mlsanityData to 14 Oct 2026

Provable Repair of Deep Neural Networks

arXiv 2104.04413 ↗First posted 9 Apr 2021cs.LGcited by 42

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Abstract (arXiv)

Deep Neural Networks (DNNs) have grown in popularity over the past decade and are now being used in safety-critical domains such as aircraft collision avoidance. This has motivated a large number of techniques for finding unsafe behavior in DNNs. In contrast, this paper tackles the problem of correcting a DNN once unsafe behavior is found. We introduce the provable repair problem, which is the problem of repairing a network N to construct a new network N' that satisfies a given specification. If the safety specification is over a finite set of points, our Provable Point Repair algorithm can find a provably minimal repair satisfying the specification, regardless of the activation functions used. For safety specifications addressing convex polytopes containing infinitely many points, our Provable Polytope Repair algorithm can find a provably minimal repair satisfying the specification for DNNs using piecewise-linear activation functions. The key insight behind both of these algorithms is the introduction of a Decoupled DNN architecture, which allows us to reduce provable repair to a linear programming problem. Our experimental results demonstrate the efficiency and effectiveness of our Provable Repair algorithms on a variety of challenging tasks.

Key facts. Cited by 42 papers in the map (data through 14 Oct 2026). Builds on 30 of its 65 references that are in the map. First posted on arXiv 9 Apr 2021.

Builds on

30 of 65 references.

References · 30

  1. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  3. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  4. 2013Intriguing properties of neural networkscited by 5,155
  5. 2019Natural Adversarial Examplescited by 1,408
  6. 2016SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model sizecited by 1,060
  7. 2016End to End Learning for Self-Driving Carscited by 1,009
  8. 2017Ensemble Adversarial Training: Attacks and Defensescited by 840
  9. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 744
  10. 2017Safe Reinforcement Learning via Shieldingcited by 449
  11. 2017Measuring Catastrophic Forgetting in Neural Networkscited by 360
  12. 2017DeepXplore: Automated Whitebox Testing of Deep Learning Systemscited by 311
18 more
  1. 2016Safety Verification of Deep Neural Networkscited by 263
  2. 2017DeepTest: Automated Testing of Deep-Neural-Network-driven Autonomous Carscited by 251
  3. 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 242
  4. 2018Verifiable Reinforcement Learning via Policy Extractioncited by 177
  5. 2019Complexity of Linear Regions in Deep Networkscited by 167
  6. 2019Deep ReLU Networks Have Surprisingly Few Activation Patternscited by 161
  7. 2020Editable Neural Networkscited by 155
  8. 2018DeepGauge: Multi-Granularity Testing Criteria for Deep Learning Systemscited by 147
  9. 2019MNIST-C: A Robustness Benchmark for Computer Visioncited by 138
  10. 2016Measuring Neural Net Robustness with Constraintscited by 90
  11. 2018TensorFuzz: Debugging Neural Networks with Coverage-Guided Fuzzingcited by 68
  12. 2018Deep Neural Network Compression for Aircraft Collision Avoidance Systemscited by 58
  13. 2018Concolic Testing for Deep Neural Networkscited by 51
  14. 2019Optimization and Abstraction: A Synergistic Approach for Analyzing Neural Network Robustnesscited by 40
  15. 2019An Inductive Synthesis Framework for Verifiable Reinforcement Learningcited by 39
  16. 2019Computing Linear Restrictions of Neural Networkscited by 15
  17. 2019Decoupling Gating from Linearitycited by 13
  18. 2021SyReNN: A Tool for Analyzing Deep Neural Networkscited by 10

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 7; 2022: 4; 2023: 10; 2024: 8; 2025: 6; 2026: 7.

42 papers.

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  1. 2021Fast Model Editing at Scalecited by 498
  2. 2022Post-hoc Concept Bottleneck Modelscited by 293
  3. 2023Transformer-Patcher: One Mistake worth One Neuroncited by 197
  4. 2022Causality-based Neural Network Repaircited by 47
  5. 2023A Survey on Knowledge Editing of Neural Networkscited by 34
  6. 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 31
  7. 2021Neural Network Repair with Reachability Analysiscited by 19
  8. 2024Eliminating Information Leakage in Hard Concept Bottleneck Models with Supervised, Hierarchical Concept Learningcited by 17
  9. 2021Minimal Multi-Layer Modifications of Deep Neural Networkscited by 14
  10. 2021Sound and Complete Neural Network Repair with Minimality and Locality Guaranteescited by 13
  11. 2023Architecture-Preserving Provable Repair of Deep Neural Networkscited by 11
  12. 2024Machine Learning Robustness: A Primercited by 8
30 more
  1. 2021SpecRepair: Counter-Example Guided Safety Repair of Deep Neural Networkscited by 6
  2. 2021Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problemscited by 6
  3. 2023Partial Network Cloningcited by 6
  4. 2024Online Safety Analysis for LLMs: a Benchmark, an Assessment, and a Path Forwardcited by 6
  5. 2024Certified Continual Learning for Neural Network Regressioncited by 5
  6. 2021Self-Correcting Neural Networks For Safe Classificationcited by 4
  7. 2022AIREPAIR: A Repair Platform for Neural Networkscited by 4
  8. 2023Repairing Deep Neural Networks Based on Behavior Imitationcited by 4
  9. 2023A Robust Optimisation Perspective on Counterexample-Guided Repair of Neural Networkscited by 3
  10. 2023Reliability Assurance for Deep Neural Network Architectures Against Numerical Defectscited by 3
  11. 2023Semantic-Based Neural Network Repaircited by 3
  12. 2023Incremental Satisfiability Modulo Theory for Verification of Deep Neural Networkscited by 2
  13. 2025A Comprehensive Study of Deep Learning Model Fixing Approachescited by 2
  14. 2022Verifying Attention Robustness of Deep Neural Networks against Semantic Perturbationscited by 1
  15. 2024Counterexample-Guided Repair of Reinforcement Learning Systems Using Safety Criticscited by 1
  16. 2025Exploring and Leveraging Class Vectors for Classifier Editingcited by 1
  17. 2026WARP: Guaranteed Inner-Layer Repair of NLP Transformerscited by 1
  18. 2023QNNRepair: Quantized Neural Network Repaircited by 0
  19. 2024Patch Synthesis for Property Repair of Deep Neural Networkscited by 0
  20. 2024An Empirical Study of Fault Localisation Techniques for Deep Learningcited by 0
  21. 2025PRUNE: A Patching Based Repair Framework for Certifiable Unlearning of Neural Networkscited by 0
  22. 2025AR2: Attention-Guided Repair for the Robustness of CNNs Against Common Corruptionscited by 0
  23. 2025DeepProv: Behavioral Characterization and Repair of Neural Networks via Inference Provenance Graph Analysiscited by 0
  24. 2025Provable Repair of Deep Neural Network Defects by Preimage Synthesis and Property Refinementcited by 0
  25. 2026Shapley-Guided Neural Repair Approach via Derivative-Free Optimizationcited by 0
  26. 2026Provable Fairness Repair for Deep Neural Networkscited by 0
  27. 2026RepTran: Search-Based Repair of Transformer Modelscited by 0
  28. 2026Security Properties of Neural Networks as Decision Problemscited by 0
  29. 2026FORGE: Verification-Gated Behavioral Repair for Generative Language Modelscited by 0
  30. 2026Mind the Gaps: From Failure Attribution to Closed-Form Repair of Code Language Modelscited by 0