Initializing ReLU networks in an expressive subspace of weights

Dayal Singh; G J Sreejith

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arXiv · 2103.12499

Initializing ReLU networks in an expressive subspace of weights

Dayal Singh·G J Sreejith

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Abstract

Using a mean-field theory of signal propagation, we analyze the evolution of correlations between two signals propagating forward through a deep ReLU network with correlated weights. Signals become highly correlated in deep ReLU networks with uncorrelated weights. We show that ReLU networks with anti-correlated weights can avoid this fate and have a chaotic phase where the signal correlations saturate below unity. Consistent with this analysis, we find that networks initialized with anti-correlated weights can train faster (in a teacher-student setting) by taking advantage of the increased expressivity in the chaotic phase. Combining this with a previously proposed strategy of using an asymmetric initialization to reduce dead node probability, we propose an initialization scheme that allows faster training and learning than the best-known initializations.

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cs.LG cond-mat.dis-nn cond-mat.stat-mech

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Dayal Singh, G J Sreejith. 2021-03-23. Initializing ReLU networks in an expressive subspace of weights. https://arxiv.org/abs/2103.12499

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