Data coarse graining can improve model performance

• URL: http://arxiv.org/abs/2509.14498v1
• Date: Thu, 18 Sep 2025 00:17:01 GMT
• Title: Data coarse graining can improve model performance
• Authors: Alex Nguyen, David J. Schwab, Vudtiwat Ngampruetikorn,
• Abstract summary: We study a paradox using a solvable model of high-dimensional, ridge-regularized linear regression under 'data coarse graining'<n>Inspired by the renormalization group in statistical physics, we analyze coarse-graining schemes that systematically discard features based on their relevance to the learning task.<n>Our results highlight a complex, nonmonotonic risk landscape shaped by the structure of the data, and illustrate how ideas from statistical physics provide a principled lens for understanding modern machine learning phenomena.
• Score: 7.325551965751601
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Lossy data transformations by definition lose information. Yet, in modern machine learning, methods like data pruning and lossy data augmentation can help improve generalization performance. We study this paradox using a solvable model of high-dimensional, ridge-regularized linear regression under 'data coarse graining.' Inspired by the renormalization group in statistical physics, we analyze coarse-graining schemes that systematically discard features based on their relevance to the learning task. Our results reveal a nonmonotonic dependence of the prediction risk on the degree of coarse graining. A 'high-pass' scheme--which filters out less relevant, lower-signal features--can help models generalize better. By contrast, a 'low-pass' scheme that integrates out more relevant, higher-signal features is purely detrimental. Crucially, using optimal regularization, we demonstrate that this nonmonotonicity is a distinct effect of data coarse graining and not an artifact of double descent. Our framework offers a clear, analytical explanation for why careful data augmentation works: it strips away less relevant degrees of freedom and isolates more predictive signals. Our results highlight a complex, nonmonotonic risk landscape shaped by the structure of the data, and illustrate how ideas from statistical physics provide a principled lens for understanding modern machine learning phenomena.

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