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Workshop: UniReps: Unifying Representations in Neural Models

Estimating shape distances on neural representations with limited samples

Dean Pospisil · Brett Larsen · Sarah Harvey · Alex Williams

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presentation: UniReps: Unifying Representations in Neural Models
Fri 15 Dec 6:15 a.m. PST — 3:15 p.m. PST


Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their statistical efficiency or quantified estimator uncertainty in data-limited regimes. Here, we derive upper and lower bounds on the worst-case convergence of standard estimators of shape distance—a measure of representational dissimilarity proposed by Williams et al. (2021). These bounds reveal the challenging nature of the problem in high-dimensional feature spaces. To overcome these challenges, we introduce a novel method-of-moments estimator with a tunable bias-variance tradeoff parameterized by an upper bound on bias. We show that this estimator achieves superior performance to standard estimators in simulation and on neural data, particularly in high-dimensional settings. Our theoretical work and estimator thus respectively define and dramatically expand the scope of neural data for which geometric similarity can be accurately measured.

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