2018/02/23 by Roman Novak, Novak, Roman, Yasaman Bahri +8 · 1 voice · 45 citations
Computer Science · Mathematics · #Adversarial Robustness in Machine Learning #Anomaly Detection Techniques and Applications #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications #Neural and Evolutionary Computing (cs.NE) #cs.AI #cs.LG #cs.NE #stat.ML
paper · pdf · doi:10.48550/arxiv.1802.08760
Published as a conference paper at ICLR 2018
openalex publication_date 2018/02/23 · arxiv published 2018/02/23 · arxiv created 2018/06/18 · arxiv updated 2018/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In practice it is often found that large over-parameterized neural networks generalize better than their smaller counterparts, an observation that appears to conflict with classical notions of function complexity, which typically favor smaller models. In this work, we investigate this tension between complexity and generalization through an extensive empirical exploration of two natural metrics of complexity related to sensitivity to input perturbations. Our experiments survey thousands of models with various fully-connected architectures, optimizers, and other hyper-parameters, as well as four different image classification datasets. We find that trained neural networks are more robust to input perturbations in the vicinity of the training data manifold, as measured by the norm of the input-output Jacobian of the network, and that it correlates well with generalization. We further establish that factors associated with poor generalization - such as full-batch training or using random labels - correspond to lower robustness, while factors associated with good generalization - such as data augmentation and ReLU non-linearities - give rise to more robust functions. Finally, we demonstrate how the input-output Jacobian norm can be predictive of generalization at the level of individual test points.