Approaching Deep Learning through the Spectral Dynamics of Weights

David Yunis, Kumar Kshitij Patel, Samuel Wheeler, Pedro Henrique Pamplona Savarese, Gal Vardi, Karen Livescu, Michael Maire, Matthew Walter

Keywords: simplicity bias, grokking, lottery tickets, linear mode connectivity

TL;DR: We show that an optimization bias in the singular values and vectors of weight matrices links together many complex phenomena in deep learning.

Abstract: We propose an empirical approach centered on the spectral dynamics of weights---the behavior of singular values and vectors during optimization---to unify and clarify several phenomena in deep learning. We identify a consistent bias in optimization across various experiments, from small-scale ``grokking'' to large-scale tasks like image classification with ConvNets, image generation with UNets, speech recognition with LSTMs, and language modeling with Transformers. We also demonstrate that weight decay enhances this bias beyond its role as a norm regularizer, even in practical systems. Moreover, we show that these spectral dynamics distinguish memorizing networks from generalizing ones, offering a novel perspective on this longstanding conundrum. Additionally, we leverage spectral dynamics to explore the emergence of well-performing sparse subnetworks (lottery tickets) and the structure of the loss surface through linear mode connectivity. Our findings suggest that spectral dynamics provide a coherent framework to better understand the behavior of neural networks across diverse settings.

Primary Area: interpretability and explainable AI

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Submission Number: 11643