# Verifying the Generalization of Deep Learning to Out-of-Distribution Domains

arXiv: https://arxiv.org/abs/2406.02024 · HTML: https://mlsanity.com/paper/2406.02024/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 45 references that are in the map.
- First posted on arXiv 4 Jun 2024.

## Builds on (most cited first, 19 of 19)

- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Practical Black-Box Attacks against Machine Learning](https://mlsanity.com/paper/1602.02697/) (2016)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [IPO: Interior-point Policy Optimization under Constraints](https://mlsanity.com/paper/1910.09615/) (2019)
- [Reachability Analysis of Deep Neural Networks with Provable Guarantees](https://mlsanity.com/paper/1805.02242/) (2018)
- [Introduction to Neural Network Verification](https://mlsanity.com/paper/2109.10317/) (2021)
- [Quantitative Verification of Neural Networks And its Security Applications](https://mlsanity.com/paper/1906.10395/) (2019)
- [Perfectly Parallel Fairness Certification of Neural Networks](https://mlsanity.com/paper/1912.02499/) (2019)
- [Formal Verification of Neural Network Controlled Autonomous Systems](https://mlsanity.com/paper/1810.13072/) (2018)
- [Optimization and Abstraction: A Synergistic Approach for Analyzing Neural Network Robustness](https://mlsanity.com/paper/1904.09959/) (2019)
- [Fastened CROWN: Tightened Neural Network Robustness Certificates](https://mlsanity.com/paper/1912.00574/) (2019)
- [Global Optimization of Objective Functions Represented by ReLU Networks](https://mlsanity.com/paper/2010.03258/) (2020)
- [Individual Fairness Guarantees for Neural Networks](https://mlsanity.com/paper/2205.05763/) (2022)
- [Weighted Automata Extraction from Recurrent Neural Networks via Regression on State Spaces](https://mlsanity.com/paper/1904.02931/) (2019)
- [Mo"ET: Mixture of Expert Trees and its Application to Verifiable Reinforcement Learning](https://mlsanity.com/paper/1906.06717/) (2019)
- [Towards Safe Machine Learning for CPS: Infer Uncertainty from Training Data](https://mlsanity.com/paper/1909.04886/) (2019)

## Built on by (most cited first, 2 of 2)

- [Towards Formal Verification of Deep Neural Networks for Object Detection](https://mlsanity.com/paper/2407.01295/) (2024)
- [On Improving Deep Active Learning with Formal Verification](https://mlsanity.com/paper/2512.14170/) (2025)

## Abstract (arXiv)

Deep neural networks (DNNs) play a crucial role in the field of machine learning, demonstrating state-of-the-art performance across various application domains. However, despite their success, DNN-based models may occasionally exhibit challenges with generalization, i.e., may fail to handle inputs that were not encountered during training. This limitation is a significant challenge when it comes to deploying deep learning for safety-critical tasks, as well as in real-world settings characterized by substantial variability. We introduce a novel approach for harnessing DNN verification technology to identify DNN-driven decision rules that exhibit robust generalization to previously unencountered input domains. Our method assesses generalization within an input domain by measuring the level of agreement between independently trained deep neural networks for inputs in this domain. We also efficiently realize our approach by using off-the-shelf DNN verification engines, and extensively evaluate it on both supervised and unsupervised DNN benchmarks, including a deep reinforcement learning (DRL) system for Internet congestion control -- demonstrating the applicability of our approach for real-world settings. Moreover, our research introduces a fresh objective for formal verification, offering the prospect of mitigating the challenges linked to deploying DNN-driven systems in real-world scenarios.