2/10 There’s been a lot of talk in the computational neuro world about how neurons are frequently correlated, confining their activity to a “low-dimensional” subspace (or manifold).
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Excited to post my preprint about RNNs, dynamics, and #manifolds! https://www.biorxiv.org/content/10.1101/2019.12.19.883207v1.full.pdf …
Here’s a quick #tweetprint explaining the main ideas: 1/10
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3/10 There have been some awesome papers looking at how low-dimensional activity relates to the way that brains (and artificial networks) solve tasks. Shoutout to
@_rdgao ao for this awesome summary of work along those lines:https://www.simonsfoundation.org/2019/07/31/searching-for-the-hidden-factors-underlying-the-neural-code/ …Prikaži ovu nit -
4/10 One method involves studying recurrent neural network (RNN) models as a dynamical system, and uses locally linear approximations of dynamics to describe what’s going on:https://twitter.com/SussilloDavid/status/1185954399849332736 …
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5/10 But what if we want to do the reverse? Maybe we’re interested in studying the connectivity of networks that solve a task in a known way, or studying the kinds of representations that are optimal for a network.
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6/10 We had the idea of flipping linearization around: what if we specify the local behavior at a bunch of points, and solve for the connectivity of networks that have the desired global dynamics?pic.twitter.com/HiO78mQIRO
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7/10 We tried this out as a way of creating ring attractors with a “semi-discrete” working memory: network dynamics quickly move onto a low-d ring, and slowly move towards a few states that are specified by a known drift functionpic.twitter.com/bsduNvfcgW
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8/10 We extended the approach to allow for inputs that could control the speed of movement around the ring. This provides a simple explanation for how inputs can flexibly change network dynamicspic.twitter.com/xvKc5rc7BC
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9/10 Finally, we asked some questions about what happens when you bend the ring into higher dimensions, showing that the geometry of the ring manifold has an effect on how stable it is
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10/10 Check out the paper for more! Special thanks to
@mjaz for being a supportive mentor throughout this projectPrikaži ovu nit
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