Feature Learning and Signal Propagation in Deep Neural Networks

Yizhang Lou; Chris Mingard; Yoonsoo Nam; Soufiane Hayou

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arXiv · 2110.11749

Feature Learning and Signal Propagation in Deep Neural Networks

Yizhang Lou·Chris Mingard·Yoonsoo Nam·Soufiane Hayou

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Abstract

Recent work by Baratin et al. (2021) sheds light on an intriguing pattern that occurs during the training of deep neural networks: some layers align much more with data compared to other layers (where the alignment is defined as the euclidean product of the tangent features matrix and the data labels matrix). The curve of the alignment as a function of layer index (generally) exhibits an ascent-descent pattern where the maximum is reached for some hidden layer. In this work, we provide the first explanation for this phenomenon. We introduce the Equilibrium Hypothesis which connects this alignment pattern to signal propagation in deep neural networks. Our experiments demonstrate an excellent match with the theoretical predictions.

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BibTeX RIS

Yizhang Lou, Chris Mingard, Yoonsoo Nam, Soufiane Hayou. 2021-10-22. Feature Learning and Signal Propagation in Deep Neural Networks. https://arxiv.org/abs/2110.11749

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