,7 @@

    Submit your feedback - +

    @@ -1495,7 +1495,7 @@

    Section 2.2: Markov Decision Process (MDP)#

    -
    +
    @@ -1514,7 +1514,7 @@

    Submit your feedback - +

    @@ -1644,7 +1644,7 @@

    Submit your feedback - +

    @@ -1656,7 +1656,7 @@

    Section 2.3: \(Q\)-values<

    Video 4: Q-values#

    -
    +
    @@ -1675,7 +1675,7 @@

    Submit your feedback - +

    @@ -1767,7 +1767,7 @@

    Submit your feedback - +

    @@ -1785,7 +1785,7 @@

    Section 3: Value iteration#

    -
    +
    @@ -1804,7 +1804,7 @@

    Submit your feedback - +

    Coding exercise 4: Implement value iteration#

    @@ -1933,7 +1933,7 @@

    Submit your feedback - +

    @@ -1948,7 +1948,7 @@

    Section 4: Policy iteration#

    -
    +
    @@ -1967,7 +1967,7 @@

    Submit your feedback - +

    Coding exercise 5: Implement policy iteration#

    @@ -2082,7 +2082,7 @@

    Submit your feedback - +

    @@ -2097,7 +2097,7 @@

    Section 5: \(Q\)-learning

    Video 7: Q-learning#

    -
    +
    @@ -2116,7 +2116,7 @@

    Submit your feedback - +

    Coding exercise 6: Implement Q-learning#

    @@ -2235,7 +2235,7 @@

    Submit your feedback - +

    @@ -2250,7 +2250,7 @@

    Section 6: \(\epsilon\)-gr

    Video 8: Epsilon-greedy exploration#

    -
    +
    @@ -2269,7 +2269,7 @@

    Submit your feedback - +

    Coding exercise 7: Implement epsilon-greedy exploration#

    @@ -2341,7 +2341,7 @@

    Submit your feedback - +

    diff --git a/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_BonusLecture.html b/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_BonusLecture.html index 9c402d9a6..6148dcfdc 100644 --- a/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_BonusLecture.html +++ b/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_BonusLecture.html @@ -58,7 +58,7 @@ const thebe_selector_output = ".output, .cell_output" - + @@ -1453,11 +1453,11 @@

    Install and import feedback gadget#

    -
    +
    -
    +
    @@ -1476,7 +1476,7 @@

    Submit your feedback
    -
    +

    diff --git a/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_Tutorial1.html b/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_Tutorial1.html index ed7e20767..05a1992ab 100644 --- a/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_Tutorial1.html +++ b/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_Tutorial1.html @@ -50,7 +50,7 @@ - + @@ -1200,7 +1200,7 @@

    Tutorial Objectives
    -
    +
    @@ -1579,7 +1579,7 @@

    Section 0: IntroductionVideo 0: Introduction#

    -
    +
    @@ -1598,7 +1598,7 @@

    Submit your feedback
    -
    +

    @@ -1610,7 +1610,7 @@

    Section 1: Create a game/agent loop for RL#

    -
    +
    @@ -1629,7 +1629,7 @@

    Submit your feedback - +

    @@ -1979,7 +1979,7 @@

    Submit your feedback - +

    @@ -2041,7 +2041,7 @@

    Section 2: Train a value function from expert game dataVideo 2: Train a value function#

    -
    +
    @@ -2060,7 +2060,7 @@

    Submit your feedback - +

    @@ -2087,8 +2087,8 @@

    Section 2.2: Define the Neural Network Architecture for Othello\(w_{l_{34}}=Q^{\pi}(s,a)\) in:

    -
    -(123)#\[\begin{equation} +
    +(123)#\[\begin{equation} V^{\pi}(s) = \sum_{a}{\pi(a,s) \cdot Q^{\pi}(s,a)} \end{equation}\]

    Note: OthelloNet has 2 outputs:

    @@ -2206,7 +2206,7 @@

    Submit your feedback -

    +

    @@ -2344,7 +2344,7 @@

    Submit your feedback - + @@ -2372,7 +2372,7 @@

    Section 2.5: Use a trained value network to play gamesVideo 3: Play games using a value function#

    -
    +
    @@ -2391,7 +2391,7 @@

    Submit your feedback - +

    @@ -2539,7 +2539,7 @@

    Submit your feedback - +

    @@ -2563,7 +2563,7 @@

    Section 3: Train a policy network from expert game dataVideo 4: Train a policy network#

    -
    +
    @@ -2582,7 +2582,7 @@

    Submit your feedback - +

    @@ -2592,8 +2592,8 @@

    Section 3.1: Define the Policy network

    Coding Exercise 3.1: Implement the PolicyNetwork#

    For computing our objective function, we will use the negative log-likelihood of targets \(t_i\) by using the cross-entropy function:

    -
    -(124)#\[\begin{equation} +
    +(124)#\[\begin{equation} L_{CE} = - \frac{1}{N} \sum_i^N t_i \cdot \log(output_i) \end{equation}\]

    Note: remember that the OthelloNet already returns the Log-softmax of the output from the 3rd linear layer…

    @@ -2734,7 +2734,7 @@

    Submit your feedback -

    +

    @@ -2764,7 +2764,7 @@

    Section 3.3: Use a trained policy network to play gamesVideo 6: Play games using a policy network#

    -
    +

    Note: in the video’s softmax function, \(T=1\) is the softmax kernel and \(z_i\) is the networks output before softmax transformation.

    @@ -2784,7 +2784,7 @@

    Submit your feedback - +
    @@ -2927,7 +2927,7 @@

    Submit your feedback - +

    @@ -3075,7 +3075,7 @@

    Section 5: Plan using Monte Carlo Rollouts#

    -
    +
    @@ -3094,7 +3094,7 @@

    Submit your feedback - +

    @@ -3142,9 +3142,7 @@

    Load in trained value and policy networks 
    Random seed 2023 has been set.
-
    -
    -
    Random seed 2023 has been set.
+Random seed 2023 has been set.
    @@ -3267,7 +3265,7 @@

    Submit your feedback - +

    @@ -3279,7 +3277,7 @@

    Section 5.2: Use Monte Carlo simulations to play gamesVideo 8: Play with planning#

    -
    +
    @@ -3298,7 +3296,7 @@

    Submit your feedback - +

    @@ -3501,7 +3499,7 @@

    Submit your feedback - +

    @@ -3565,7 +3563,7 @@

    Section 6: Ethical aspects#

    -
    +
    @@ -3584,7 +3582,7 @@

    Submit your feedback - +

    @@ -3602,7 +3600,7 @@

    Summary#

    -
    +
    @@ -3621,7 +3619,7 @@

    Submit your feedback - +

    diff --git a/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_Tutorial2.html b/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_Tutorial2.html index dbcfd17c6..adb48d86e 100644 --- a/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_Tutorial2.html +++ b/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_Tutorial2.html @@ -48,7 +48,7 @@ const thebe_selector_output = ".output, .cell_output" - + @@ -941,7 +941,7 @@

    Tutorial 2: Deep Learning Thinking 3#

    -
    +
    @@ -991,7 +991,7 @@

    Section 1: Intro to Deep Learning Thinking 3#

    -
    +
    @@ -1010,7 +1010,7 @@

    Submit your feedback
    -
    +

    @@ -1022,7 +1022,7 @@

    Section 2: The FutureVideo 2: The Future Vignette#

    -
    +
    @@ -1041,7 +1041,7 @@

    Submit your feedback - +

    @@ -1087,7 +1087,7 @@

    Submit your feedback - +

    @@ -1100,7 +1100,7 @@

    Section 3: In-context Learning#

    -
    +
    @@ -1119,7 +1119,7 @@

    Submit your feedback - +

    @@ -1163,7 +1163,7 @@

    Submit your feedback - +

    @@ -1176,7 +1176,7 @@

    Section 4: Memories#

    -
    +
    @@ -1195,7 +1195,7 @@

    Submit your feedback - +

    @@ -1239,7 +1239,7 @@

    Submit your feedback - +

    @@ -1252,7 +1252,7 @@

    Section 5: Multiple Information Sources#

    -
    +
    @@ -1271,7 +1271,7 @@

    Submit your feedback - +

    @@ -1313,7 +1313,7 @@

    Submit your feedback - +

    @@ -1326,7 +1326,7 @@

    Section 6: Language for Robotics#

    -
    +
    @@ -1345,7 +1345,7 @@

    Submit your feedback - +

    @@ -1384,7 +1384,7 @@

    Submit your feedback - +

    diff --git a/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_Tutorial3.html b/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_Tutorial3.html index 7024d96a5..f175eb85d 100644 --- a/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_Tutorial3.html +++ b/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/W3D5_Tutorial3.html @@ -50,7 +50,7 @@ - + @@ -887,7 +887,7 @@

    Tutorial Objectives
    -
    +

    These are the slides for the videos in the tutorial. If you want to locally download the slides, click here.

    @@ -2033,7 +2033,7 @@

    Section 1: Plan using Monte Carlo Tree Search (MCTS)Video 1: Plan with MCTS#

    -
    +
    @@ -2052,14 +2052,14 @@

    Submit your feedback
    -
    +

    Coding Exercise 1: MCTS planner#

    In building the MCTS planner, we will focus on the action selection part, particularly the objective function used. MCTS will use a combination of the current action-value function \(Q\) and the policy prior as follows:

    -
    -(125)#\[\begin{equation} +
    +(125)#\[\begin{equation} \underset{a}{\operatorname{argmax}} (Q(s_t, a)+u(s_t, a)) \end{equation}\]

    with \(u(s_t, a)=c_{puct} \cdot P(s,a) \cdot \frac{\sqrt{\sum_b N(s,b)}}{1+N(s,a)}\). This effectively implements an Upper Confidence bound applied to Trees (UCT). UCT balances exploration and exploitation by taking the values stored from the MCTS into account. The trade-off is parametrized by \(c_{puct}\).

    @@ -2216,7 +2216,7 @@

    Submit your feedback -

    +
    @@ -2236,7 +2236,7 @@

    Section 2: Use MCTS to play games#

    -
    +
    @@ -2255,7 +2255,7 @@

    Submit your feedback - +

    @@ -2545,7 +2545,7 @@

    Submit your feedback - +

    diff --git a/tutorials/intro.html b/tutorials/intro.html index 4947fd1d3..d20bd8366 100644 --- a/tutorials/intro.html +++ b/tutorials/intro.html @@ -58,7 +58,7 @@ const thebe_selector_output = ".output, .cell_output" - + @@ -1415,7 +1415,7 @@

    Introduction#

    -
    +