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The brain can be modelled as a high-dimensional dynamical system. Despite its high dimensionality, many components of the brain during specific functions can be understood through some lower-dimensional representation. We call this representation ”the hidden dynamics” that underlie the activity of the brain’s neurons.These hidden dynamics provide a good description of whatever function the brain is performing. Here, we firstly attempt to understand whether dynamics can be extracted as a low dimensional embedding of neural population (corresponding roughly to different layers in V1 ). On the other hand, we try to determine how many latent dimensions are needed to cluster - or classify - different neural populations activities. We hypothesized that, given the noisy activity of many neurons, the relevant dynamics may be seen as a nonlinear combination of a small fraction of the total neurons in each physiological layer. Using the Stringer dataset [1][2], we trained an LSTM [3] (i.e. RNN ) to encode a layer of neurons. This encoding was accomplished by training the neuron to reconstruct the input at the output while passing the input through a low-dimensional hidden layer to force the network to compress the input data. Assuming that the network is able to get a good reconstruction, this hidden layer contains the compression of the neurons into a lower-dimensional space. During the preliminary phase of our work, by running several hyperparameter optimization sweeps, we discovered that the optimal dimension - in a reconstruction task - for the latent space is rather limited,- 75 dims out of 1131 neurons per layer - i.e. 7% of the original signals dimension. This is an encouraging result, which apparently testify our starting hypothesis. Now, given that the reconstruction error is minimized, we can shift our attention on the latent dynamics representation for each anatomical layer. Possible future directions will explore the existence of multi-scale temporal dynamics and how to efficiently extract them. From this perspective, either more advanced RNN’s regularization techniques or the use of architectures, e.g. LFADS [4] more grounded on dynamical systems aspects.
[1] Stringer, Carsen, et al. “Spontaneous behaviors drive multidimensional, brainwide activity.” Science 364.6437 (2019).
[2] Stringer, Carsen, et al. “High-precision coding in visual cortex.” Cell 184.10 (2021): 2767-2778.
[3] Hocreiter, Sepp, et al. ”Long Short-Term Memory”, Neural Computation Volume 9 Issue 8 (1997)
[4] Pandarinath, Chethan, et al. ”Inferring single-trial neural population dynamics using sequential auto-encoders” Nature Methods 15, 805–815 (2018)
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ToDo - List of libraries
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git clone https://github.com/sazio/NMAs.git
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See the open issues for a list of proposed features (and known issues).
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git commit -m 'Add some AmazingFeature') - Push to the Branch (
git push origin feature/AmazingFeature) - Open a Pull Request
MIT License
Copyright (c) 2021 Simone Azeglio, Chetan Dhulipalla , Khalid Saifullah
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Simone Azeglio - email : [email protected] - linkedin - twitter
Chetan Dhulipalla - email : - linkedin - twitter
Khalid Saifullah - email : - linkedin - twitter
Project Link: https://github.com/sazio/NMAs
