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+# Sphinx build info version 1
+# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
+config: c6b51c10e20ffa45be5c63e767b50c1b
+tags: 645f666f9bcd5a90fca523b33c5a78b7

_sources/index.rst.txt

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+.. Lateral Connections documentation master file, created by
+   sphinx-quickstart on Mon May 22 17:18:05 2023.
+   You can adapt this file completely to your liking, but it should at least
+   contain the root `toctree` directive.
+
+Self-Organisation in a Biologically Inspired Learning Framework Based on Bernoulli Neurons
+==========================================================================================
+
+Welcome to the online showcase of my master's thesis, titled "Self-Organisation in a Biologically Inspired Learning Framework Based on Bernoulli Neurons." This exploration delves into the crossroads of neuroscience and machine learning, focusing on the fascinating phenomenon of self-organisation within an novel learning framework.
+Please find the abstract, the full thesis, and videos presenting the results below.
+
+.. toctree::
+   :maxdepth: 1
+   :caption: Contents
+
+   presentation
+   thesis
+   results/final_results
+
+---
+
+.. raw:: html
+
+  <embed>
+      <p><a href="_static/results/msc_thesis-Pascal_Sager-V1_0.pdf" target="_blank">Download</a> the thesis as PDF.</p>
+  </embed>
+
+

_sources/presentation.rst.txt

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+Presentation
+============
+
+.. video:: _static/results/thesis_defence_presentation.mp4
+  :width: 800

_sources/results/final_results.rst.txt

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+Results
+=======
+
+In the following, video visualisations of the results presented in the thesis are shown.
+The input into the model is a line that is rotating counter-clockwise around the origin.
+This input is fed into the sensory system that is shown in the center of the video.
+The sensory system has 4 filters to extract different features. These features are visualised with different colors.
+
+The output of the sensory system is fed into the *S1*, the network with lateral connections building net fragments.
+These net fragments are visualised in the top right corner of the video, using the same colors per feature channel as the sensory system.
+
+The net fragments are fed into *S2*, that maps the net fragments to a 1D representation of length :math:`16`. This 1D vector is visualised
+as circles in the bottom center of the video. Thereby, a green circle corresponds to an active neuron, while a red circle corresponds
+to an inactive neuron.
+The reconstructed net fragment of *S2* is shown in the bottom right corner of the video.
+
+In the following, the results from multiple experiments are visualised. For each experiment, two videos are shown:
+Both videos are produced by the same model using the same weights. However, the first
+video shows the activations if a fixed threshold of :math:`0.5` (*S1*) and :math:`0.9` (*S2*) for each neuron is used (i.e. probabilities :math:`\geq 0.5` / :math:`\geq 0.9` lead to an activation of a neuron).
+This helps to better understand the behaviour of the model.
+The second video shows the activations if the neurons are sampled from a Bernoulli distribution.
+This corresponds to the behaviour of the model during training.
+
+Please not that the model has only seen horizontal, vertical, and diagonal lines during training.
+Therefore, *S2* only stored these lines in its memory.
+However, *S1* can also build net fragments for data not seen during training.
+
+.. warning::
+   If the videos are not shown, the encoding is not supported by your browser.
+   Please try a Chromium-based browser (e.g. Google Chrome, Brave Browser, etc.).
+
+
+Rotating Line
+~~~~~~~~~~~~~
+
+The following videos show the behaviour of the model if the line is rotated around the origin.
+
+
+**Fixed Threshold**
+
+
+.. video:: ../_static/results/final_results/threshold/normal.mp4
+   :width: 450
+
+**Bernoulli Sampling**
+
+.. video:: ../_static/results/final_results/bernoulli/normal.mp4
+   :width: 450
+
+
+Noise in the Input
+~~~~~~~~~~~~~~~~~~
+
+The following videos show the behaviour of the model if each *input* pixel is flipped with a probability of :math:`0.005`.
+The model is not able to filter all noise. A reason is that each filter activates quite strongly to noise in the input data,
+leading to many active neurons at the same position. This noise roughly correspond to the same pattern that can
+be observed at line endings. Therefore, the noise receives lateral support and is not properly suppressed by inhibitory signals.
+
+**Fixed Threshold**
+
+.. video:: ../_static/results/final_results/threshold/005_noise.mp4
+   :width: 450
+
+**Bernoulli Sampling**
+
+.. video:: ../_static/results/final_results/bernoulli/005_noise.mp4
+   :width: 450
+
+
+Noise in the Feature Channels
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The same experiment is repeated, but this time the noise is added to each *feature channel* after the filter has been applied.
+Thus, the same amount of noise is added, but not at the same position per channel.
+As it can be observed, the model is able to filter the noise much better.
+The reason is that the noise is not concentrated at the same position per channel, but is distributed over the whole image.
+Therefore, the noise does not receive enough lateral support and is suppressed.
+
+**Fixed Threshold**
+
+.. video:: ../_static/results/final_results/threshold/005_noise_per_channel.mp4
+   :width: 450
+
+**Bernoulli Sampling**
+
+.. video:: ../_static/results/final_results/bernoulli/005_noise_per_channel.mp4
+   :width: 450
+
+
+Interrupted Line
+~~~~~~~~~~~~~~~~
+
+The following videos show the behaviour of the model if the line is interrupted in the middle.
+Due to the lateral support, the model is able to reconstruct the line if up to :math:`8` pixels are missing.
+This is quite remarkable, as the model has never seen such a line during training and the lateral support range
+is limited to :math:`11` pixels.
+
+
+5 Missing Pixels
+^^^^^^^^^^^^^^^^
+
+**Fixed Threshold**
+
+.. video:: ../_static/results/final_results/threshold/5_black_pixels.mp4
+   :width: 450
+
+**Bernoulli Sampling**
+
+.. video:: ../_static/results/final_results/bernoulli/5_black_pixels.mp4
+   :width: 450
+
+8 Missing Pixels
+^^^^^^^^^^^^^^^^
+
+**Fixed Threshold**
+
+.. video:: ../_static/results/final_results/threshold/8_black_pixels.mp4
+   :width: 450
+
+**Bernoulli Sampling**
+
+.. video:: ../_static/results/final_results/bernoulli/8_black_pixels.mp4
+   :width: 450
+
+10 Missing Pixels
+^^^^^^^^^^^^^^^^^
+
+**Fixed Threshold**
+
+.. video:: ../_static/results/final_results/threshold/10_black_pixels.mp4
+   :width: 450
+
+**Bernoulli Sampling**
+
+.. video:: ../_static/results/final_results/bernoulli/10_black_pixels.mp4
+   :width: 450

_sources/thesis.rst.txt

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+Thesis
+======
+
+.. raw:: html
+
+  <embed>
+    <object data="_static/results/msc_thesis-Pascal_Sager-V1_0.pdf" type="application/pdf" width="100%" height="600px">
+      <p>Unable to display PDF file. <a href="_static/results/msc_thesis-Pascal_Sager-V1_0.pdf" target="_blank">Download</a> instead.</p>
+    </object>
+  </embed>