2/ A Nobel prize discovery was that cells in the entorhinal cortex of mice (a brain region thought to mediate navigation) fire in hexagonal patterns as the mouse moves thru space. But if these hexagonal grids are the answer to a computational question, then what is the question?
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3/ We show that networks trained to path-integrate, by converting velocity inputs to position outputs, spontaneously generate hexagonal firing patterns in their hidden reps under simple biological firing rate constraints.
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4/ Previous work training neural networks to path-integrate instead developed either square or more amorphous firing fields (see citations in paper, including work by
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5/ To explain and unify these diverse numerical results, we also developed a mathematical theory, based on the theory of pattern formation, that explains when and why grid structure emerges, and what lattice (amorphous, square or hexagonal) would dominate under diff. conditionspic.twitter.com/c39XQY05Xh
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6/ In upcoming work we will explain how the connectivity and dynamics of these trained neural networks conspire to both achieve path integration and generate hexagonal grid cells.
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These patterns remind me of the principal components of natural, unaligned images: (image from http://cs231n.github.io/neural-networks-2/ …)pic.twitter.com/ozvPHAqR9F
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Will be interested to see how this theory might complement
@Numenta’s expanded notion of grid cells.@rhyolightHvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi
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Is it your view that grid cells work in some sort of cartesian coordinates paradigm?
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No one knows why this is happening yet.
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Very interesting, I need to reread carefully to understand.. how general is the multiple plane wave solution to path integration? It has cropped up before, e.g. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3972729/ …, https://www.jneurosci.org/content/34/18/6224.short …, and may relate to periodic non-grids toohttps://science.sciencemag.org/content/337/6096/853 …
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