Towards Understanding Learning Representations: To What Extent Do Different Neural Networks Learn the Same Representation

TL;DR

This paper investigates the similarity of learned representations in neural networks with identical architectures but different initializations, revealing that such representations are less similar than previously assumed, based on a new theoretical framework and experiments.

Contribution

It introduces a novel neuron activation subspace match model and algorithms to quantify representation similarity between neural networks.

Findings

Representations in the same convolutional layers are less similar than expected.

The proposed theory characterizes the structure of neuron activation matches.

Experimental results challenge the assumption of high similarity in learned representations.

Abstract

It is widely believed that learning good representations is one of the main reasons for the success of deep neural networks. Although highly intuitive, there is a lack of theory and systematic approach quantitatively characterizing what representations do deep neural networks learn. In this work, we move a tiny step towards a theory and better understanding of the representations. Specifically, we study a simpler problem: How similar are the representations learned by two networks with identical architecture but trained from different initializations. We develop a rigorous theory based on the neuron activation subspace match model. The theory gives a complete characterization of the structure of neuron activation subspace matches, where the core concepts are maximum match and simple match which describe the overall and the finest similarity between sets of neurons in two networks respectively. We also propose efficient algorithms to find the maximum match and simple matches. Finally, we conduct extensive experiments using our algorithms. Experimental results suggest that, surprisingly, representations learned by the same convolutional layers of networks trained from different initializations are not as similar as prevalently expected, at least in terms of subspace match.