| Abstract: |
| Populations of neurons in the brain encode complex information through the aggregate activity -- so called \emph{spikes} -- of neurons in those populations. Dimensionality reduction methods are commonly used to qualitatively investigate such population activity, driving much modern understanding of the function of neural systems. However, when the represented information carries non-trivial topology, these methods can obscure salient structure.
Topological methods have been successfully employed to characterize non-linear organizing principles of neural population activity. As these work without dimensionality reduction, we can use them to investigate fundamental questions about population behavior. For example, is propagation of nonlinear coordinate systems a generic feature of biological neural networks, or must this be learned? If learning is necessary, what mechanisms can produce it?
In this talk, we will apply recent developments in TDA to demonstrate that simple Hebbian spike-timing dependent plasticity reorganizes feed-forward networks to correctly propagate toroidal coordinate systems. We also observe the emergence of geometrically non-local receptive field types, postdicting several experimentally observed phenomena. These observations provide quantitative support for the hypothesis that simple biologically plausible plasticity mechanisms suffice explain topological organization observed in real neural systems. |
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