Insights on representational similarity in neural networks with canonical correlation

TL;DR

This paper introduces an improved projection weighted CCA method to compare neural network representations, revealing how network architecture, training dynamics, and task type influence representational similarity in CNNs and RNNs.

Contribution

The paper develops an enhanced CCA technique for neural representation comparison and applies it to analyze CNNs and RNNs, providing new insights into their training and functional dynamics.

Findings

Networks that generalize have more similar representations than those that memorize.

Wider networks converge to more similar solutions than narrower ones.

RNNs show bottom-up convergence during training and high variability in hidden states.

Abstract

Comparing different neural network representations and determining how representations evolve over time remain challenging open questions in our understanding of the function of neural networks. Comparing representations in neural networks is fundamentally difficult as the structure of representations varies greatly, even across groups of networks trained on identical tasks, and over the course of training. Here, we develop projection weighted CCA (Canonical Correlation Analysis) as a tool for understanding neural networks, building off of SVCCA, a recently proposed method (Raghu et al., 2017). We first improve the core method, showing how to differentiate between signal and noise, and then apply this technique to compare across a group of CNNs, demonstrating that networks which generalize converge to more similar representations than networks which memorize, that wider networks converge to more similar solutions than narrow networks, and that trained networks with identical topology but different learning rates converge to distinct clusters with diverse representations. We also investigate the representational dynamics of RNNs, across both training and sequential timesteps, finding that RNNs converge in a bottom-up pattern over the course of training and that the hidden state is highly variable over the course of a sequence, even when accounting for linear transforms. Together, these results provide new insights into the function of CNNs and RNNs, and demonstrate the utility of using CCA to understand representations.