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.

This work attempts to provide a theory/definition for how to define a match between two clusters of neurons (e.g. two layers), each from a neural network. The definition (Definition 1, in paper) allows one to study the similarity between a pair of neural clusters (of the same size). In this paper, this definition of match is employed in this paper to study two networks of the same architecture but trained with different random initializations. This work seems to be a follow-up work from Convergent Learning [1] and SVCCA [2]. The authors characterize the representation of a neural cluster C as the subspace spanned by the set of activation vectors of C.

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.

This paper is an interesting work which tries to explain similarities and differences between representation learned by different networks in the same architecture. To the extend of their experiments, they train 4 different AlexNet and compare the units of these networks by correlation and mutual information analysis. My discussion: We see that different networks learn similar representations with some level of accompanying uniqueness. It is intriguing to see that, after this paper, these are the unique representations causing performance differences between networks and whether the effect is improving or worsening. Additionally, maybe we might combine these differences at the end to improve network performances by some set of smart tricks.