# Verifying Generalization in Deep Learning

arXiv: https://arxiv.org/abs/2302.05745 · HTML: https://mlsanity.com/paper/2302.05745/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 68 of its 121 references that are in the map.
- First posted on arXiv 11 Feb 2023.

## Builds on (most cited first, 30 of 68)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Deep Reinforcement Learning: An Overview](https://mlsanity.com/paper/1701.07274/) (2017)
- [Adversarial Attacks on Neural Network Policies](https://mlsanity.com/paper/1702.02284/) (2017)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [Safety Verification of Deep Neural Networks](https://mlsanity.com/paper/1610.06940/) (2016)
- [Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks](https://mlsanity.com/paper/1705.01320/) (2017)
- [Randomized Prior Functions for Deep Reinforcement Learning](https://mlsanity.com/paper/1806.03335/) (2018)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [Assessing Generalization in Deep Reinforcement Learning](https://mlsanity.com/paper/1810.12282/) (2018)
- [An approach to reachability analysis for feed-forward ReLU neural networks](https://mlsanity.com/paper/1706.07351/) (2017)
- [A General Framework for Uncertainty Estimation in Deep Learning](https://mlsanity.com/paper/1907.06890/) (2019)
- [Reachability Analysis of Deep Neural Networks with Provable Guarantees](https://mlsanity.com/paper/1805.02242/) (2018)
- [Sample Efficient Reinforcement Learning with REINFORCE](https://mlsanity.com/paper/2010.11364/) (2020)
- [Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks](https://mlsanity.com/paper/1708.03322/) (2017)
- [Towards More Practical Adversarial Attacks on Graph Neural Networks](https://mlsanity.com/paper/2006.05057/) (2020)
- [An Abstraction-Based Framework for Neural Network Verification](https://mlsanity.com/paper/1910.14574/) (2019)
- [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)
- [An SMT-Based Approach for Verifying Binarized Neural Networks](https://mlsanity.com/paper/2011.02948/) (2020)

## Built on by (most cited first, 11 of 11)

- [Formally Explaining Neural Networks within Reactive Systems](https://mlsanity.com/paper/2308.00143/) (2023)
- [Local vs. Global Interpretability: A Computational Complexity Perspective](https://mlsanity.com/paper/2406.02981/) (2024)
- [Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificates](https://mlsanity.com/paper/2405.14058/) (2024)
- [Verification-Guided Shielding for Deep Reinforcement Learning](https://mlsanity.com/paper/2406.06507/) (2024)
- [Hard to Explain: On the Computational Hardness of In-Distribution Model Interpretation](https://mlsanity.com/paper/2408.03915/) (2024)
- [Analyzing Adversarial Inputs in Deep Reinforcement Learning](https://mlsanity.com/paper/2402.05284/) (2024)
- [Towards Formal Verification of Deep Neural Networks for Object Detection](https://mlsanity.com/paper/2407.01295/) (2024)
- [Safe and Reliable Training of Learning-Based Aerospace Controllers](https://mlsanity.com/paper/2407.07088/) (2024)
- [PICID: Proof-Driven Clause Learning in Neural Network Verification](https://mlsanity.com/paper/2503.12083/) (2025)
- [Incremental Neural Network Verification via Learned Conflicts](https://mlsanity.com/paper/2603.12232/) (2026)
- [Aquatic Navigation: A Challenging Benchmark for Deep Reinforcement Learning](https://mlsanity.com/paper/2405.20534/) (2024)

## Abstract (arXiv)

Deep neural networks (DNNs) are the workhorses of deep learning, which constitutes the state of the art in numerous application domains. However, DNN-based decision rules are notoriously prone to poor generalization, i.e., may prove inadequate on inputs not encountered during training. This limitation poses a significant obstacle to employing deep learning for mission-critical tasks, and also in real-world environments that exhibit high variability. We propose a novel, verification-driven methodology for identifying DNN-based decision rules that generalize well to new input domains. Our approach quantifies generalization to an input domain by the extent to which decisions reached by independently trained DNNs are in agreement for inputs in this domain. We show how, by harnessing the power of DNN verification, our approach can be efficiently and effectively realized. We evaluate our verification-based approach on three deep reinforcement learning (DRL) benchmarks, including a system for Internet congestion control. Our results establish the usefulness of our approach. More broadly, our work puts forth a novel objective for formal verification, with the potential for mitigating the risks associated with deploying DNN-based systems in the wild.