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This paper critically examines the theoretical debate surrounding benign interpolation in deep learning, arguing that recent appeals to "simplicity" as an explanation lack rigorous mathematical grounding compared to classical statistical learning theory. The authors contend that current interpretations conflate substantive assumptions with Occam's razor without provable connections between individual model properties and generalization performance. This analysis is essential for researchers seeking a clearer understanding of the foundational limits of modern machine learning explanations.
Benign interpolation and Occam's razor
arXiv:2608.03386v1 Announce Type: new Abstract: Contemporary deep learning methods generalize well even when they fit their training data perfectly, a phenomenon known as benign interpolation. This phenomenon cannot be accounted for by classical statistical learning theory and has prompted a range of attempted new explanations in the statistics and machine learning literature. A common feature of these new proposals is an appeal to a simplicity preference among interpolating models, often presented as a form of Occam's razor. We clarify this debate for a philosophical audience and argue that this new appeal to simplicity creates an explanatory gap. The classical theory offers theorems which connect the simplicity of model classes to good generalization, thus underwriting methodological simplicity norms. The new accounts instead appeal to properties of individual models, which they interpret as a kind of simplicity. Lacking a provable connection to generalization, it is the name "simplicity" that does the work a theorem used to do, making a substantive and unargued assumption look like the application of a familiar methodological principle.
Abstract:Contemporary deep learning methods generalize well even when they fit their training data perfectly, a phenomenon known as benign interpolation. This phenomenon cannot be accounted for by classical statistical learning theory and has prompted a range of attempted new explanations in the statistics and machine learning literature. A common feature of these new proposals is an appeal to a simplicity preference among interpolating models, often presented as a form of Occam's razor. We clarify this debate for a philosophical audience and argue that this new appeal to simplicity creates an explanatory gap. The classical theory offers theorems which connect the simplicity of model classes to good generalization, thus underwriting methodological simplicity norms. The new accounts instead appeal to properties of individual models, which they interpret as a kind of simplicity. Lacking a provable connection to generalization, it is the name "simplicity" that does the work a theorem used to do, making a substantive and unargued assumption look like the application of a familiar methodological principle.
Machine Learning (cs.LG)
arXiv:2608.03386 [cs.LG]
(or arXiv:2608.03386v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.03386 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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