The Complexity Dynamics of Grokking
Keywords: Compression, Complexity, Generalization, Grokking, Minimum Description Length
TL;DR: We track the complexity dynamics of neural networks during training to understand grokking, using insights from the theory of Kolmogorov complexity.
Abstract: We investigate the phenomenon of generalization through the lens of compression. In particular, we study the complexity dynamics of neural networks to explain \emph{grokking}, where networks suddenly transition from memorizing to generalizing solutions long after over-fitting the training data. To this end we introduce a new measure of intrinsic complexity for neural networks based on the theory of Kolmogorov complexity. Tracking this metric throughout network training, we find a consistent pattern in training dynamics, consisting of a rise and fall in complexity. We demonstrate that this corresponds to memorization followed by generalization. Based on insights from rate--distortion theory and the minimum description length principle, we lay out a principled approach to lossy compression of neural networks, and connect our complexity measure to explicit generalization bounds. Based on a careful analysis of information capacity in neural networks, we propose a new regularization method which encourages networks towards low-rank representations by penalizing their spectral entropy, and find that our regularizer outperforms baselines in total compression of the dataset.
Primary Area: learning theory
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Submission Number: 8354
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