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Expand Up @@ -378,7 +378,7 @@
"\n",
"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.\n",
"\n",
"In modern transformer systems, such as GPT, all words are used parallelly. In that sense, the transformers generalize the encoding/decoding idea. Examples of this strategy include all the modern large language models (such as GPT)."
"In modern transformer systems, such as GPT, all words are used in parallel. In that sense, the transformers generalize the encoding/decoding idea. Examples of this strategy include all the modern large language models (such as GPT)."
]
},
{
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4 changes: 2 additions & 2 deletions projects/ComputerVision/data_augmentation.html
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Expand Up @@ -1763,8 +1763,8 @@ <h2>Cutout<a class="headerlink" href="#cutout" title="Permalink to this heading"
<section id="mixup">
<h2>Mixup<a class="headerlink" href="#mixup" title="Permalink to this heading">#</a></h2>
<p>Mixup is a data augmentation technique that combines pairs of examples via a convex combination of the images and the labels. Given images <span class="math notranslate nohighlight">\(x_i\)</span> and <span class="math notranslate nohighlight">\(x_j\)</span> with labels <span class="math notranslate nohighlight">\(y_i\)</span> and <span class="math notranslate nohighlight">\(y_j\)</span>, respectively, and <span class="math notranslate nohighlight">\(\lambda \in [0, 1]\)</span>, mixup creates a new image <span class="math notranslate nohighlight">\(\hat{x}\)</span> with label <span class="math notranslate nohighlight">\(\hat{y}\)</span> the following way:</p>
<div class="amsmath math notranslate nohighlight" id="equation-1fee2fe6-b220-4c40-8d08-7b46f712535c">
<span class="eqno">(128)<a class="headerlink" href="#equation-1fee2fe6-b220-4c40-8d08-7b46f712535c" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-44e940bd-c292-4eed-bcf0-b364c176cb30">
<span class="eqno">(128)<a class="headerlink" href="#equation-44e940bd-c292-4eed-bcf0-b364c176cb30" title="Permalink to this equation">#</a></span>\[\begin{align}
\hat{x} &amp;= \lambda x_i + (1 - \lambda) x_j \\
\hat{y} &amp;= \lambda y_i + (1 - \lambda) y_j
\end{align}\]</div>
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68 changes: 34 additions & 34 deletions projects/modelingsteps/Example_Deep_Learning_Project.html
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Expand Up @@ -2067,33 +2067,33 @@ <h2>Build model<a class="headerlink" href="#build-model" title="Permalink to thi
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch [100/500], Step [1/2], Loss: 0.8369, Accuracy: 71.51%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch [100/500], Step [1/2], Loss: 0.8982, Accuracy: 72.67%
------------------------------------------
Epoch [100/500], Step [2/2], Loss: 0.9079, Accuracy: 67.83%
Epoch [100/500], Step [2/2], Loss: 0.9187, Accuracy: 68.80%
------------------------------------------
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch [200/500], Step [1/2], Loss: 0.6369, Accuracy: 77.52%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch [200/500], Step [1/2], Loss: 0.6901, Accuracy: 77.13%
------------------------------------------
Epoch [200/500], Step [2/2], Loss: 0.5581, Accuracy: 81.40%
Epoch [200/500], Step [2/2], Loss: 0.6060, Accuracy: 79.26%
------------------------------------------
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch [300/500], Step [1/2], Loss: 0.5327, Accuracy: 80.23%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch [300/500], Step [1/2], Loss: 0.5478, Accuracy: 81.20%
------------------------------------------
Epoch [300/500], Step [2/2], Loss: 0.4692, Accuracy: 85.08%
Epoch [300/500], Step [2/2], Loss: 0.4853, Accuracy: 83.91%
------------------------------------------
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch [400/500], Step [1/2], Loss: 0.3940, Accuracy: 87.98%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch [400/500], Step [1/2], Loss: 0.4423, Accuracy: 83.53%
------------------------------------------
Epoch [400/500], Step [2/2], Loss: 0.4626, Accuracy: 82.56%
Epoch [400/500], Step [2/2], Loss: 0.5842, Accuracy: 78.88%
------------------------------------------
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch [500/500], Step [1/2], Loss: 0.3307, Accuracy: 90.50%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch [500/500], Step [1/2], Loss: 0.3525, Accuracy: 89.15%
------------------------------------------
Epoch [500/500], Step [2/2], Loss: 0.3613, Accuracy: 87.60%
Epoch [500/500], Step [2/2], Loss: 0.3686, Accuracy: 87.02%
------------------------------------------
</pre></div>
</div>
Expand Down Expand Up @@ -2123,7 +2123,7 @@ <h2>Build model<a class="headerlink" href="#build-model" title="Permalink to thi
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Test Accuracy of the model on the 172 test moves: 84.302%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Test Accuracy of the model on the 172 test moves: 79.070%
</pre></div>
</div>
</div>
Expand All @@ -2137,7 +2137,7 @@ <h2>Build model<a class="headerlink" href="#build-model" title="Permalink to thi
</div>
</div>
<div class="cell_output docutils container">
<img alt="../../_images/78566d46f1f05e3965d54f9bb1efec22378c1d3f0317e8f5faf8b50b2220d972.png" src="../../_images/78566d46f1f05e3965d54f9bb1efec22378c1d3f0317e8f5faf8b50b2220d972.png" />
<img alt="../../_images/64058d37f289e3656e6d296491b14d5cfc7641127067f41d0c6a3f6a91b7e179.png" src="../../_images/64058d37f289e3656e6d296491b14d5cfc7641127067f41d0c6a3f6a91b7e179.png" />
</div>
</div>
<p>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.</p>
Expand Down Expand Up @@ -2225,10 +2225,10 @@ <h1>Step 8: Modeling completion<a class="headerlink" href="#step-8-modeling-comp
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>73.83720930232558
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>71.51162790697676
</pre></div>
</div>
<img alt="../../_images/3d16ae3899ad056181e31c4171b56e0d6efa3a29eb3ddf32ed9cf0fdc143a92b.png" src="../../_images/3d16ae3899ad056181e31c4171b56e0d6efa3a29eb3ddf32ed9cf0fdc143a92b.png" />
<img alt="../../_images/4d22edbf348f43256d1e465ca1629b5d492e11651a4230519554fc5c37f7d2f0.png" src="../../_images/4d22edbf348f43256d1e465ca1629b5d492e11651a4230519554fc5c37f7d2f0.png" />
</div>
</div>
<p>That is some pretty good performance based on only 6 / 24 joints!</p>
Expand Down Expand Up @@ -2274,32 +2274,32 @@ <h1>Step 9: Model evaluation<a class="headerlink" href="#step-9-model-evaluation
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>*** FITTING: Left Leg
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>limb performance: 72.67%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>limb performance: 78.49%

*** FITTING: Right Leg
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>limb performance: 70.93%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>limb performance: 66.28%

*** FITTING: Left Arm
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>limb performance: 66.86%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>limb performance: 56.40%

*** FITTING: Right Arm
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>limb performance: 38.95%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>limb performance: 40.12%

*** FITTING: Torso
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>limb performance: 79.65%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>limb performance: 78.49%

*** FITTING: Head
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>limb performance: 50.00%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>limb performance: 47.67%
</pre></div>
</div>
</div>
Expand Down Expand Up @@ -2353,44 +2353,44 @@ <h1>Step 9: Model evaluation<a class="headerlink" href="#step-9-model-evaluation
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>*** FITTING: limbs only
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 76.16%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 79.65%
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 68.02%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 62.21%
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 75.58%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 80.81%
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 73.26%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 69.77%
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 70.35%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 74.42%
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 85.47%
median performance: 74.42%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 84.30%
median performance: 77.03%

*** FITTING: limbs+torso+head
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 81.98%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 74.42%
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 81.98%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 71.51%
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 86.63%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 78.49%
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 79.07%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 78.49%
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 79.65%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 75.00%
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 86.05%
median performance: 81.98%
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>performance: 83.14%
median performance: 76.74%
</pre></div>
</div>
</div>
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18 changes: 9 additions & 9 deletions projects/modelingsteps/TrainIllusionDataProjectDL.html
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Expand Up @@ -1772,8 +1772,8 @@ <h1>Question<a class="headerlink" href="#question" title="Permalink to this head
<p><em>Part of Step 1</em></p>
<p>Previous literature predicts that accumulated sensory evidence from vestibular signals determines the decision of whether self-motion is experienced or not. We now have vestibular neuron data (simulated in our case, but let’s pretend) and would like to see if that prediction holds true.</p>
<p>The data contains <span class="math notranslate nohighlight">\(N\)</span> neurons and <span class="math notranslate nohighlight">\(M\)</span> trials for each of 3 motion conditions: no self-motion, slowly accelerating self-motion and faster accelerating self-motion.</p>
<div class="amsmath math notranslate nohighlight" id="equation-bb3937f8-4c44-4fa8-8836-702c2e8c1ecc">
<span class="eqno">(126)<a class="headerlink" href="#equation-bb3937f8-4c44-4fa8-8836-702c2e8c1ecc" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-a4c3eca8-183e-47ce-90c7-56eb9e4b6f63">
<span class="eqno">(126)<a class="headerlink" href="#equation-a4c3eca8-183e-47ce-90c7-56eb9e4b6f63" title="Permalink to this equation">#</a></span>\[\begin{align}
N &amp;= 40 \\
M &amp;= 400
\end{align}\]</div>
Expand Down Expand Up @@ -1824,7 +1824,7 @@ <h1>Background<a class="headerlink" href="#background" title="Permalink to this
</div>
</div>
<div class="cell_output docutils container">
<img alt="../../_images/691998358ad0b84a3aa3e260513e493dea28f2884db29c3b72d2ae13d752d828.png" src="../../_images/691998358ad0b84a3aa3e260513e493dea28f2884db29c3b72d2ae13d752d828.png" />
<img alt="../../_images/12309e1b0f5f8b2678fe9ce4f50df80f08c0a5c46dd3ef0d18aefa6382df374b.png" src="../../_images/12309e1b0f5f8b2678fe9ce4f50df80f08c0a5c46dd3ef0d18aefa6382df374b.png" />
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<p>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:</p>
Expand All @@ -1836,9 +1836,9 @@ <h1>Background<a class="headerlink" href="#background" title="Permalink to this
</div>
</div>
<div class="cell_output docutils container">
<img alt="../../_images/86d5ecbd5807f4033da9d40d5f7cda9fe5964ddc6b6f1329e5e61217afe379ff.png" src="../../_images/86d5ecbd5807f4033da9d40d5f7cda9fe5964ddc6b6f1329e5e61217afe379ff.png" />
<img alt="../../_images/54885e65427d84d7b01f9a435a4e143802b2c70c468ce6468848a91c2138d1ea.png" src="../../_images/54885e65427d84d7b01f9a435a4e143802b2c70c468ce6468848a91c2138d1ea.png" />
<img alt="../../_images/d8aea21b3d80d298463d9b5b90da9a832b7a4cfa982949836b3ac13c8ae399b7.png" src="../../_images/d8aea21b3d80d298463d9b5b90da9a832b7a4cfa982949836b3ac13c8ae399b7.png" />
<img alt="../../_images/6fbd1e5b4f33d1bd8d6047d2263785e28305ea8ee5c46874e97cb634148224a4.png" src="../../_images/6fbd1e5b4f33d1bd8d6047d2263785e28305ea8ee5c46874e97cb634148224a4.png" />
<img alt="../../_images/434b95f0afef8e61b449992591137c1368f3dace3f520f30e5de25a90e62bc3d.png" src="../../_images/434b95f0afef8e61b449992591137c1368f3dace3f520f30e5de25a90e62bc3d.png" />
<img alt="../../_images/c66b47652a1108d84fc48ff6084ec8a491fc75c66614eccf023d769bb9d1889e.png" src="../../_images/c66b47652a1108d84fc48ff6084ec8a491fc75c66614eccf023d769bb9d1889e.png" />
</div>
</div>
<p>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.</p>
Expand Down Expand Up @@ -1986,7 +1986,7 @@ <h1>Model implementation<a class="headerlink" href="#model-implementation" title
</div>
</div>
<div class="cell_output docutils container">
<img alt="../../_images/657b75caf157f5e8a44e7e14cd2f691d4f1560628aa3d1d8a2e085eeec1c3356.png" src="../../_images/657b75caf157f5e8a44e7e14cd2f691d4f1560628aa3d1d8a2e085eeec1c3356.png" />
<img alt="../../_images/f0e8f6d99d4b7ea50d65e7ac08504675500847058d0a74bb06e228699b609634.png" src="../../_images/f0e8f6d99d4b7ea50d65e7ac08504675500847058d0a74bb06e228699b609634.png" />
</div>
</div>
<p>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.</p>
Expand Down Expand Up @@ -2037,7 +2037,7 @@ <h1>Model implementation<a class="headerlink" href="#model-implementation" title
</div>
</div>
<div class="cell_output docutils container">
<img alt="../../_images/657b75caf157f5e8a44e7e14cd2f691d4f1560628aa3d1d8a2e085eeec1c3356.png" src="../../_images/657b75caf157f5e8a44e7e14cd2f691d4f1560628aa3d1d8a2e085eeec1c3356.png" />
<img alt="../../_images/f0e8f6d99d4b7ea50d65e7ac08504675500847058d0a74bb06e228699b609634.png" src="../../_images/f0e8f6d99d4b7ea50d65e7ac08504675500847058d0a74bb06e228699b609634.png" />
</div>
</div>
<p>This is the exact same figure as before, so our function <code class="docutils literal notranslate"><span class="pre">classifyMotionFromSpikes()</span></code> also works as intended.</p>
Expand Down Expand Up @@ -2174,7 +2174,7 @@ <h1>Model evaluation &amp; testing<a class="headerlink" href="#model-evaluation-
</div>
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<p>Well, that’s interesting! The logistic regression doesn’t do a perfect job, but there is information in these results.</p>
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