@inproceedings{
pospisil2023estimating,
title={Estimating shape distances on neural representations with limited samples},
author={Dean A Pospisil and Brett W. Larsen and Sarah E Harvey and Alex H Williams},
booktitle={UniReps:  the First Workshop on Unifying Representations in Neural Models},
year={2023},
url={https://openreview.net/forum?id=iEnGqvuI8W}
}
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.
Estimating shape distances on neural representations with limited samples
Dean A Pospisil Brett W. Larsen Sarah E Harvey Alex H Williams