+
+
+
Introduction#
Welcome to the Neuromatch deep learning course!
@@ -1415,7 +1415,7 @@Introduction#
-
+
-
+![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\"/){kind=icon}
"
+ " ![\"Open](\"https://kaggle.com/static/images/open-in-kaggle.svg\"/)
"
]
},
{
@@ -16,8 +17,7 @@
"execution": {},
"pycharm": {
"name": "#%% md\n"
- },
- "id": "rV1aHp-Og4ZB"
+ }
},
"source": [
"# Introduction\n",
@@ -28,8 +28,7 @@
{
"cell_type": "markdown",
"metadata": {
- "execution": {},
- "id": "idpprpJEg4ZF"
+ "execution": {}
},
"source": [
"
Welcome to the Neuromatch Academy! We’re really excited to bring deep learning to such a wide and varied audience. We’re preparing an amazing set of lectures and tutorials for you!
+Welcome to the Neuromatch Academy! We’re really excited to bring deep learning to such a wide and varied audience. We’re preparing an amazing set of lectures and tutorials for you!
People are coming to this course from a wide range of disciplines and with varying levels of background, and we want to make sure everybody is able to follow and enjoy the school from day 1. This means you need to know the basics of programming in Python and some core math concepts. Below we provide more details.
diff --git a/projects/ComputerVision/data_augmentation.html b/projects/ComputerVision/data_augmentation.html index 1422c1683..f9b9a0427 100644 --- a/projects/ComputerVision/data_augmentation.html +++ b/projects/ComputerVision/data_augmentation.html @@ -1763,8 +1763,8 @@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:
-Project mentors are more senior figures in the field, typically senior postdocs, professors, or industry researchers. Each project group will have a mentor to help them refine their hypotheses and navigate the scientific process. They won’t be around as often as the TAs, but they are another source of guidance and perspective.
-Depending on your time slot, you may or may not have project time on the first day of the course. Regardless of whether your first project meeting is day 1 or day 2, spend your first session doing the following:
Split into groups alphabetically. First sort yourselves by the first letter of your name. The first half of the students are in group 1, the second in group 2. If the split is not well-balanced, move one or two people around.
Split into groups. We recommend intentionally creating groups with diverse skill sets. Groups should have students who are very confident in Python and those who are just learning. Through the project, students can work together to strengthen each other’s skills. We want to make sure that all members of each group get a chance to do all parts of the project. We ask that folks who are good with Python share what they know and hand off tasks to peers who are learning so they can improve their skills.
Introductions (30 min = 2 min/student): say a few things about yourself, then about your research area or research interests. What are you really curious about, that you might explore in your NMA project?
Listen carefully as others talk about their interests.
Individual reading time (30 min): browse the projects booklet which includes this guide (skim the entire thing) + 16 project templates with slides and code + docs with further ideas and datasets
If you are using a project template, your goal is to translate the information from the slide and colab notebook into the 10-steps format. Some information might not be readily available in the slide or notebook, and you might have to find it in your literature review later this day.
Try to write down a few sentences for each of the two steps applied to your project. Putting thoughts into well-defined sentences and paragraphs helps at all stages of a project.
Stay tuned for your mentor assignments. Once you receive them, reach out to your mentor to set up a first meeting this week. Also try to arrange a meeting for W2D1, ideally the second half of the day, when their feedback on your abstract could be useful.
Edit the abstract individually in your own google doc. At this stage, it is also important to control the flow of the abstract, in addition to keeping the structure from the 10 rules-paper. The flow relates to the “writing style”, which is generally no different for researchers than for other writers. Most importantly, make sure each sentence continues from where the previous one left, and do not use jargon without defining it first. Check out this book about writing if you have time (book, especially chapter 3 about “cohesion” and flow.
You should now have as many copies of your abstract as there are students in your group. Put them all into the same google doc, and try to see what you all did the same / differently. What sounds better? Pick and choose different sentences from different abstracts.
Try to schedule a meeting with your project TA and/or mentor during this day and show them your abstract. Try to get explicit feedback and edit the abstract together in a google doc.
+Try to schedule a meeting with your project TA during this day and show them your abstract. Try to get explicit feedback and edit the abstract together in a google doc.
Likewise, it is always revealing to present your research to someone who has never heard about it. Take turns in your pod to read the other group’s abstract and provide feedback. What did you understand and what didn’t make sense? Give detailed writing feedback if you can (use “suggestion mode” in google docs). If there is no other project group in your pod, ask your TA to reach out to other pods to find a group you can workshop your abstract with.
Finally, with your group, has the abstract refined or changed your question? Use the rest of this day to make a concrete plan for the final week of your project. If you already answered your question, then you will need to plan for control analyses, maybe including some simulated data that you need to also generate yourself.
Once you are done, please submit the abstract here.
@@ -1578,7 +1568,7 @@Please see final day schedule and shared calendars for timing details: https://deeplearning.neuromatch.io/tutorials/Schedule/daily_schedules.html#w3d5-final-day-of-course
-This is the day where you present your project to other groups. Your mentor and your project TAs can be invited too, but they are busy so they might not make it. The groups will take turns to share their screens. You can use figures and other graphics, but this is meant to be told as a story, and everyone from your group should take a turn telling a part of the story. Tell us about the different hypotheses you’ve had at different points and how you refined them using some of the tools we taught.
+This is the day where you present your project to other groups. Your project TAs can be invited too, but they are busy so they might not make it. The groups will take turns to share their screens. You can use figures and other graphics, but this is meant to be told as a story, and everyone from your group should take a turn telling a part of the story. Tell us about the different hypotheses you’ve had at different points and how you refined them using some of the tools we taught.
Epoch [100/500], Step [1/2], Loss: 1.0948, Accuracy: 59.88%
+Epoch [100/500], Step [1/2], Loss: 1.0587, Accuracy: 62.60%
------------------------------------------
-Epoch [100/500], Step [2/2], Loss: 1.0626, Accuracy: 65.31%
+Epoch [100/500], Step [2/2], Loss: 1.0646, Accuracy: 63.37%
------------------------------------------
-Epoch [200/500], Step [1/2], Loss: 0.8579, Accuracy: 69.77%
+Epoch [200/500], Step [1/2], Loss: 0.7002, Accuracy: 76.36%
------------------------------------------
-Epoch [200/500], Step [2/2], Loss: 0.7267, Accuracy: 74.61%
+Epoch [200/500], Step [2/2], Loss: 0.6983, Accuracy: 73.26%
------------------------------------------
-Epoch [300/500], Step [1/2], Loss: 0.6314, Accuracy: 77.33%
+Epoch [300/500], Step [1/2], Loss: 0.5926, Accuracy: 80.43%
------------------------------------------
-Epoch [300/500], Step [2/2], Loss: 0.6846, Accuracy: 74.03%
+Epoch [300/500], Step [2/2], Loss: 0.6010, Accuracy: 77.33%
------------------------------------------
-Epoch [400/500], Step [1/2], Loss: 0.6484, Accuracy: 74.81%
+Epoch [400/500], Step [1/2], Loss: 0.5081, Accuracy: 82.95%
------------------------------------------
-Epoch [400/500], Step [2/2], Loss: 0.6024, Accuracy: 76.94%
+Epoch [400/500], Step [2/2], Loss: 0.5129, Accuracy: 80.81%
------------------------------------------
-Epoch [500/500], Step [1/2], Loss: 0.5755, Accuracy: 78.29%
+Epoch [500/500], Step [1/2], Loss: 0.3980, Accuracy: 86.43%
------------------------------------------
-Epoch [500/500], Step [2/2], Loss: 0.5940, Accuracy: 78.29%
+Epoch [500/500], Step [2/2], Loss: 0.3824, Accuracy: 87.02%
------------------------------------------
@@ -2123,7 +2123,7 @@ Build model
-Test Accuracy of the model on the 172 test moves: 73.256%
+Test Accuracy of the model on the 172 test moves: 80.814%
@@ -2137,7 +2137,7 @@ Build model
-
+
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
-69.76744186046511
+71.51162790697676
-
+
That is some pretty good performance based on only 6 / 24 joints!
@@ -2274,7 +2274,7 @@ Step 9: Model evaluation*** FITTING: Left Leg
-limb performance: 67.44%
+limb performance: 75.00%
*** FITTING: Right Leg
@@ -2284,22 +2284,22 @@ Step 9: Model evaluationlimb performance: 62.79%
+limb performance: 51.74%
*** FITTING: Right Arm
-limb performance: 38.95%
+limb performance: 31.40%
*** FITTING: Torso
-limb performance: 76.74%
+limb performance: 77.91%
*** FITTING: Head
-limb performance: 45.93%
+limb performance: 50.58%
@@ -2353,44 +2353,44 @@ Step 9: Model evaluation*** FITTING: limbs only
-performance: 83.72%
+performance: 68.02%
-performance: 76.74%
+performance: 44.77%
-performance: 82.56%
+performance: 66.86%
-performance: 58.72%
+performance: 74.42%
-performance: 67.44%
+performance: 84.30%
-performance: 73.84%
-median performance: 75.29%
+performance: 72.67%
+median performance: 70.35%
*** FITTING: limbs+torso+head
-performance: 80.23%
+performance: 86.63%
-performance: 80.23%
+performance: 81.98%
-performance: 74.42%
+performance: 83.14%
-performance: 81.40%
+performance: 74.42%
-performance: 76.16%
+performance: 82.56%
-performance: 80.23%
-median performance: 80.23%
+performance: 80.81%
+median performance: 82.27%
diff --git a/projects/modelingsteps/ModelingSteps_10_DL.html b/projects/modelingsteps/ModelingSteps_10_DL.html
index de9942169..01fcbd541 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 dbddba434..1ed5cb8e0 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 1e995d610..d9c1b046f 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 1df028de9..912245582 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 33fdc2ae3..79bc1a809 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 46d464c90..728a8c573 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.
-
Blue is the no-motion condition, and produces flat average spike counts across the 3 s time interval. The orange and green line do show a bell-shaped curve that corresponds to the acceleration profile. But there also seems to be considerable noise: exactly what we need. Let’s see what the spike trains for a single trial look like:
@@ -1836,9 +1836,9 @@ Background
-
-
-
+
+
+
You can change the trial number in the bit of code above to compare what the rasterplots look like in different trials. You’ll notice that they all look kind of the same: the 3 conditions are very hard (impossible?) to distinguish by eye-balling.
@@ -1986,7 +1986,7 @@ Model implementation
-
+
We asked for 8 cross validations, which show up as the blue dots in the graph (two have the same accuracy). Prediction accuracy ranges from 56% to 72%, with the average at 65%, and the orange line is the median. Given the noisy data, that is not too bad actually.
@@ -2037,7 +2037,7 @@ Model implementation
-
+
This is the exact same figure as before, so our function classifyMotionFromSpikes() also works as intended.
@@ -2174,7 +2174,7 @@ Model evaluation & testing
-
+
Well, that’s interesting! The logistic regression doesn’t do a perfect job, but there is information in these results.
diff --git a/projects/modelingsteps/TrainIllusionModelingProjectDL.html b/projects/modelingsteps/TrainIllusionModelingProjectDL.html
index 154bf1824..0e2bf9a47 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 generatorText(0, 0.5, 'vestibular signal (a.u.)')
-
+
+
+
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 @@ Motion detected for no-motion: 32.2% and motion: 57.8%
+ Motion detected for no-motion: 30.8% and motion: 59.5%
+
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 26d2c46a0..a269f1742 100644 --- a/reports/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial1.err.log +++ b/reports/tutorials/W2D4_GenerativeModels/student/W2D4_Tutorial1.err.log @@ -4,7 +4,7 @@ Traceback (most recent call last): 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/3.9.19/x64/lib/python3.9/site-packages/jupyter_client/channels.py", line 230, in get_msg - res = self._recv() + return res _queue.Empty During handling of the above exception, another exception occurred: diff --git a/reports/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/W3D3_Tutorial1.err.log b/reports/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/W3D3_Tutorial1.err.log deleted file mode 100644 index a7510f36d..000000000 --- a/reports/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/W3D3_Tutorial1.err.log +++ /dev/null @@ -1,44 +0,0 @@ -Traceback (most recent call last): - 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/3.9.19/x64/lib/python3.9/site-packages/jupyter_core/utils/__init__.py", line 198, in ensure_async - result = await obj - File "/opt/hostedtoolcache/Python/3.9.19/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/3.9.19/x64/lib/python3.9/site-packages/jupyter_cache/executors/utils.py", line 58, in single_nb_execution - executenb( - File "/opt/hostedtoolcache/Python/3.9.19/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/3.9.19/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/3.9.19/x64/lib/python3.9/asyncio/base_events.py", line 647, in run_until_complete - return future.result() - 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/3.9.19/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/3.9.19/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/3.9.19/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. -Here is a preview of the cell contents: -------------------- -# Call this before any dataset/network initializing or training, -# to ensure reproducibility -set_seed(SEED) - -print("Training all models using the control, unbiased training dataset\n") -full_training_procedure( - train_sampler_bias_ctrl, test_sampler_for_bias_ctrl, - title="Classifier performances with control, unbiased training dataset", - dataset_type="bias_ctrl" # For loading correct pre-trained networks - ) -------------------- - diff --git a/searchindex.js b/searchindex.js index 2caddc663..11f2a1476 100644 --- a/searchindex.js +++ b/searchindex.js @@ -1 +1 @@ -Search.setIndex({"docnames": ["prereqs/DeepLearning", "projects/ComputerVision/README", "projects/ComputerVision/data_augmentation", "projects/ComputerVision/em_synapses", "projects/ComputerVision/ideas_and_datasets", "projects/ComputerVision/screws", "projects/ComputerVision/slides", "projects/ComputerVision/spectrogram_analysis", "projects/ComputerVision/transfer_learning", "projects/NaturalLanguageProcessing/README", "projects/NaturalLanguageProcessing/ideas_and_datasets", "projects/NaturalLanguageProcessing/machine_translation", "projects/NaturalLanguageProcessing/sentiment_analysis", "projects/NaturalLanguageProcessing/slides", "projects/Neuroscience/README", "projects/Neuroscience/algonauts_videos", "projects/Neuroscience/blurry_vision", "projects/Neuroscience/cellular_segmentation", "projects/Neuroscience/finetuning_fmri", "projects/Neuroscience/ideas_and_datasets", "projects/Neuroscience/neuro_seq_to_seq", "projects/Neuroscience/pose_estimation", 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"pair": 94, "shot": 94, "benefit": 94, "short": 94, "scenario": 94, "e": 94, "when": 94, "fraction": 94, "advantag": 94, "disadvantag": 94, "type": 94, "under": 94, "variou": 94, "chealsea": 96, "finn": 96, "chelsea": 96, "grid": 97, "shortest": 97, "path": 97, "planner": [97, 100, 102], "gridworld": 97, "gridworldplann": 97, "try": 97, "harder": 97, "markov": 97, "mdp": 97, "go": 97, "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}}) \ No newline at end of file diff --git a/tutorials/Bonus_DeployModels/student/Bonus_Tutorial1.html b/tutorials/Bonus_DeployModels/student/Bonus_Tutorial1.html index 96b292c06..551a99bbb 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" - + @@ -1077,7 +1077,7 @@ERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.
-notebook 6.5.6 requires jupyter-client<8,>=5.3.4, but you have jupyter-client 8.6.1 which is incompatible.
+notebook 6.5.7 requires jupyter-client<8,>=5.3.4, but you have jupyter-client 8.6.2 which is incompatible.
ERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.
-notebook 6.5.6 requires jupyter-client<8,>=5.3.4, but you have jupyter-client 8.6.1 which is incompatible.
+notebook 6.5.7 requires jupyter-client<8,>=5.3.4, but you have jupyter-client 8.6.2 which is incompatible.
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.
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.
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.
@@ -1451,7 +1451,7 @@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).
@@ -1551,7 +1551,7 @@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.
@@ -1671,7 +1671,7 @@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.
@@ -1780,7 +1780,7 @@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.
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.
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.
@@ -2040,7 +2040,7 @@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.
@@ -2070,7 +2070,7 @@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.
@@ -2133,7 +2133,7 @@You are now ready to create the files needed for your application. For now, you need just 2 files.
app.py
Before we can deploy on Heroku there are a couple of things we need to prepare.
Create Procfile
You are now finally ready to deploy to Heroku! There are just a couple of steps needed.
1. Create a Heroku account
@@ -2405,7 +2405,7 @@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 4e0e4748b..f6b54c097 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 @@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.
@@ -1510,14 +1510,14 @@Discuss with your pod: What do you hope to get out of this course? [in about 100 words]
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:
@@ -1645,7 +1645,7 @@Tensor a: tensor([[0.6074, 0.5259, 0.2556]])
-Tensor b: tensor([[ 0.0321, 0.4572, -0.7278, 1.7366],
- [-1.3376, 1.2469, 0.8855, -2.6794],
- [-0.4959, -0.5610, -0.4999, 0.3948]])
+Tensor a: tensor([[0.1210, 0.7033, 0.5249]])
+Tensor b: tensor([[-0.3902, -0.4056, 0.6887, 1.1748],
+ [-0.2030, 0.8191, 1.5884, 2.0658],
+ [-0.0748, 0.4944, -0.4757, -0.4005]])
Tensor c: tensor([[0., 0., 0.]])
-Tensor d: tensor([[0.0059, 0.4353, 0.6674]])
+Tensor d: tensor([[0.1466, 0.0092, 0.0549]])
Tensor-Tensor operations
We can perform operations on tensors using methods under torch..
Mean values of the rows of x tensor([0.2522, 0.6170, 0.5267])
+Mean values of the rows of x tensor([0.2522, 0.6170, 0.5267])
Below are two expressions involving operations on matrices.
-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.
@@ -2407,9 +2405,7 @@x: tensor([ 0.2659, -0.5148, -0.0613, 0.5046, 0.1385]) | x type: torch.FloatTensor
y: [ 0.26593232 -0.5148316 -0.06128114 0.5046449 0.13848118] | y type: <class 'numpy.ndarray'>
-z: tensor([ 0.2659, -0.5148, -0.0613, 0.5046, 0.1385]) | z type: torch.FloatTensor
+z: tensor([ 0.2659, -0.5148, -0.0613, 0.5046, 0.1385]) | z type: torch.FloatTensor
By default, when we create a tensor it will not live on the GPU!
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?
@@ -2911,7 +2907,7 @@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.
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.
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.
Batch size: torch.Size([64, 3, 32, 32])
+
Transformations
@@ -3240,7 +3236,7 @@
+
Prepare Data for PyTorch
@@ -3384,7 +3380,7 @@For this example we want to have a simple neural network consisting of 3 layers:
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.
Epoch 14000 loss is 0.2128836214542389
+
Plot the loss during training
@@ -3824,7 +3820,7 @@Text(0, 0.5, 'Loss')
+
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:
-Try to set the weights and biases to implement this function after you played enough :)
Play with the parameters to solve XOR
Do you think we can solve the discrete XOR (only 4 possibilities) with only 2 hidden units?
AUTHOR
-
+
-
+
@@ -1453,11 +1453,11 @@ Install and import feedback gadget#
-
+
-
+
@@ -1476,7 +1476,7 @@ Submit your feedback
-
+
diff --git a/tutorials/W1D2_LinearDeepLearning/student/W1D2_Tutorial1.html b/tutorials/W1D2_LinearDeepLearning/student/W1D2_Tutorial1.html
index 2838e7c93..d5e352331 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
-
+
@@ -1350,7 +1350,7 @@ Section 0: IntroductionVideo 0: Introduction#
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.
Given the following function:
-find the gradient vector:
-Hint: Use the chain rule!
Chain rule: For a composite function \(F(x) = g(h(x)) \equiv (g \circ h)(x)\):
-or differently denoted:
-We can rewrite the function as a composite function:
-Using the chain rule:
-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 \(\mathbf{w}\).
-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.
@@ -1594,8 +1594,8 @@Hence, all we need is to calculate the gradient of the loss function with respect to the learnable parameters (i.e., weights):
- +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:
-We can build a so-called computational graph (shown below) to break the original function into smaller and more approachable expressions.
@@ -1662,8 +1662,8 @@
By breaking the computation into simple operations on intermediate variables, we can use the chain rule to calculate any gradient:
-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.
@@ -1673,8 +1673,8 @@For more: Calculus on Computational Graphs: Backpropagation
@@ -1694,7 +1694,7 @@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.
Gradient function = <AddBackward0 object at 0x7f8a41a4b9d0>
+Gradient function = <AddBackward0 object at 0x7fb42e99f280>
nn module#
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:
@@ -1988,7 +1988,7 @@Random seed 2021 has been set.
+
Let’s define a very wide (512 neurons) neural net with one hidden layer and nn.Tanh() activation function.
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:
As you may have already asked yourself, we can analytically find \(w_1\) and \(w_2\) without using gradient descent:
-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:
@@ -2283,7 +2283,7 @@
+
Here, we also visualize the loss landscape in a 3-D plot, with two training trajectories for different initial conditions. @@ -2295,7 +2295,7 @@
+
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:
@@ -2389,13 +2389,13 @@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.
@@ -2662,7 +2662,7 @@
+
Complete the function ex_initializer_, such that the weights are sampled from the following distribution:
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.
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.
@@ -2212,7 +2212,7 @@
+
---------------------------------------------------------------
Input Dimension: 8
Output Dimension: 10000
@@ -2266,7 +2266,7 @@ Make sure you execute this cell to train the network and plot
-
+
Think!
@@ -2333,7 +2333,7 @@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:
-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.
@@ -2466,7 +2466,7 @@
+---------------------------------------------------------------------------
+AttributeError Traceback (most recent call last)
+Cell In[24], line 23
+ 16 # Training
+ 17 losses, modes, *_ = train(dlnn_model,
+ 18 label_tensor,
+ 19 feature_tensor,
+ 20 n_epochs=n_epochs,
+ 21 lr=lr)
+---> 23 plot_loss_sv_twin(losses, modes)
+
+Cell In[5], line 208, in plot_loss_sv_twin(loss_array, sv_array)
+ 206 n_sing_values = sv_array.shape[1]
+ 207 sv_array = sv_array / np.max(sv_array)
+--> 208 cmap = plt.cm.get_cmap("winter", n_sing_values)
+ 210 fig = plt.figure(figsize=(10, 5))
+ 211 ax1 = plt.gca()
+
+AttributeError: module 'matplotlib.cm' has no attribute 'get_cmap'
+Think!
@@ -2528,14 +2548,14 @@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:
-where \(\mathbf{H} = \mathbf{X} \mathbf{W_1}\) is the activity of hidden neurons for a given batch \(\mathbf{X}\).
@@ -2706,7 +2726,7 @@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.
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.
@@ -2819,7 +2839,7 @@
+
You can see the new feature shown in the last column of the plot above.
@@ -2874,7 +2894,23 @@
+---------------------------------------------------------------------------
+AttributeError Traceback (most recent call last)
+Cell In[38], line 32
+ 29 ill_label = f"Prediction for {item_names[illusion_idx]} {its_label}"
+ 31 # Plotting
+---> 32 plot_ills_sv_twin(ill_predictions, modes, ill_label)
+
+Cell In[5], line 246, in plot_ills_sv_twin(ill_array, sv_array, ill_label)
+ 244 n_sing_values = sv_array.shape[1]
+ 245 sv_array = sv_array / np.max(sv_array)
+--> 246 cmap = plt.cm.get_cmap("winter", n_sing_values)
+ 248 fig = plt.figure(figsize=(10, 5))
+ 249 ax1 = plt.gca()
+
+AttributeError: module 'matplotlib.cm' has no attribute 'get_cmap'
+It seems that the network starts by learning an “illusory correlation” that sharks have bones, and in later epochs, as it learns deeper representations, it can see (learn) beyond the illusory correlation. This is important to remember that we never presented the network with any data saying that sharks have bones.
@@ -2910,7 +2946,7 @@
+
+---------------------------------------------------------------------------
+AttributeError Traceback (most recent call last)
+Cell In[40], line 32
+ 29 ill_label = f"Prediction for {item_names[illusion_idx]} {its_label}"
+ 31 # Plotting
+---> 32 plot_ills_sv_twin(ill_predictions, modes, ill_label)
+
+Cell In[5], line 246, in plot_ills_sv_twin(ill_array, sv_array, ill_label)
+ 244 n_sing_values = sv_array.shape[1]
+ 245 sv_array = sv_array / np.max(sv_array)
+--> 246 cmap = plt.cm.get_cmap("winter", n_sing_values)
+ 248 fig = plt.figure(figsize=(10, 5))
+ 249 ax1 = plt.gca()
+
+AttributeError: module 'matplotlib.cm' has no attribute 'get_cmap'
+The multivariate regression model can be written as:
-or it can be written in matrix format as:
-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:
-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.
@@ -3106,30 +3158,30 @@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:
-Given the Squared Error loss function, we have:
-So, using matrix notation, the optimization problem is given by:
-To solve the minimization problem, we can simply set the derivative of the loss with respect to \(\mathbf{W}\) to zero.
-
+
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:
- +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.
Leaky ReLU is described by the following mathematical formula:
-The main loss function we could use out of the box for multi-class classification for N samples and C number of classes is:
(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,
-A batch of labels with shape (N, ) that ranges from 0 to C-1
Returns the average loss \(L\) calculated according to:
- +Before we could start optimizing these loss functions, we need a dataset!
Let’s turn this fancy-looking equation into a classification dataset
-Random seed 2021 has been set.
+
And we need to make a Pytorch data loader out of it. Data loading in PyTorch can be separated in 2 parts:
Now let’s put everything together and train your first deep-ish 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,
-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):
-where \(t_{\rm sp}\) is the spike time when \(V_{m}(t)\) just exceeded \(V_{\rm th}\).
@@ -2331,8 +2331,8 @@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,
-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:
-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.
Random seed 2021 has been set.
Accuracy on the 3200 training samples: 69.88
+Accuracy on the 3200 training samples: 69.88
Accuracy on the 800 testing samples: 72.62
-
+
Number of features: 1325
@@ -1939,7 +1939,7 @@ Submit your feedback
-
+
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,
-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:
-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:
-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 \(\sigma^2=\frac{2}{(n_{in}+n_{out})}\),
-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
-This explanation is mainly taken from here.
@@ -2288,8 +2288,8 @@Let’s derive the optimal gain for LeakyReLU following similar steps.
LeakyReLU is described mathematically:
-Considering a single layer with this activation function gives,
-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:
-Therefore, following the rest of derivation as before,
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 \(\sigma^2\).
diff --git a/tutorials/W1D5_Optimization/student/W1D5_Tutorial1.html b/tutorials/W1D5_Optimization/student/W1D5_Tutorial1.html index 1efef2f6f..696d91274 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 @@
+
+
@@ -1912,7 +1912,7 @@ 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.
In this exercise you will implement the momentum update given by:
-It is convenient to re-express this update rule in terms of a recursion. For that, we define ‘velocity’ as the quantity:
-which leads to the two-step update rule:
-Random seed 2021 has been set.
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.
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.
@@ -3205,7 +3205,7 @@In this exercise you will implement the update of the RMSprop optimizer:
- +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.
@@ -3520,7 +3520,7 @@Random seed 2021 has been set.
[VALID] Epoch 1 - Batch 200 - Loss: 2.235 - Acc: 38.193%
+[VALID] Epoch 1 - Batch 200 - Loss: 2.235 - Acc: 38.193%
[TRAIN] Epoch 1 - Batch 200 - Loss: 2.274 - Acc: 30.930%
@@ -3876,7 +3876,7 @@ Exercise Bonus: Train your own model
-
+
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.
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”.
@@ -1670,8 +1670,8 @@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.
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!!
@@ -1797,7 +1797,7 @@
Using the last function, calculate_frobenius_norm, we can also obtain the Frobenius norm per layer for a whole ANN model and use the plot_weigts function to visualize them.
Random seed 2021 has been set.
+
Let’s create an overparametrized Neural Network that can fit on the dataset that we just created and train it.
@@ -2013,7 +2013,7 @@Random seed 2021 has been set.
Now that we have finished training, let’s see how the model has evolved over the training process.
+
+
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
@@ -2197,7 +2197,7 @@
+
Finally, you can compare the Frobenius norm per layer in the model, before and after training.
@@ -2221,8 +2221,8 @@
-
+
+
@@ -2466,10 +2466,10 @@ Random seed 2021 has been set.
Time to memorize the dataset: 225.04949498176575
+Time to memorize the dataset: 53.55902695655823
-
+
-
+
+
The image belongs to : cat
+
Now let’s train the network on the shuffled data and see if it memorizes.
@@ -2594,7 +2594,7 @@Random seed 2021 has been set.
+
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.
@@ -2608,7 +2608,7 @@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.
@@ -2756,7 +2756,7 @@Random seed 2021 has been set.
+
+
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 e88401437..2a974cc33 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 @@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.
Random seed 2021 has been set.
+
Maximum Validation Accuracy reached: 51.0
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):
-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:
-where \(\text{sgn}(\cdot)\) is the sign function, such that
-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.
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:
-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
-Thus the weight update rule becomes:
-where \(\eta\) is the learning rate.
@@ -2343,7 +2343,7 @@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.
Now, let’s run a model with both L1 and L2 regularization terms.
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.
Random seed 2021 has been set.
Random seed 2021 has been set.
Now that we have finished the training, let’s see how the model has evolved over the training process.
Animation! (Run Me!)
@@ -2793,7 +2793,7 @@
+
Plot the train and test losses with epoch
@@ -2819,7 +2819,7 @@
+
Plot the train and test losses with epoch
@@ -2845,7 +2845,7 @@
+
Plot model weights with epoch
@@ -2870,7 +2870,7 @@
+
Random seed 2021 has been set.
Random seed 2021 has been set.
+Random seed 2021 has been set.
-
+
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:
@@ -3206,10 +3206,10 @@Random seed 2021 has been set.
Random seed 2021 has been set.
+Random seed 2021 has been set.
-
+
+
Random seed 2021 has been set.
Random seed 2021 has been set.
+Random seed 2021 has been set.
-Random seed 2021 has been set.
+Random seed 2021 has been set.
-
+
Plot Train and Validation accuracy (Run me)
+
Plot parametric norms (Run me)
@@ -3472,7 +3472,7 @@
+
In the model above, we observe something different from what we expected. Why do you think this is happening?
@@ -3487,7 +3487,7 @@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.
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.
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.
@@ -1949,7 +1949,7 @@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.
@@ -2071,8 +2071,8 @@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:
-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).
-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!
As you can see, this kernel detects vertical edges (the black stripe corresponds to a highly positive result, while the white stripe corresponds to a highly negative result. However, to display the image, all the pixels are normalized between 0=black and 1=white).
@@ -2668,7 +2668,7 @@
+
@@ -2893,7 +2893,7 @@ <matplotlib.image.AxesImage at 0x7f640d90d8e0>
+<matplotlib.image.AxesImage at 0x7f7c306de550>
-
+
We apply the filters to the images.
+
+
Discuss with your pod how the ReLU activations help strengthen the features necessary to detect an \(X\).
@@ -3259,7 +3259,7 @@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.
@@ -3337,7 +3337,7 @@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.
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.
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:
Take a minute with your pod and talk about which classes you think would be most confusable. How hard will it be to differentiate t-shirt/tops from shirts?
@@ -4375,7 +4375,7 @@Test accuracy: 93.07%
+Test accuracy: 93.07%
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?
@@ -1057,7 +1057,7 @@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:
-So this poisson distribution may be relevant if we want to, in a way, have a good model for the spiking of neurons.
@@ -1135,28 +1135,28 @@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:
-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:
-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:
-And last but not least, we want to make it negative so we can minimize instead of maximize:
- +Check out the papers mentioned in the above video:
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:
-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.
-And, as before, we want to take the log of this for numerical reasons and convert to negative log likelihood:
-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!
@@ -1347,14 +1347,14 @@Check out the papers mentioned in the above video:
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:
-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:
-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:
-We could compare \(n\) to both \(a\) and \(p\):
-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:
-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?
- +Check out the papers mentioned in the above video:
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:
-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:
- +
+
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.
@@ -3402,7 +3402,7 @@
+
Now we want to look at the number of parameters.
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.
@@ -4147,15 +4147,15 @@['Charmander',
- 'Charmeleon',
+['Blastoise',
+ 'Charmander',
+ 'Squirtle',
'Ivysaur',
+ 'Wartortle',
'Charizard',
+ 'Charmeleon',
'Bulbasaur',
- 'Blastoise',
- 'Squirtle',
- 'Venusaur',
- 'Wartortle']
+ 'Venusaur']
+
+
@@ -4390,7 +4390,7 @@ 
+
@@ -4468,7 +4468,7 @@ 
+
@@ -4497,7 +4497,7 @@ 
+
@@ -4521,7 +4521,7 @@ 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.
@@ -4863,7 +4863,7 @@ These are the slides for the videos in this tutorial. If you want to download locally the slides, click here.
@@ -1221,7 +1221,7 @@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.
@@ -1287,7 +1287,7 @@
+
+
@@ -1375,7 +1375,7 @@ 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.
+
Great! The images corresponding to each individual are separated from each other in the embedding space!
@@ -1477,7 +1477,7 @@
+
+
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.
@@ -1746,8 +1746,8 @@ 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 715a929b1..a53da08d6 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 @@Download BigGAN (a generative model) and a few standard image datasets
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.
@@ -2245,7 +2245,7 @@
+
Let’s model these data with a single principal component. Given that the thermometers are measuring the same actual temperature, the principal component axes will be the identity line. The direction of this axes can be indicated by the unit vector \([1 ~~ 1]~/~\sqrt2\). We could estimate this axes by applying PCA. We can plot this axes, it tells us something about the data, but we can’t generate from it:
@@ -2271,7 +2271,7 @@
+
Step 1: Calculate the parameters of the pPCA model
@@ -2304,8 +2304,8 @@Download MNIST and CIFAR10 datasets
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:
-The loss function we’ll use will simply be mean squared error (MSE) quantifying how well the reconstruction (\(\mathbf{x'}\)) matches the original image (\(\mathbf{x}\)):
-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 @@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 @@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.)
---------------------------------------------------------------------------
+
@@ -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 ff9142154..866d506b2 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
-
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.
-\(d\mathbf w\) 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:
-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 \(\mathbf x_0\):
-The key quantity to note is the \(\sigma_t\) which is the integrated noise scale at time \(t\). \(I\) denotes the identity matrix.
-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.
-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.
-
+
+
@@ -1811,7 +1811,7 @@ 
+
@@ -1845,7 +1845,7 @@ 
+
@@ -1872,7 +1872,7 @@ 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
-Then the following process (reverse SDE) will be its time reversal:
-where time \(t\) runs backward.
@@ -1901,8 +1901,8 @@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:
-where \(\mathbf{z}_t \sim \mathcal{N}(\mathbf{0}, I)\) and \(g(t)=\lambda^t\).
@@ -2036,7 +2036,7 @@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.
-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!
-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:
-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 (\(t\sim 0\)):
-To put it in plain language, this objective is simply doing the following steps:
@@ -2114,7 +2114,7 @@There exists a reverse time stochastic process (reverse SDE)
-and a probability flow Ordinary Differential Equation (ODE)
-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 @@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.
-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
-The objective simplifies into
-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.
-(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:
-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.
-In the next cell, you will implement the denoising score matching (DSM) objective as we used in the last tutorial.
-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 @@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 @@Now you can let loose your imagination and create artworks from text!
Example prompts:
@@ -1985,7 +1985,7 @@ERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.
+facenet-pytorch 2.6.0 requires torch<2.3.0,>=2.2.0, but you have torch 2.3.1 which is incompatible.
+torchvision 0.17.2 requires torch==2.2.2, but you have torch 2.3.1 which is incompatible.
+
+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 +1908,7 @@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.
In this exercise, let’s compute the scaled dot product attention using its matrix form.
-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 +2253,7 @@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.
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.
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.
- +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 +3073,7 @@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 @@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!
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
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.
[(0.8162637948989868, 'queen')]
[(0.8568049669265747, 'paris')]
-[(0.7037209272384644, 'flower')]
+[(0.7037209272384644, 'flower')]
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.
@@ -2243,7 +2245,7 @@---------------------------------------------------------------------------
+ContextualVersionConflict Traceback (most recent call last)
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/lightning_utilities/core/imports.py:132, in RequirementCache._check_requirement(self)
+ 130 try:
+ 131 # first try the pkg_resources requirement
+--> 132 pkg_resources.require(self.requirement)
+ 133 self.available = True
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/pkg_resources/__init__.py:886, in WorkingSet.require(self, *requirements)
+ 878 """Ensure that distributions matching `requirements` are activated
+ 879
+ 880 `requirements` must be a string or a (possibly-nested) sequence
+ (...)
+ 884 included, even if they were already activated in this working set.
+ 885 """
+--> 886 needed = self.resolve(parse_requirements(requirements))
+ 888 for dist in needed:
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/pkg_resources/__init__.py:777, in WorkingSet.resolve(self, requirements, env, installer, replace_conflicting, extras)
+ 776 dependent_req = required_by[req]
+--> 777 raise VersionConflict(dist, req).with_context(dependent_req)
+ 779 # push the new requirements onto the stack
+
+ContextualVersionConflict: (torch 2.3.1 (/opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages), Requirement.parse('torch==2.2.2'), {'torchvision'})
+
+During handling of the above exception, another exception occurred:
+
+RuntimeError Traceback (most recent call last)
+Cell In[4], line 7
+ 5 from tqdm.notebook import tqdm
+ 6 from typing import Dict
+----> 7 import pytorch_lightning as pl
+ 9 import torch
+ 10 import torch.nn as nn
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/pytorch_lightning/__init__.py:27
+ 25 from lightning_fabric.utilities.seed import seed_everything # noqa: E402
+ 26 from lightning_fabric.utilities.warnings import disable_possible_user_warnings # noqa: E402
+---> 27 from pytorch_lightning.callbacks import Callback # noqa: E402
+ 28 from pytorch_lightning.core import LightningDataModule, LightningModule # noqa: E402
+ 29 from pytorch_lightning.trainer import Trainer # noqa: E402
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/pytorch_lightning/callbacks/__init__.py:14
+ 1 # Copyright The Lightning AI team.
+ 2 #
+ 3 # Licensed under the Apache License, Version 2.0 (the "License");
+ (...)
+ 12 # See the License for the specific language governing permissions and
+ 13 # limitations under the License.
+---> 14 from pytorch_lightning.callbacks.batch_size_finder import BatchSizeFinder
+ 15 from pytorch_lightning.callbacks.callback import Callback
+ 16 from pytorch_lightning.callbacks.checkpoint import Checkpoint
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/pytorch_lightning/callbacks/batch_size_finder.py:26
+ 23 from typing_extensions import override
+ 25 import pytorch_lightning as pl
+---> 26 from pytorch_lightning.callbacks.callback import Callback
+ 27 from pytorch_lightning.tuner.batch_size_scaling import _scale_batch_size
+ 28 from pytorch_lightning.utilities.exceptions import MisconfigurationException, _TunerExitException
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/pytorch_lightning/callbacks/callback.py:22
+ 19 from torch.optim import Optimizer
+ 21 import pytorch_lightning as pl
+---> 22 from pytorch_lightning.utilities.types import STEP_OUTPUT
+ 25 class Callback:
+ 26 r"""Abstract base class used to build new callbacks.
+ 27
+ 28 Subclass this class and override any of the relevant hooks
+ 29
+ 30 """
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/pytorch_lightning/utilities/types.py:41
+ 39 from torch import Tensor
+ 40 from torch.optim import Optimizer
+---> 41 from torchmetrics import Metric
+ 42 from typing_extensions import NotRequired, Required
+ 44 from lightning_fabric.utilities.types import _TORCH_LRSCHEDULER, LRScheduler, ProcessGroup, ReduceLROnPlateau
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torchmetrics/__init__.py:26
+ 23 if not hasattr(PIL, "PILLOW_VERSION"):
+ 24 PIL.PILLOW_VERSION = PIL.__version__
+---> 26 from torchmetrics import functional # noqa: E402
+ 27 from torchmetrics.aggregation import ( # noqa: E402
+ 28 CatMetric,
+ 29 MaxMetric,
+ (...)
+ 34 SumMetric,
+ 35 )
+ 36 from torchmetrics.audio._deprecated import _PermutationInvariantTraining as PermutationInvariantTraining # noqa: E402
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torchmetrics/functional/__init__.py:50
+ 23 from torchmetrics.functional.audio._deprecated import _signal_noise_ratio as signal_noise_ratio
+ 24 from torchmetrics.functional.classification import (
+ 25 accuracy,
+ 26 auroc,
+ (...)
+ 48 stat_scores,
+ 49 )
+---> 50 from torchmetrics.functional.detection._deprecated import _panoptic_quality as panoptic_quality
+ 51 from torchmetrics.functional.image._deprecated import (
+ 52 _error_relative_global_dimensionless_synthesis as error_relative_global_dimensionless_synthesis,
+ 53 )
+ 54 from torchmetrics.functional.image._deprecated import _image_gradients as image_gradients
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torchmetrics/functional/detection/__init__.py:24
+ 16 from torchmetrics.utilities.imports import (
+ 17 _TORCHVISION_AVAILABLE,
+ 18 _TORCHVISION_GREATER_EQUAL_0_8,
+ 19 _TORCHVISION_GREATER_EQUAL_0_13,
+ 20 )
+ 22 __all__ = ["modified_panoptic_quality", "panoptic_quality"]
+---> 24 if _TORCHVISION_AVAILABLE and _TORCHVISION_GREATER_EQUAL_0_8:
+ 25 from torchmetrics.functional.detection.giou import generalized_intersection_over_union
+ 26 from torchmetrics.functional.detection.iou import intersection_over_union
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/lightning_utilities/core/imports.py:164, in RequirementCache.__bool__(self)
+ 162 def __bool__(self) -> bool:
+ 163 """Format as bool."""
+--> 164 self._check_available()
+ 165 return self.available
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/lightning_utilities/core/imports.py:158, in RequirementCache._check_available(self)
+ 156 return
+ 157 if self.requirement:
+--> 158 self._check_requirement()
+ 159 if getattr(self, "available", True) and self.module:
+ 160 self._check_module()
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/lightning_utilities/core/imports.py:142, in RequirementCache._check_requirement(self)
+ 140 module = self.requirement if self.module is None else self.module
+ 141 # sometimes `pkg_resources.require()` fails but the module is importable
+--> 142 self.available = module_available(module)
+ 143 if self.available:
+ 144 self.message = f"Module {module!r} available"
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/lightning_utilities/core/imports.py:61, in module_available(module_path)
+ 59 return False
+ 60 try:
+---> 61 importlib.import_module(module_path)
+ 62 except ImportError:
+ 63 return False
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/importlib/__init__.py:127, in import_module(name, package)
+ 125 break
+ 126 level += 1
+--> 127 return _bootstrap._gcd_import(name[level:], package, level)
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torchvision/__init__.py:6
+ 3 from modulefinder import Module
+ 5 import torch
+----> 6 from torchvision import _meta_registrations, datasets, io, models, ops, transforms, utils
+ 8 from .extension import _HAS_OPS
+ 10 try:
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torchvision/_meta_registrations.py:164
+ 153 torch._check(
+ 154 grad.dtype == rois.dtype,
+ 155 lambda: (
+ (...)
+ 158 ),
+ 159 )
+ 160 return grad.new_empty((batch_size, channels, height, width))
+ 163 @torch._custom_ops.impl_abstract("torchvision::nms")
+--> 164 def meta_nms(dets, scores, iou_threshold):
+ 165 torch._check(dets.dim() == 2, lambda: f"boxes should be a 2d tensor, got {dets.dim()}D")
+ 166 torch._check(dets.size(1) == 4, lambda: f"boxes should have 4 elements in dimension 1, got {dets.size(1)}")
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/library.py:467, in impl_abstract.<locals>.inner(func)
+ 464 else:
+ 465 func_to_register = func
+--> 467 handle = entry.abstract_impl.register(func_to_register, source)
+ 468 if lib is not None:
+ 469 lib._registration_handles.append(handle)
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/_library/abstract_impl.py:30, in AbstractImplHolder.register(self, func, source)
+ 24 if self.kernel is not None:
+ 25 raise RuntimeError(
+ 26 f"impl_abstract(...): the operator {self.qualname} "
+ 27 f"already has an abstract impl registered at "
+ 28 f"{self.kernel.source}."
+ 29 )
+---> 30 if torch._C._dispatch_has_kernel_for_dispatch_key(self.qualname, "Meta"):
+ 31 raise RuntimeError(
+ 32 f"impl_abstract(...): the operator {self.qualname} "
+ 33 f"already has an DispatchKey::Meta implementation via a "
+ (...)
+ 36 f"impl_abstract."
+ 37 )
+ 39 if torch._C._dispatch_has_kernel_for_dispatch_key(
+ 40 self.qualname, "CompositeImplicitAutograd"
+ 41 ):
+
+RuntimeError: operator torchvision::nms does not exist
+
-
-WARNING: For this notebook to perform best, if possible, in the menu under `Runtime` -> `Change runtime type.` select `GPU`
-Random seed 2021 has been set.
-
-
-
+
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.
@@ -1255,7 +1447,7 @@
-
-
-(The ## means that the token is a continuation of the previous chunk.)
Try playing around with the hyperparameters and the tokenizing algorithms to see how they affect the tokenizer’s output. There can be some very major differences!
@@ -1523,7 +1703,7 @@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.
class SimpleAdder {
public:
- def __init__(self, name, parent):
- self.name = name
- self.parent = parent
- self.children = []
-
- def addChild(self, child):
- self.children.append(child)
- return child
-
- def getChildren(self):
- return self.children
-
- def getName(self):
- return self.name
-
- def getParent(self):
- return self.parent
-
- def getChildren(self
+ class SimpleAdder(Adder):
+ def __init__(self, *args, **kwargs):
+ super().__init__(*args, **kwargs)
+ self.name = "SimpleAdder"
+ self.type = "SimpleAdder"
+ self.params = {}
+ self.params["name"] = "SimpleAdder"
+ self.params["type"] = "SimpleAdder"
+ self.params["params"] =
{'code': <class 'str'>, 'repo_name': <class 'str'>, 'path': <class 'str'>, 'language': <class 'str'>, 'license': <class 'str'>, 'size': <class 'int'>}
+---------------------------------------------------------------------------
+ValueError Traceback (most recent call last)
+Cell In[39], line 2
+ 1 # Unlike _some_ code-generator models on the market, we'll limit our training data by license :)
+----> 2 dataset = load_dataset(
+ 3 "codeparrot/github-code",
+ 4 streaming=True,
+ 5 split="train",
+ 6 languages=["JavaScript"],
+ 7 licenses=["mit", "isc", "apache-2.0"],
+ 8 )
+ 9 # Print the schema of the first example from the training set:
+ 10 print({k: type(v) for k, v in next(iter(dataset)).items()})
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/datasets/load.py:2594, in load_dataset(path, name, data_dir, data_files, split, cache_dir, features, download_config, download_mode, verification_mode, ignore_verifications, keep_in_memory, save_infos, revision, token, use_auth_token, task, streaming, num_proc, storage_options, trust_remote_code, **config_kwargs)
+ 2589 verification_mode = VerificationMode(
+ 2590 (verification_mode or VerificationMode.BASIC_CHECKS) if not save_infos else VerificationMode.ALL_CHECKS
+ 2591 )
+ 2593 # Create a dataset builder
+-> 2594 builder_instance = load_dataset_builder(
+ 2595 path=path,
+ 2596 name=name,
+ 2597 data_dir=data_dir,
+ 2598 data_files=data_files,
+ 2599 cache_dir=cache_dir,
+ 2600 features=features,
+ 2601 download_config=download_config,
+ 2602 download_mode=download_mode,
+ 2603 revision=revision,
+ 2604 token=token,
+ 2605 storage_options=storage_options,
+ 2606 trust_remote_code=trust_remote_code,
+ 2607 _require_default_config_name=name is None,
+ 2608 **config_kwargs,
+ 2609 )
+ 2611 # Return iterable dataset in case of streaming
+ 2612 if streaming:
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/datasets/load.py:2266, in load_dataset_builder(path, name, data_dir, data_files, cache_dir, features, download_config, download_mode, revision, token, use_auth_token, storage_options, trust_remote_code, _require_default_config_name, **config_kwargs)
+ 2264 download_config = download_config.copy() if download_config else DownloadConfig()
+ 2265 download_config.storage_options.update(storage_options)
+-> 2266 dataset_module = dataset_module_factory(
+ 2267 path,
+ 2268 revision=revision,
+ 2269 download_config=download_config,
+ 2270 download_mode=download_mode,
+ 2271 data_dir=data_dir,
+ 2272 data_files=data_files,
+ 2273 cache_dir=cache_dir,
+ 2274 trust_remote_code=trust_remote_code,
+ 2275 _require_default_config_name=_require_default_config_name,
+ 2276 _require_custom_configs=bool(config_kwargs),
+ 2277 )
+ 2278 # Get dataset builder class from the processing script
+ 2279 builder_kwargs = dataset_module.builder_kwargs
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/datasets/load.py:1914, in dataset_module_factory(path, revision, download_config, download_mode, dynamic_modules_path, data_dir, data_files, cache_dir, trust_remote_code, _require_default_config_name, _require_custom_configs, **download_kwargs)
+ 1909 if isinstance(e1, FileNotFoundError):
+ 1910 raise FileNotFoundError(
+ 1911 f"Couldn't find a dataset script at {relative_to_absolute_path(combined_path)} or any data file in the same directory. "
+ 1912 f"Couldn't find '{path}' on the Hugging Face Hub either: {type(e1).__name__}: {e1}"
+ 1913 ) from None
+-> 1914 raise e1 from None
+ 1915 else:
+ 1916 raise FileNotFoundError(
+ 1917 f"Couldn't find a dataset script at {relative_to_absolute_path(combined_path)} or any data file in the same directory."
+ 1918 )
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/datasets/load.py:1880, in dataset_module_factory(path, revision, download_config, download_mode, dynamic_modules_path, data_dir, data_files, cache_dir, trust_remote_code, _require_default_config_name, _require_custom_configs, **download_kwargs)
+ 1878 pass
+ 1879 # Otherwise we must use the dataset script if the user trusts it
+-> 1880 return HubDatasetModuleFactoryWithScript(
+ 1881 path,
+ 1882 revision=revision,
+ 1883 download_config=download_config,
+ 1884 download_mode=download_mode,
+ 1885 dynamic_modules_path=dynamic_modules_path,
+ 1886 trust_remote_code=trust_remote_code,
+ 1887 ).get_module()
+ 1888 else:
+ 1889 return HubDatasetModuleFactoryWithoutScript(
+ 1890 path,
+ 1891 revision=revision,
+ (...)
+ 1895 download_mode=download_mode,
+ 1896 ).get_module()
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/datasets/load.py:1525, in HubDatasetModuleFactoryWithScript.get_module(self)
+ 1518 importable_file_path = _get_importable_file_path(
+ 1519 dynamic_modules_path=dynamic_modules_path,
+ 1520 module_namespace="datasets",
+ 1521 subdirectory_name=hash,
+ 1522 name=self.name,
+ 1523 )
+ 1524 if not os.path.exists(importable_file_path):
+-> 1525 trust_remote_code = resolve_trust_remote_code(self.trust_remote_code, self.name)
+ 1526 if trust_remote_code:
+ 1527 _create_importable_file(
+ 1528 local_path=local_path,
+ 1529 local_imports=local_imports,
+ (...)
+ 1535 download_mode=self.download_mode,
+ 1536 )
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/datasets/load.py:133, in resolve_trust_remote_code(trust_remote_code, repo_id)
+ 130 signal.alarm(0)
+ 131 except Exception:
+ 132 # OS which does not support signal.SIGALRM
+--> 133 raise ValueError(
+ 134 f"The repository for {repo_id} contains custom code which must be executed to correctly "
+ 135 f"load the dataset. You can inspect the repository content at https://hf.co/datasets/{repo_id}.\n"
+ 136 f"Please pass the argument `trust_remote_code=True` to allow custom code to be run."
+ 137 )
+ 138 else:
+ 139 # For the CI which might put the timeout at 0
+ 140 _raise_timeout_error(None, None)
+
+ValueError: The repository for codeparrot/github-code contains custom code which must be executed to correctly load the dataset. You can inspect the repository content at https://hf.co/datasets/codeparrot/github-code.
+Please pass the argument `trust_remote_code=True` to allow custom code to be run.
---------------------------------------------------------------------------
+ValueError Traceback (most recent call last)
+Cell In[40], line 14
+ 6 training_args = TrainingArguments(
+ 7 output_dir="./codeparrot",
+ 8 max_steps=100,
+ 9 per_device_train_batch_size=1,
+ 10 )
+ 12 tokenizer.pad_token = tokenizer.eos_token
+---> 14 encoded_dataset = dataset.map(
+ 15 lambda x: tokenizer(x["code"], truncation=True, padding="max_length"),
+ 16 batched=True,
+ 17 remove_columns=["code"],
+ 18 )
+ 21 # Metrics for loss:
+ 22 def compute_metrics(eval_pred):
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/datasets/arrow_dataset.py:602, in transmit_tasks.<locals>.wrapper(*args, **kwargs)
+ 600 self: "Dataset" = kwargs.pop("self")
+ 601 # apply actual function
+--> 602 out: Union["Dataset", "DatasetDict"] = func(self, *args, **kwargs)
+ 603 datasets: List["Dataset"] = list(out.values()) if isinstance(out, dict) else [out]
+ 604 for dataset in datasets:
+ 605 # Remove task templates if a column mapping of the template is no longer valid
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/datasets/arrow_dataset.py:567, in transmit_format.<locals>.wrapper(*args, **kwargs)
+ 560 self_format = {
+ 561 "type": self._format_type,
+ 562 "format_kwargs": self._format_kwargs,
+ 563 "columns": self._format_columns,
+ 564 "output_all_columns": self._output_all_columns,
+ 565 }
+ 566 # apply actual function
+--> 567 out: Union["Dataset", "DatasetDict"] = func(self, *args, **kwargs)
+ 568 datasets: List["Dataset"] = list(out.values()) if isinstance(out, dict) else [out]
+ 569 # re-apply format to the output
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/datasets/arrow_dataset.py:3081, in Dataset.map(self, function, with_indices, with_rank, input_columns, batched, batch_size, drop_last_batch, remove_columns, keep_in_memory, load_from_cache_file, cache_file_name, writer_batch_size, features, disable_nullable, fn_kwargs, num_proc, suffix_template, new_fingerprint, desc)
+ 3079 missing_columns = set(remove_columns) - set(self._data.column_names)
+ 3080 if missing_columns:
+-> 3081 raise ValueError(
+ 3082 f"Column to remove {list(missing_columns)} not in the dataset. Current columns in the dataset: {self._data.column_names}"
+ 3083 )
+ 3085 load_from_cache_file = load_from_cache_file if load_from_cache_file is not None else is_caching_enabled()
+ 3087 if fn_kwargs is None:
+
+ValueError: Column to remove ['code'] not in the dataset. Current columns in the dataset: ['text']
+| Step | -Training Loss | -
|---|
TrainOutput(global_step=100, training_loss=2.263228759765625, metrics={'train_runtime': 609.8398, 'train_samples_per_second': 0.164, 'train_steps_per_second': 0.164, 'total_flos': 52258406400000.0, 'train_loss': 2.263228759765625, 'epoch': 1.0})
-class SimpleAdder {
- public class SimpleAdder {
- public static void add(int x, int y) {
- return x + y;
+ public:
+ void main()
+ {
+ printf("Hello World!");
}
}
}
-class SimpleAdder {
- public class SimpleAdder {
- public static void add(int x, int y) {
- return x + y;
+# Adder is a simple class that can be used as a decorator.
+class SimpleAdder2 {
+ public:
+ void main()
+ {
+ printf("Hello World!");
}
}
}
-class SimpleAdder {
- public class SimpleAdder {
- public static void add(int x, int
+# Adder is a simple class that can be used as a decorator.
+class SimpleAdder3 {
+
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:
-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 @@Cosine Similarity between HI and HELLO: 0.7028388977050781
-Cosine Similarity between BONJOUR and HELLO: 0.5818601846694946
+Cosine Similarity between BONJOUR and HELLO: 0.5818600654602051
Cosine Similarity between cat and chatte: 0.4327270984649658
-Cosine Similarity between cat and chat: 0.6866628527641296
-Cosine Similarity between chatte and chat: 0.6003133654594421
+Cosine Similarity between cat and chatte: 0.432727187871933
+Cosine Similarity between cat and chat: 0.6866632699966431
+Cosine Similarity between chatte and chat: 0.6003134250640869
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 @@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.
Check out the paper mentioned in the above video:
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 @@Check out the paper mentioned in the above video:
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.
The key is to realize that if both embeddings contain the same information, they should be correlated.
Looking at the formula for Pearson correlation:
Check out the paper mentioned in the above video:
In this tutorial, we saw several tricks on how to do well when there is very limited data we saw:
<module 'neuromatch_ssl_tutorial.modules.plot_util' from '/home/runner/work/course-content-dl/course-content-dl/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/neuromatch_ssl_tutorial/modules/plot_util.py'>
+---------------------------------------------------------------------------
+RuntimeError Traceback (most recent call last)
+Cell In[4], line 3
+ 1 # Imports
+ 2 import torch
+----> 3 import torchvision
+ 4 import numpy as np
+ 5 import matplotlib.pyplot as plt
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torchvision/__init__.py:6
+ 3 from modulefinder import Module
+ 5 import torch
+----> 6 from torchvision import _meta_registrations, datasets, io, models, ops, transforms, utils
+ 8 from .extension import _HAS_OPS
+ 10 try:
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torchvision/_meta_registrations.py:164
+ 153 torch._check(
+ 154 grad.dtype == rois.dtype,
+ 155 lambda: (
+ (...)
+ 158 ),
+ 159 )
+ 160 return grad.new_empty((batch_size, channels, height, width))
+ 163 @torch._custom_ops.impl_abstract("torchvision::nms")
+--> 164 def meta_nms(dets, scores, iou_threshold):
+ 165 torch._check(dets.dim() == 2, lambda: f"boxes should be a 2d tensor, got {dets.dim()}D")
+ 166 torch._check(dets.size(1) == 4, lambda: f"boxes should have 4 elements in dimension 1, got {dets.size(1)}")
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/library.py:467, in impl_abstract.<locals>.inner(func)
+ 464 else:
+ 465 func_to_register = func
+--> 467 handle = entry.abstract_impl.register(func_to_register, source)
+ 468 if lib is not None:
+ 469 lib._registration_handles.append(handle)
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/_library/abstract_impl.py:30, in AbstractImplHolder.register(self, func, source)
+ 24 if self.kernel is not None:
+ 25 raise RuntimeError(
+ 26 f"impl_abstract(...): the operator {self.qualname} "
+ 27 f"already has an abstract impl registered at "
+ 28 f"{self.kernel.source}."
+ 29 )
+---> 30 if torch._C._dispatch_has_kernel_for_dispatch_key(self.qualname, "Meta"):
+ 31 raise RuntimeError(
+ 32 f"impl_abstract(...): the operator {self.qualname} "
+ 33 f"already has an DispatchKey::Meta implementation via a "
+ (...)
+ 36 f"impl_abstract."
+ 37 )
+ 39 if torch._C._dispatch_has_kernel_for_dispatch_key(
+ 40 self.qualname, "CompositeImplicitAutograd"
+ 41 ):
+
+RuntimeError: operator torchvision::nms does not exist
Random seed 2021 has been set.
-WARNING: For this notebook to perform best, if possible, in the menu under `Runtime` -> `Change runtime type.` select `GPU`
-Next, we use the dSpritesDataset class method show_images() to plot a few images from the dataset, with their latent dimension values printed below.
Interactive Demo: View a different set of randomly sampled images by passing the random state argument randst any integer or the value None. (The original setting is randst=SEED.)
-To better understand the posX and posY latent dimensions (which will be most relevant in Bonus 2), we plot the images with some annotations. The annotations (in red) do not modify the actual images; they are added purely for visualization purposes, and show:
-
-
+
+
The following code:
Random seed 2021 has been set.
-Dataset size: 16000 training, 4000 test images
-As we can observe, the classifier trained directly on the images performs only a bit above chance (39.55%) on the test set, after 25 training epochs.
Shape classification results using different feature encoders:
@@ -2275,7 +2311,7 @@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 +2343,7 @@
-
+
+
@@ -2535,7 +2571,7 @@ 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 +2880,7 @@Random seed 2021 has been set.
-Loading VAE encoder from 'neuromatch_ssl_tutorial/checkpoints/vae_encoder_300ep_bs500_seed2021.pth'.
- => trained for 300 epochs (batch_size of 500) on the full dSprites subset dataset.
-Loading VAE decoder from 'neuromatch_ssl_tutorial/checkpoints/vae_decoder_300ep_bs500_seed2021.pth'.
- => trained for 300 epochs (batch_size of 500) on the full dSprites subset dataset.
-
-Plotting RSMs...
-
-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 +3229,7 @@Random seed 2021 has been set.
-
-We can now train the SimCLR encoder with the custom contrastive loss for a few epochs.
Loading SimCLR encoder from 'neuromatch_ssl_tutorial/checkpoints/simclr_encoder_60ep_bs1000_deg90_trans0-2_scale0-8to1-2_seed2021.pth'.
- => trained for 60 epochs (batch_size of 1000) on the full dSprites subset dataset
-with the following random affine transforms:
- degrees=90
- translation=(0.2, 0.2)
- scale=(0.8, 1.2).
-Random seed 2021 has been set.
-Training a classifier on the pre-trained SimCLR encoder representations...
-Network performance after 10 classifier training epochs (chance: 33.33%):
- Training accuracy: 97.83%
- Testing accuracy: 97.53%
-
-Network performance after 10 classifier training epochs (chance: 33.33%):
Training accuracy: 97.83%
@@ -3589,7 +3585,7 @@ 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 +3622,7 @@Random seed 2021 has been set.
-Biased dataset: 5808 training, 1000 test images
-Bias control dataset: 5808 training, 1000 test images
-We plot some images sampled with train_sampler_biased to observe the pattern described above where shape and posX are now correlated.
To better visualize the bias introduced, we will plot them with annotations that show, in red:
@@ -3713,12 +3703,7 @@Plotting first 20 images from the biased training dataset.
-
-We also plot some images sampled with train_sampler_bias_ctrl to verify visually that this biased pattern does not appear in the control dataset.
Again, the annotations are added, purely for visualization purposes.
@@ -3729,12 +3714,7 @@Plotting sample images from the bias control training dataset.
-
-Random seed 2021 has been set.
-Training all models using the control, unbiased training dataset
-
-Loading VAE encoder from 'neuromatch_ssl_tutorial/checkpoints/vae_encoder_bias_ctrl_450ep_bs500_seed2021.pth'.
- => trained for 450 epochs (batch_size of 500) on the bias_ctrl dSprites subset dataset.
-Loading SimCLR encoder from 'neuromatch_ssl_tutorial/checkpoints/simclr_encoder_bias_ctrl_150ep_bs1000_deg90_trans0-2_scale0-8to1-2_seed2021.pth'.
- => trained for 150 epochs (batch_size of 1000) on the bias_ctrl dSprites subset dataset
-with the following random affine transforms:
- degrees=90
- translation=(0.2, 0.2)
- scale=(0.8, 1.2).
-
-Training supervised encoder and classifier for 80 epochs, and all other classifiers for 30 epochs each.
-Using the following default labelled fraction values: 0.05, 0.1, 0.2, 0.4, 0.75, 1.0
-
-Supervised encoder: training classifiers and encoders*...
-Random encoder: training classifiers...
----------------------------------------------------------------------------
-KeyboardInterrupt Traceback (most recent call last)
-Cell In[72], line 6
- 3 set_seed(SEED)
- 5 print("Training all models using the control, unbiased training dataset\n")
-----> 6 full_training_procedure(
- 7 train_sampler_bias_ctrl, test_sampler_for_bias_ctrl,
- 8 title="Classifier performances with control, unbiased training dataset",
- 9 dataset_type="bias_ctrl" # For loading correct pre-trained networks
- 10 )
-
-Cell In[71], line 52, in full_training_procedure(train_sampler, test_sampler, title, dataset_type, verbose)
- 49 num_clf_epochs = [80, 30, 30, 30]
- 50 print(f"\nTraining supervised encoder and classifier for {num_clf_epochs[0]} "
- 51 f"epochs, and all other classifiers for {num_clf_epochs[1]} epochs each.")
----> 52 _ = models.train_encoder_clfs_by_fraction_labelled(
- 53 encoders=encoders,
- 54 dataset=dSprites_torchdataset,
- 55 train_sampler=train_sampler,
- 56 test_sampler=test_sampler,
- 57 num_epochs=num_clf_epochs,
- 58 freeze_features=freeze_features,
- 59 subset_seed=SEED,
- 60 encoder_labels=encoder_labels,
- 61 title=title,
- 62 verbose=verbose
- 63 )
-
-File ~/work/course-content-dl/course-content-dl/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/neuromatch_ssl_tutorial/modules/models.py:1234, in train_encoder_clfs_by_fraction_labelled(encoders, dataset, train_sampler, test_sampler, labelled_fractions, num_epochs, freeze_features, batch_size, subset_seed, use_cuda, encoder_labels, plot_accuracies, title, verbose)
- 1232 test_accs = np.full((len(encoders), len(labelled_fractions)), np.nan)
- 1233 for e, encoder in enumerate(encoders):
--> 1234 train_accs[e], test_accs[e] = train_clfs_by_fraction_labelled(
- 1235 encoder, dataset, train_sampler, test_sampler,
- 1236 labelled_fractions=labelled_fractions, num_epochs=num_epochs[e],
- 1237 freeze_features=freeze_features[e], batch_size=batch_size,
- 1238 subset_seed=subset_seed, use_cuda=use_cuda,
- 1239 encoder_label=encoder_labels[e], plot_accuracies=plot_accuracies,
- 1240 ax=ax, plot_chance=False, color=colors[e], marker=markers[e],
- 1241 verbose=verbose
- 1242 )
- 1244 if plot_accuracies:
- 1245 return train_accs, test_accs, ax
-
-File ~/work/course-content-dl/course-content-dl/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/neuromatch_ssl_tutorial/modules/models.py:1064, in train_clfs_by_fraction_labelled(encoder, dataset, train_sampler, test_sampler, labelled_fractions, num_epochs, freeze_features, batch_size, subset_seed, use_cuda, encoder_label, plot_accuracies, ax, title, plot_chance, color, marker, verbose)
- 1062 if not freeze_features: # obtain new fresh version
- 1063 encoder = copy.deepcopy(orig_encoder)
--> 1064 _, _, train_acc[i], test_acc[i] = train_classifier(
- 1065 encoder, dataset, train_sampler, test_sampler,
- 1066 num_epochs=num_epochs_use_all[i],
- 1067 fraction_of_labels=labelled_fractions[i],
- 1068 freeze_features=freeze_features, subset_seed=subset_seed,
- 1069 batch_size=batch_size, progress_bar=False, verbose=False
- 1070 )
- 1072 if plot_accuracies:
- 1073 if ax is None:
-
-File ~/work/course-content-dl/course-content-dl/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/neuromatch_ssl_tutorial/modules/models.py:292, in train_classifier(encoder, dataset, train_sampler, test_sampler, num_epochs, fraction_of_labels, batch_size, freeze_features, subset_seed, use_cuda, progress_bar, verbose)
- 289 classification_optimizer.zero_grad()
- 291 if freeze_features:
---> 292 features = encoder.get_features(X.to(device))
- 293 else:
- 294 features = encoder(X.to(device))
-
-File ~/work/course-content-dl/course-content-dl/tutorials/W3D3_UnsupervisedAndSelfSupervisedLearning/student/neuromatch_ssl_tutorial/modules/models.py:165, in EncoderCore.get_features(self, X)
- 163 def get_features(self, X):
- 164 with torch.no_grad():
---> 165 feats_extr = self.feature_extractor(X)
- 166 feats_flat = torch.flatten(feats_extr, 1)
- 167 feats_proj = self.linear_projections(feats_flat)
-
-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/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/3.9.19/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/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:
-
-A similar pattern is observed here as with the full dataset, though notably most performances are a bit weaker, likely due to us (A) using a smaller training dataset, and (B) training and pre-training for fewer iterations, considering the dataset size, for time-efficiency reasons.
Using the same parameters, we now repeat the analysis with the biased training data sampler.
@@ -4007,6 +3827,7 @@Interestingly, the SimCLR network encoder is not only the only network to perform well, it even outperforms its control performance (which uses the same test dataset), at least with this particular dataset and biasing.
Note on performance improvement: This improvement for the SimCLR encoder is reflected in the pre-training loss curves (not shown here), which show that the encoder trained with the biased dataset learns faster than the encoder trained with the unbiased training set. It is possible that the dataset biasing, by reducing the variability in the dataset, makes the contrastive task easier, thus enabling the network to learn a good feature space for the classification task in fewer epochs
@@ -4032,6 +3853,8 @@
+
+After dropping the number of negative pairs used per image in pre-training a SimCLR encoder, classification accuracy drops to 66.75% on the test dataset, even after 50 classifier training epochs.
Shape classification results using different feature encoders:
@@ -4466,6 +4322,8 @@
+---------------------------------------------------------------------------
+RuntimeError Traceback (most recent call last)
+Cell In[9], line 38
+ 36 from othello.OthelloLogic import Board
+ 37 # from othello.OthelloGame import OthelloGame
+---> 38 from othello.pytorch.NNet import NNetWrapper as NNet
+
+File ~/work/course-content-dl/course-content-dl/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/nma_rl_games/alpha-zero/othello/pytorch/NNet.py:15
+ 12 import torch
+ 13 import torch.optim as optim
+---> 15 from .OthelloNNet import OthelloNNet as onnet
+ 17 args = dotdict({
+ 18 'lr': 0.001,
+ 19 'dropout': 0.3,
+ (...)
+ 23 'num_channels': 512,
+ 24 })
+ 27 class NNetWrapper(NeuralNet):
+
+File ~/work/course-content-dl/course-content-dl/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/nma_rl_games/alpha-zero/othello/pytorch/OthelloNNet.py:10
+ 8 import torch.nn.functional as F
+ 9 import torch.optim as optim
+---> 10 from torchvision import datasets, transforms
+ 11 from torch.autograd import Variable
+ 13 class OthelloNNet(nn.Module):
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torchvision/__init__.py:6
+ 3 from modulefinder import Module
+ 5 import torch
+----> 6 from torchvision import _meta_registrations, datasets, io, models, ops, transforms, utils
+ 8 from .extension import _HAS_OPS
+ 10 try:
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torchvision/_meta_registrations.py:164
+ 153 torch._check(
+ 154 grad.dtype == rois.dtype,
+ 155 lambda: (
+ (...)
+ 158 ),
+ 159 )
+ 160 return grad.new_empty((batch_size, channels, height, width))
+ 163 @torch._custom_ops.impl_abstract("torchvision::nms")
+--> 164 def meta_nms(dets, scores, iou_threshold):
+ 165 torch._check(dets.dim() == 2, lambda: f"boxes should be a 2d tensor, got {dets.dim()}D")
+ 166 torch._check(dets.size(1) == 4, lambda: f"boxes should have 4 elements in dimension 1, got {dets.size(1)}")
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/library.py:467, in impl_abstract.<locals>.inner(func)
+ 464 else:
+ 465 func_to_register = func
+--> 467 handle = entry.abstract_impl.register(func_to_register, source)
+ 468 if lib is not None:
+ 469 lib._registration_handles.append(handle)
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/_library/abstract_impl.py:30, in AbstractImplHolder.register(self, func, source)
+ 24 if self.kernel is not None:
+ 25 raise RuntimeError(
+ 26 f"impl_abstract(...): the operator {self.qualname} "
+ 27 f"already has an abstract impl registered at "
+ 28 f"{self.kernel.source}."
+ 29 )
+---> 30 if torch._C._dispatch_has_kernel_for_dispatch_key(self.qualname, "Meta"):
+ 31 raise RuntimeError(
+ 32 f"impl_abstract(...): the operator {self.qualname} "
+ 33 f"already has an DispatchKey::Meta implementation via a "
+ (...)
+ 36 f"impl_abstract."
+ 37 )
+ 39 if torch._C._dispatch_has_kernel_for_dispatch_key(
+ 40 self.qualname, "CompositeImplicitAutograd"
+ 41 ):
+
+RuntimeError: operator torchvision::nms does not exist
+The hyperparameters used throughout the notebook.
@@ -1579,7 +1653,7 @@PolicyNetwork#For computing our objective function, we will use the negative log-likelihood of targets \(t_i\) by using the cross-entropy function:
- +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 +2858,7 @@Random seed 2023 has been set.
-Random seed 2023 has been set.
+Random seed 2023 has been set.
Random seed 2023 has been set.
-Number of games won by player1 = 19, number of games won by player2 = 1, out of 20 games
@@ -3501,7 +3569,7 @@ Submit your feedback
-
These are the slides for the videos in the tutorial. If you want to locally download the slides, click here.
@@ -1149,6 +1149,80 @@Add the nma_rl_games in the path and import the modules.
---------------------------------------------------------------------------
+RuntimeError Traceback (most recent call last)
+Cell In[8], line 38
+ 36 from othello.OthelloLogic import Board
+ 37 # from othello.OthelloGame import OthelloGame
+---> 38 from othello.pytorch.NNet import NNetWrapper as NNet
+
+File ~/work/course-content-dl/course-content-dl/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/nma_rl_games/alpha-zero/othello/pytorch/NNet.py:15
+ 12 import torch
+ 13 import torch.optim as optim
+---> 15 from .OthelloNNet import OthelloNNet as onnet
+ 17 args = dotdict({
+ 18 'lr': 0.001,
+ 19 'dropout': 0.3,
+ (...)
+ 23 'num_channels': 512,
+ 24 })
+ 27 class NNetWrapper(NeuralNet):
+
+File ~/work/course-content-dl/course-content-dl/tutorials/W3D5_ReinforcementLearningForGamesAndDlThinking3/student/nma_rl_games/alpha-zero/othello/pytorch/OthelloNNet.py:10
+ 8 import torch.nn.functional as F
+ 9 import torch.optim as optim
+---> 10 from torchvision import datasets, transforms
+ 11 from torch.autograd import Variable
+ 13 class OthelloNNet(nn.Module):
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torchvision/__init__.py:6
+ 3 from modulefinder import Module
+ 5 import torch
+----> 6 from torchvision import _meta_registrations, datasets, io, models, ops, transforms, utils
+ 8 from .extension import _HAS_OPS
+ 10 try:
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torchvision/_meta_registrations.py:164
+ 153 torch._check(
+ 154 grad.dtype == rois.dtype,
+ 155 lambda: (
+ (...)
+ 158 ),
+ 159 )
+ 160 return grad.new_empty((batch_size, channels, height, width))
+ 163 @torch._custom_ops.impl_abstract("torchvision::nms")
+--> 164 def meta_nms(dets, scores, iou_threshold):
+ 165 torch._check(dets.dim() == 2, lambda: f"boxes should be a 2d tensor, got {dets.dim()}D")
+ 166 torch._check(dets.size(1) == 4, lambda: f"boxes should have 4 elements in dimension 1, got {dets.size(1)}")
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/library.py:467, in impl_abstract.<locals>.inner(func)
+ 464 else:
+ 465 func_to_register = func
+--> 467 handle = entry.abstract_impl.register(func_to_register, source)
+ 468 if lib is not None:
+ 469 lib._registration_handles.append(handle)
+
+File /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/torch/_library/abstract_impl.py:30, in AbstractImplHolder.register(self, func, source)
+ 24 if self.kernel is not None:
+ 25 raise RuntimeError(
+ 26 f"impl_abstract(...): the operator {self.qualname} "
+ 27 f"already has an abstract impl registered at "
+ 28 f"{self.kernel.source}."
+ 29 )
+---> 30 if torch._C._dispatch_has_kernel_for_dispatch_key(self.qualname, "Meta"):
+ 31 raise RuntimeError(
+ 32 f"impl_abstract(...): the operator {self.qualname} "
+ 33 f"already has an DispatchKey::Meta implementation via a "
+ (...)
+ 36 f"impl_abstract."
+ 37 )
+ 39 if torch._C._dispatch_has_kernel_for_dispatch_key(
+ 40 self.qualname, "CompositeImplicitAutograd"
+ 41 ):
+
+RuntimeError: operator torchvision::nms does not exist
+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:
-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 +2290,7 @@Random seed 2023 has been set.
-Number of games won by player1 = 19, num of games won by player2 = 1, out of 20 games
@@ -2434,9 +2504,7 @@ 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.
Welcome to the Neuromatch deep learning course!
@@ -1415,7 +1415,7 @@