Extended critical regimes of deep neural networks

Cheng Kevin Qu; Asem Wardak; Pulin Gong

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arXiv · 2203.12967

Extended critical regimes of deep neural networks

Cheng Kevin Qu·Asem Wardak·Pulin Gong

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Abstract

Deep neural networks (DNNs) have been successfully applied to many real-world problems, but a complete understanding of their dynamical and computational principles is still lacking. Conventional theoretical frameworks for analysing DNNs often assume random networks with coupling weights obeying Gaussian statistics. However, non-Gaussian, heavy-tailed coupling is a ubiquitous phenomenon in DNNs. Here, by weaving together theories of heavy-tailed random matrices and non-equilibrium statistical physics, we develop a new type of mean field theory for DNNs which predicts that heavy-tailed weights enable the emergence of an extended critical regime without fine-tuning parameters. In this extended critical regime, DNNs exhibit rich and complex propagation dynamics across layers. We further elucidate that the extended criticality endows DNNs with profound computational advantages: balancing the contraction as well as expansion of internal neural representations and speeding up training processes, hence providing a theoretical guide for the design of efficient neural architectures.

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

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BibTeX RIS

Cheng Kevin Qu, Asem Wardak, Pulin Gong. 2022-03-24. Extended critical regimes of deep neural networks. https://arxiv.org/abs/2203.12967

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