mlsanityData to 14 Oct 2026

Verifying Generalization in Deep Learning

arXiv 2302.05745 ↗First posted 11 Feb 2023cs.LG cs.LOcited by 11

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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.

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

68 of 121 references.

References · 68

  1. 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,364
  2. 2017Proximal Policy Optimization Algorithmscited by 15,215
  3. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  4. 2018Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actorcited by 4,885
  5. 2013Playing Atari with Deep Reinforcement Learningcited by 3,274
  6. 2016Adversarial examples in the physical worldcited by 1,769
  7. 2015Deep Reinforcement Learning with Double Q-learningcited by 1,745
  8. 2019Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shiftcited by 1,287
  9. 2016An overview of gradient descent optimization algorithmscited by 1,033
  10. 2016End to End Learning for Self-Driving Carscited by 1,009
  11. 2020A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challengescited by 819
  12. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 744
38 more
  1. 2017Deep Reinforcement Learning: An Overviewcited by 333
  2. 2017Adversarial Attacks on Neural Network Policiescited by 320
  3. 2021Ensemble deep learning: A reviewcited by 284
  4. 2016Safety Verification of Deep Neural Networkscited by 263
  5. 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 242
  6. 2018Randomized Prior Functions for Deep Reinforcement Learningcited by 219
  7. 2018Formal Security Analysis of Neural Networks using Symbolic Intervalscited by 185
  8. 2018Assessing Generalization in Deep Reinforcement Learningcited by 133
  9. 2017An approach to reachability analysis for feed-forward ReLU neural networkscited by 127
  10. 2019A General Framework for Uncertainty Estimation in Deep Learningcited by 119
  11. 2018Reachability Analysis of Deep Neural Networks with Provable Guaranteescited by 93
  12. 2020Sample Efficient Reinforcement Learning with REINFORCEcited by 86
  13. 2017Output Reachable Set Estimation and Verification for Multi-Layer Neural Networkscited by 80
  14. 2020Towards More Practical Adversarial Attacks on Graph Neural Networkscited by 76
  15. 2019An Abstraction-Based Framework for Neural Network Verificationcited by 68
  16. 2021Introduction to Neural Network Verificationcited by 63
  17. 2019Quantitative Verification of Neural Networks And its Security Applicationscited by 56
  18. 2020An SMT-Based Approach for Verifying Binarized Neural Networkscited by 47
  19. 2019Perfectly Parallel Fairness Certification of Neural Networkscited by 42
  20. 2018Formal Verification of Neural Network Controlled Autonomous Systemscited by 41
  21. 2019Optimization and Abstraction: A Synergistic Approach for Analyzing Neural Network Robustnesscited by 40
  22. 2019Fastened CROWN: Tightened Neural Network Robustness Certificatescited by 39
  23. 2020Parallelization Techniques for Verifying Neural Networkscited by 36
  24. 2021Neural Network Robustness as a Verification Property: A Principled Case Studycited by 35
  25. 2020Abstraction based Output Range Analysis for Neural Networkscited by 34
  26. 2021Towards Scalable Verification of Deep Reinforcement Learningcited by 33
  27. 2022Verifying Learning-Based Robotic Navigation Systemscited by 33
  28. 2021Diversity and Generalization in Neural Network Ensemblescited by 32
  29. 2020DeepAbstract: Neural Network Abstraction for Accelerating Verificationcited by 31
  30. 2020Verifying Recurrent Neural Networks using Invariant Inferencecited by 26
  31. 2021NNrepair: Constraint-based Repair of Neural Network Classifierscited by 26
  32. 2020Global Optimization of Objective Functions Represented by ReLU Networkscited by 24
  33. 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networkscited by 24
  34. 2022Efficient Neural Network Analysis with Sum-of-Infeasibilitiescited by 24
  35. 2022Neural Network Verification with Proof Productioncited by 22
  36. 2019Weighted Automata Extraction from Recurrent Neural Networks via Regression on State Spacescited by 21
  37. 2020Into the Unknown: Active Monitoring of Neural Networkscited by 19
  38. 2021Neural Network Repair with Reachability Analysiscited by 19

50 most cited of 68 All 68 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 8; 2025: 1; 2026: 1.

11 papers.

  1. 2023Formally Explaining Neural Networks within Reactive Systemscited by 24
  2. 2024Local vs. Global Interpretability: A Computational Complexity Perspectivecited by 23
  3. 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificatescited by 16
  4. 2024Verification-Guided Shielding for Deep Reinforcement Learningcited by 13
  5. 2024Hard to Explain: On the Computational Hardness of In-Distribution Model Interpretationcited by 11
  6. 2024Analyzing Adversarial Inputs in Deep Reinforcement Learningcited by 7
  7. 2024Towards Formal Verification of Deep Neural Networks for Object Detectioncited by 4
  8. 2024Safe and Reliable Training of Learning-Based Aerospace Controllerscited by 4
  9. 2025PICID: Proof-Driven Clause Learning in Neural Network Verificationcited by 3
  10. 2026Incremental Neural Network Verification via Learned Conflictscited by 2
  11. 2024Aquatic Navigation: A Challenging Benchmark for Deep Reinforcement Learningcited by 1