Non-vacuous Generalization Bounds for Deep Neural Networks without any modification to the trained models

ArXi:2503.07325v2 Announce Type: replace Understanding and certifying the behavior of modern deep neural networks remains a fundamental challenge in reliable machine learning. We Our approach reveals that generalization is governed by the interaction between the trained model and the geometry of the data distribution. We decompose the generalization error into two interpretable components: a distributional complexity term, capturing how the data mass is distributed across the input space, and local model-behavior terms, capturing the network's behavior within individual regions.