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

arXiv: https://arxiv.org/abs/2606.16883 · HTML: https://mlsanity.com/paper/2606.16883/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 13 of 13)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Robust Large Margin Deep Neural Networks](https://mlsanity.com/paper/1605.08254/) (2016)
- [A Comprehensive Evaluation Framework for Deep Model Robustness](https://mlsanity.com/paper/2101.09617/) (2021)
- [Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes](https://mlsanity.com/paper/1908.02419/) (2019)
- [Generalization in Neural Networks: A Broad Survey](https://mlsanity.com/paper/2209.01610/) (2022)
- [Detecting Brittle Decisions for Free: Leveraging Margin Consistency in Deep Robust Classifiers](https://mlsanity.com/paper/2406.18451/) (2024)
- [Predicting the generalization gap in neural networks using topological data analysis](https://mlsanity.com/paper/2203.12330/) (2022)
- [Negative Selection Approach to support Formal Verification and Validation of BlackBox Models' Input Constraints](https://mlsanity.com/paper/2209.01411/) (2022)
- [Generalization and Risk Bounds for Recurrent Neural Networks](https://mlsanity.com/paper/2411.02784/) (2024)

## Abstract (arXiv)

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.