Generalized Shape Metrics on Neural Representations

Title: Generalized Shape Metrics on Neural Representations
Authors: Alex H. Williams, Erin Kunz, Simon Kornblith, Scott W. Linderman
Published: 27th October 2021 (Wednesday) @ 19:48:55
Link: http://arxiv.org/abs/2110.14739v2

Abstract

Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are trained on, or biologically adapted to, similar tasks. A standardized set of analysis tools is now needed to identify how network-level covariates — such as architecture, anatomical brain region, and model organism — impact neural representations (hidden layer activations). Here, we provide a rigorous foundation for these analyses by defining a broad family of metric spaces that quantify representational dissimilarity. Using this framework we modify existing representational similarity measures based on canonical correlation analysis to satisfy the triangle inequality, formulate a novel metric that respects the inductive biases in convolutional layers, and identify approximate Euclidean embeddings that enable network representations to be incorporated into essentially any off-the-shelf machine learning method. We demonstrate these methods on large-scale datasets from biology (Allen Institute Brain Observatory) and deep learning (NAS-Bench-101). In doing so, we identify relationships between neural representations that are interpretable in terms of anatomical features and model performance.

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Lecture: https://youtu.be/e02DWc2z8Hc