On the Weight Dynamics of Deep Normalized Networks

• URL: http://arxiv.org/abs/2306.00700v3
• Date: Fri, 24 May 2024 14:12:25 GMT
• Title: On the Weight Dynamics of Deep Normalized Networks
• Authors: Christian H. X. Ali Mehmeti-Göpel, Michael Wand,
• Abstract summary: High disparities in effective learning rates (ELRs) across layers in deep neural networks can negatively affect trainability. We formalize how these disparities evolve over time by modeling weight dynamics of networks with normalization layers. We prove that when training with any constant learning rate, ELR ratios converge to 1, despite initial gradient explosion.
• Score: 5.250288418639077
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Recent studies have shown that high disparities in effective learning rates (ELRs) across layers in deep neural networks can negatively affect trainability. We formalize how these disparities evolve over time by modeling weight dynamics (evolution of expected gradient and weight norms) of networks with normalization layers, predicting the evolution of layer-wise ELR ratios. We prove that when training with any constant learning rate, ELR ratios converge to 1, despite initial gradient explosion. We identify a ``critical learning rate" beyond which ELR disparities widen, which only depends on current ELRs. To validate our findings, we devise a hyper-parameter-free warm-up method that successfully minimizes ELR spread quickly in theory and practice. Our experiments link ELR spread with trainability, a relationship that is most evident in very deep networks with significant gradient magnitude excursions.

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