Canonical Regularisation of Wide Feature-Learning Neural Networks
Researchers have identified a fundamental gap in how gradient flow training behaves across neural network regimes. While kernel-regime networks converge to a well-understood ridge solution that enables noise modeling, feature-learning networks (the backbone of modern deep learning) exhibit different regularization dynamics even as regularization vanishes. This finding challenges assumptions underlying current theoretical frameworks and suggests the inductive biases shaping practical deep networks differ more substantially from their theoretical cousins than previously recognized. The work matters because it exposes a blind spot in our understanding of why wide networks generalize.
Modelwire context
ExplainerThe paper's core finding is not just that feature-learning networks regularize differently, but that this difference persists even as explicit regularization vanishes. This suggests the networks are learning implicit regularization patterns that don't map cleanly onto the ridge solution framework that has dominated theoretical work.
This connects directly to the VAE posterior collapse work from earlier today (the simplex witness certificate paper). Both expose failure modes or hidden behaviors in neural network training that standard theory misses. Where that paper showed how to detect when encoders silently ignore inputs, this one reveals that wide feature-learning networks may be solving optimization problems in ways our mathematical models don't capture. The broader pattern across recent coverage is a shift from assuming networks behave as theory predicts to empirically auditing what they actually do.
If researchers can show that the implicit regularization identified here correlates with generalization gaps on held-out test sets in standard benchmarks (CIFAR-10, ImageNet), that would confirm the finding has practical relevance beyond theory. If the effect vanishes on smaller networks or with explicit regularization reintroduced, that narrows the scope to a specific regime and weakens the claim about fundamental differences.
Coverage we drew on
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MentionsCanonical Regularisation · Neural Networks · Gradient Flow · Ridge Regularisation · NN-GP Correspondence
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