Upper Bounds on the Generalization Error of Deep Learning Models via Local Robustness and Stability

• URL: http://arxiv.org/abs/2606.16883v1
• Date: Mon, 15 Jun 2026 15:55:22 GMT
• Title: Upper Bounds on the Generalization Error of Deep Learning Models via Local Robustness and Stability
• Abstract summary: Generalization is a critical property of data-driven models, particularly deep learning models deployed in safety-critical applications.<n>Most existing bounds suffer from vacuousness in practical settings, yielding loose upper bounds that greatly exceed the actual error rates.<n>We propose a generalization bound that scales the robustness term according to the number of stable and unstable samples within each sub-region.
• Score: 0.6717411448500911
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Generalization is a critical property of data-driven models, particularly deep learning models deployed in safety-critical applications. Robustness-based generalization bounds have gained attention as a principled way to link robustness properties to generalization performance, often in a data-dependent manner. However, most existing bounds suffer from vacuousness in practical settings, yielding loose upper bounds that greatly exceed the actual error rates and limiting their usefulness for real-world evaluation. While this issue is often attributed to the uncertainty term, a substantial part of the problem originates from the robustness term itself, particularly for the 0-1 loss. Existing approaches typically treat the robustness term as a global measure, ignoring its variation across different sub-regions of the input space. In this work, we propose a generalization bound that addresses this limitation by scaling the robustness term according to the number of stable and unstable samples within each sub-region. Our bounds incorporate both data- and model-dependent factors while maintaining practical relevance (yielding tighter upper bounds on true error). Experiments on models trained on the ImageNet dataset show that our bounds remain consistently non-vacuous and achieve the tightest estimates among existing methods, closely aligning with empirical performance across a range of robust deep neural networks.

Related papers

• Improving Adversarial Robustness of Attribution via Implicit Regularization [9.78455276849371]
  adversarial robustness of attributions is a fundamental requirement for reliable explainability in deep learning.<n>We show that robustness can arise implicitly from the learning dynamics of standard gradient descent.<n>Our results highlight learning dynamics as a principled and practical mechanism for robust explainability.
  arXiv  Detail & Related papers  (2026-05-28T14:19:39Z)
• Out of Context: Reliability in Multimodal Anomaly Detection Requires Contextual Inference [54.774686416991386]
  We argue that multimodal anomaly detection should be reframed as a cross-modal contextual inference problem.<n>This perspective has implications for model design, evaluation protocols, and benchmark construction.
  arXiv  Detail & Related papers  (2026-04-14T19:32:55Z)
• Practical Global and Local Bounds in Gaussian Process Regression via Chaining [4.500208956289746]
  We propose a chaining-based framework for estimating upper and lower bounds on the expected extreme values over unseen data.<n>We also develop a novel method for local uncertainty quantification at specified inputs.
  arXiv  Detail & Related papers  (2025-11-12T09:30:01Z)
• It's All in the Mix: Wasserstein Classification and Regression with Mixed Features [2.2685251390114565]
  We develop and analyze distributionally robust prediction models that faithfully account for the presence of discrete features.<n>We demonstrate that our models can significantly outperform existing methods that are agnostic to the presence of discrete features.
  arXiv  Detail & Related papers  (2023-12-19T15:15:52Z)
• RobustMQ: Benchmarking Robustness of Quantized Models [54.15661421492865]
  Quantization is an essential technique for deploying deep neural networks (DNNs) on devices with limited resources. We thoroughly evaluated the robustness of quantized models against various noises (adrial attacks, natural corruptions, and systematic noises) on ImageNet. Our research contributes to advancing the robust quantization of models and their deployment in real-world scenarios.
  arXiv  Detail & Related papers  (2023-08-04T14:37:12Z)
• Quantifying Model Uncertainty for Semantic Segmentation using Operators in the RKHS [20.348825818435767]
  We present a framework for high-resolution predictive uncertainty quantification of semantic segmentation models. We use a multi-moment functional definition of uncertainty associated with the model's feature space in the kernel reproducing the Hilbert space (RKHS) This leads to a significantly more accurate view of model uncertainty than conventional Bayesian methods.
  arXiv  Detail & Related papers  (2022-11-03T17:10:49Z)
• Instance-Dependent Generalization Bounds via Optimal Transport [51.71650746285469]
  Existing generalization bounds fail to explain crucial factors that drive the generalization of modern neural networks. We derive instance-dependent generalization bounds that depend on the local Lipschitz regularity of the learned prediction function in the data space. We empirically analyze our generalization bounds for neural networks, showing that the bound values are meaningful and capture the effect of popular regularization methods during training.
  arXiv  Detail & Related papers  (2022-11-02T16:39:42Z)
• Robustness Implies Generalization via Data-Dependent Generalization Bounds [24.413499775513145]
  This paper proves that robustness implies generalization via data-dependent generalization bounds. We present several examples, including ones for lasso and deep learning, in which our bounds are provably preferable.
  arXiv  Detail & Related papers  (2022-06-27T17:58:06Z)
• Improving Generalization via Uncertainty Driven Perturbations [107.45752065285821]
  We consider uncertainty-driven perturbations of the training data points. Unlike loss-driven perturbations, uncertainty-guided perturbations do not cross the decision boundary. We show that UDP is guaranteed to achieve the robustness margin decision on linear models.
  arXiv  Detail & Related papers  (2022-02-11T16:22:08Z)
• Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustness [68.97830259849086]
  Most datasets only capture a simpler subproblem and likely suffer from spurious features. We study adversarial robustness - a local generalization property - to reveal hard, model-specific instances and spurious features. Unlike in other applications, where perturbation models are designed around subjective notions of imperceptibility, our perturbation models are efficient and sound. Surprisingly, with such perturbations, a sufficiently expressive neural solver does not suffer from the limitations of the accuracy-robustness trade-off common in supervised learning.
  arXiv  Detail & Related papers  (2021-10-21T07:28:11Z)
• GenDICE: Generalized Offline Estimation of Stationary Values [108.17309783125398]
  We show that effective estimation can still be achieved in important applications. Our approach is based on estimating a ratio that corrects for the discrepancy between the stationary and empirical distributions. The resulting algorithm, GenDICE, is straightforward and effective.
  arXiv  Detail & Related papers  (2020-02-21T00:27:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.