Representational Dissimilarity Metric Spaces for Stochastic Neural NetworksDownload PDF

Published: 01 Feb 2023, Last Modified: 14 Jul 2024ICLR 2023 posterReaders: Everyone
Keywords: stochastic neural networks, noise, representational geometry, dissimilarity metrics
TL;DR: Representational dissimilarity metrics that account for noise geometry in biological and artificial neural responses.
Abstract: Quantifying similarity between neural representations---e.g. hidden layer activation vectors---is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks that lack stochastic layers) or averaged responses (e.g., trial-averaged firing rates in biological data). However, these measures of _deterministic_ representational similarity ignore the scale and geometric structure of noise, both of which play important roles in neural computation. To rectify this, we generalize previously proposed shape metrics (Williams et al. 2021) to quantify differences in _stochastic_ representations. These new distances satisfy the triangle inequality, and thus can be used as a rigorous basis for many supervised and unsupervised analyses. Leveraging this novel framework, we find that the stochastic geometries of neurobiological representations of oriented visual gratings and naturalistic scenes respectively resemble untrained and trained deep network representations. Further, we are able to more accurately predict certain network attributes (e.g. training hyperparameters) from its position in stochastic (versus deterministic) shape space.
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