Neural Expansion: A Unified Mechanism for How Deep Neural Networks Generalize

Deep neural networks demonstrate remarkable generalization despite being highly over-parameterized, challenging traditional statistical learning theories. While several theoretical paradigms such as margin-based bounds, PAC-Bayesian analyses, and neural tangent kernels provide global explanations, they often lack mechanistic insight into how generalization emerges from training dynamics. We introduce Neural Expansion, a unified geometric framework that characterizes generalization through the expansion of directionally-selective ray coverage in the input space. Using Generalization Intervals…

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