Disentangling Fact from Grid Cell Fiction in Trained Deep Path Integrators

Authors: Rylan Schaeffer, Mikail Khona, Adrian Bertagnoli, Sanmi Koyejo, Ila Rani Fiete

Venue: Biorxiv 2023

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Summary

If you thought our #NeurIPS 2022 paper was spicy, our newest preprint brings twice the heat 🌶️🌶️

🤔🧠 Disentangling Fact from Grid Cell Fiction in Trained Deep Path Integrators 🤔🧠

Joint / @KhonaMikail @FieteGroup @mitbrainandcog @mcgovernmit

🧵👇

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Over the past 5 years, high-profile papers in @NaturePortfolio @NeuroCellPress @NeurIPSConf @iclr_conf claimed that training deep networks to path integrate robustly, generically and surprisingly produce grid-like units matching those in the mammalian medial entorhinal cortex 🧠

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Our #NeurIPS 2022 paper NFL challenged this path integration hypothesis by showing

1) grid-like tuning does not emerge in deep networks trained to path integrate

2) unless researchers insert grid-like tuning via mechanism unrelated to path integration to induce grids

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@SuryaGanguli @dyamins @lisa_giocomo @aran_nayebi & Ben Sorscher wrote a Response to NFL defending the path integration hypothesis

and advocating their preferred “Unified theory for the origin of grid cells”

https://www.biorxiv.org/content/10.1101/2022.11.14.516537v1

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Takeaways:

Path integration insufficient to produce grid cells
Unified Theory is at best occasionally suggestive
Neural regressions methodology should be investigated
For more promising alternative of grid cells, check back in a day 😉

<TODO: Link Biorxiv preprint>

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Unified Theory: “We forge a link between the problem of path integration and the existence of hexagonal grids”

Actually:

Unified Theory designs supervised targets to induce grid-like tuning
Targets don’t affect path integration
Targets biologically unlikely

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The Unified Theory is at best occasionally suggestive

2a) Even with Fourier annulus, grid-like tuning emerges inconsistently, the “Difference of Softmaxes” supervised target provides critical boost not captured by theory, and grid-like tuning is highly seed dependent

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2b) Gaussian supervised targets do not generically produce grid-like tuning. New code by Response achieves grids via unstated implementation details: high dropout = 0.5, large learning rate ~ 0.1, specific optimizers drive grid-like tuning, not path integration

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2b) Densely sweeping recommended hyperparameters using original code by @nayebi_aran @dyamins @SuryaGanguli @lisa_giocomo again shows no grid-like tuning from Gaussian targets

2b) Independent work by @dehongxu @RuiqiGao @weixx2 shows Gaussian supervised targets do not generically produce grid-like tuning

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2c) The Unified Theory predicts that non-negativity constraint should favor hexagonal lattices. We show Tanh->ReLU produces hexagonal AND square lattices in deep path integrators

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2d) We reconfirm NFL’s finding that even with ideal handcrafted targets, grid-like tuning is highly sensitive to hyperparameters

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We conclude by questioning neural regressions. #NeurIPS 2021 Spotlight by @aran_nayebi @dyamins @SuryaGanguli @lisa_giocomo concluded these deep path integrators predict MEC recordings up to noise ceiling

How did neural regressions draw wrong conclusion so confidently?

12/N

NFL hypothesized trained networks might achieve higher neural predictivity scores than competitors simply by providing higher dimensional, richer basis functions

2 indep papers by @EricElmoznino @GretaTuckute found similar trends in different species, modalities, regions

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Preprint: <TODO: Link preprint>

This work was done at & financially supported by @stai_research @StanfordData @StanfordAILab @mitbrainandcog @mcgovernmit

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