# Provable Repair of Deep Neural Networks

arXiv: https://arxiv.org/abs/2104.04413 · HTML: https://mlsanity.com/paper/2104.04413/

## 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 (most cited first, 30 of 30)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [Measuring Catastrophic Forgetting in Neural Networks](https://mlsanity.com/paper/1708.02072/) (2017)
- [DeepXplore: Automated Whitebox Testing of Deep Learning Systems](https://mlsanity.com/paper/1705.06640/) (2017)
- [Safety Verification of Deep Neural Networks](https://mlsanity.com/paper/1610.06940/) (2016)
- [DeepTest: Automated Testing of Deep-Neural-Network-driven Autonomous Cars](https://mlsanity.com/paper/1708.08559/) (2017)
- [Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks](https://mlsanity.com/paper/1705.01320/) (2017)
- [Verifiable Reinforcement Learning via Policy Extraction](https://mlsanity.com/paper/1805.08328/) (2018)
- [Complexity of Linear Regions in Deep Networks](https://mlsanity.com/paper/1901.09021/) (2019)
- [Deep ReLU Networks Have Surprisingly Few Activation Patterns](https://mlsanity.com/paper/1906.00904/) (2019)
- [Editable Neural Networks](https://mlsanity.com/paper/2004.00345/) (2020)
- [DeepGauge: Multi-Granularity Testing Criteria for Deep Learning Systems](https://mlsanity.com/paper/1803.07519/) (2018)
- [MNIST-C: A Robustness Benchmark for Computer Vision](https://mlsanity.com/paper/1906.02337/) (2019)
- [Measuring Neural Net Robustness with Constraints](https://mlsanity.com/paper/1605.07262/) (2016)
- [TensorFuzz: Debugging Neural Networks with Coverage-Guided Fuzzing](https://mlsanity.com/paper/1807.10875/) (2018)
- [Deep Neural Network Compression for Aircraft Collision Avoidance Systems](https://mlsanity.com/paper/1810.04240/) (2018)
- [Concolic Testing for Deep Neural Networks](https://mlsanity.com/paper/1805.00089/) (2018)
- [Optimization and Abstraction: A Synergistic Approach for Analyzing Neural Network Robustness](https://mlsanity.com/paper/1904.09959/) (2019)
- [An Inductive Synthesis Framework for Verifiable Reinforcement Learning](https://mlsanity.com/paper/1907.07273/) (2019)
- [Computing Linear Restrictions of Neural Networks](https://mlsanity.com/paper/1908.06214/) (2019)
- [Decoupling Gating from Linearity](https://mlsanity.com/paper/1906.05032/) (2019)
- [SyReNN: A Tool for Analyzing Deep Neural Networks](https://mlsanity.com/paper/2101.03263/) (2021)

## Built on by (most cited first, 30 of 42)

- [Fast Model Editing at Scale](https://mlsanity.com/paper/2110.11309/) (2021)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Transformer-Patcher: One Mistake worth One Neuron](https://mlsanity.com/paper/2301.09785/) (2023)
- [Causality-based Neural Network Repair](https://mlsanity.com/paper/2204.09274/) (2022)
- [A Survey on Knowledge Editing of Neural Networks](https://mlsanity.com/paper/2310.19704/) (2023)
- [HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees](https://mlsanity.com/paper/2410.10807/) (2024)
- [Neural Network Repair with Reachability Analysis](https://mlsanity.com/paper/2108.04214/) (2021)
- [Eliminating Information Leakage in Hard Concept Bottleneck Models with Supervised, Hierarchical Concept Learning](https://mlsanity.com/paper/2402.05945/) (2024)
- [Minimal Multi-Layer Modifications of Deep Neural Networks](https://mlsanity.com/paper/2110.09929/) (2021)
- [Sound and Complete Neural Network Repair with Minimality and Locality Guarantees](https://mlsanity.com/paper/2110.07682/) (2021)
- [Architecture-Preserving Provable Repair of Deep Neural Networks](https://mlsanity.com/paper/2304.03496/) (2023)
- [Machine Learning Robustness: A Primer](https://mlsanity.com/paper/2404.00897/) (2024)
- [SpecRepair: Counter-Example Guided Safety Repair of Deep Neural Networks](https://mlsanity.com/paper/2106.01917/) (2021)
- [Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems](https://mlsanity.com/paper/2112.08091/) (2021)
- [Partial Network Cloning](https://mlsanity.com/paper/2303.10597/) (2023)
- [Online Safety Analysis for LLMs: a Benchmark, an Assessment, and a Path Forward](https://mlsanity.com/paper/2404.08517/) (2024)
- [Certified Continual Learning for Neural Network Regression](https://mlsanity.com/paper/2407.06697/) (2024)
- [Self-Correcting Neural Networks For Safe Classification](https://mlsanity.com/paper/2107.11445/) (2021)
- [AIREPAIR: A Repair Platform for Neural Networks](https://mlsanity.com/paper/2211.15387/) (2022)
- [Repairing Deep Neural Networks Based on Behavior Imitation](https://mlsanity.com/paper/2305.03365/) (2023)
- [A Robust Optimisation Perspective on Counterexample-Guided Repair of Neural Networks](https://mlsanity.com/paper/2301.11342/) (2023)
- [Reliability Assurance for Deep Neural Network Architectures Against Numerical Defects](https://mlsanity.com/paper/2302.06086/) (2023)
- [Semantic-Based Neural Network Repair](https://mlsanity.com/paper/2306.07995/) (2023)
- [Incremental Satisfiability Modulo Theory for Verification of Deep Neural Networks](https://mlsanity.com/paper/2302.06455/) (2023)
- [A Comprehensive Study of Deep Learning Model Fixing Approaches](https://mlsanity.com/paper/2512.23745/) (2025)
- [Verifying Attention Robustness of Deep Neural Networks against Semantic Perturbations](https://mlsanity.com/paper/2207.05902/) (2022)
- [Counterexample-Guided Repair of Reinforcement Learning Systems Using Safety Critics](https://mlsanity.com/paper/2405.15430/) (2024)
- [Exploring and Leveraging Class Vectors for Classifier Editing](https://mlsanity.com/paper/2510.11268/) (2025)
- [WARP: Guaranteed Inner-Layer Repair of NLP Transformers](https://mlsanity.com/paper/2604.00938/) (2026)
- [QNNRepair: Quantized Neural Network Repair](https://mlsanity.com/paper/2306.13793/) (2023)

## 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.