mlsanityData to 7 Oct 2026

Abstraction based Output Range Analysis for Neural Networks

arXiv 2007.09527 ↗First posted 18 Jul 2020cs.LGcited by 34

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Abstract (arXiv)

In this paper, we consider the problem of output range analysis for feed-forward neural networks with ReLU activation functions. The existing approaches reduce the output range analysis problem to satisfiability and optimization solving, which are NP-hard problems, and whose computational complexity increases with the number of neurons in the network. To tackle the computational complexity, we present a novel abstraction technique that constructs a simpler neural network with fewer neurons, albeit with interval weights called interval neural network (INN), which over-approximates the output range of the given neural network. We reduce the output range analysis on the INNs to solving a mixed integer linear programming problem. Our experimental results highlight the trade-off between the computation time and the precision of the computed output range.

Key facts. Cited by 34 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Jul 2020.

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Citing papers per year: 2021: 5; 2022: 9; 2023: 14; 2024: 4; 2025: 1; 2026: 1.

34 papers.

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  1. 2022The Third International Verification of Neural Networks Competition (VNN-COMP 2022): Summary and Resultscited by 39
  2. 2021A Review of Formal Methods applied to Machine Learningcited by 33
  3. 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networkscited by 24
  4. 2022Formalising the Robustness of Counterfactual Explanations for Neural Networkscited by 24
  5. 2023Formally Explaining Neural Networks within Reactive Systemscited by 24
  6. 2023Provably Robust and Plausible Counterfactual Explanations for Neural Networks via Robust Optimisationcited by 20
  7. 2022Verification-Aided Deep Ensemble Selectioncited by 18
  8. 2023SpArX: Sparse Argumentative Explanations for Neural Networks [Technical Report]cited by 18
  9. 2023Provable Preimage Under-Approximation for Neural Networks (Full Version)cited by 13
  10. 2022Abstraction and Refinement: Towards Scalable and Exact Verification of Neural Networkscited by 11
  11. 2023Verifying Generalization in Deep Learningcited by 11
  12. 2022Tighter Abstract Queries in Neural Network Verificationcited by 8
22 more
  1. 2024PREMAP: A Unifying PREiMage APproximation Framework for Neural Networkscited by 8
  2. 2024Interval Abstractions for Robust Counterfactual Explanationscited by 7
  3. 2021Bisimulations for Neural Network Reductioncited by 6
  4. 2023Fully Automatic Neural Network Reduction for Formal Verificationcited by 6
  5. 2023Towards a Certified Proof Checker for Deep Neural Network Verificationcited by 6
  6. 2024Rigorous Probabilistic Guarantees for Robust Counterfactual Explanationscited by 6
  7. 2024Safe and Reliable Training of Learning-Based Aerospace Controllerscited by 4
  8. 2021Learning on Abstract Domains: A New Approach for Verifiable Guarantee in Reinforcement Learningcited by 3
  9. 2023DelBugV: Delta-Debugging Neural Network Verifierscited by 3
  10. 2023On the verification of Embeddings using Hybrid Markov Logiccited by 2
  11. 2025Verification of Bit-Flip Attacks against Quantized Neural Networkscited by 2
  12. 2021Online Verification of Deep Neural Networks under Domain Shift or Network Updatescited by 1
  13. 2023Boosting Verified Training for Robust Image Classifications via Abstractioncited by 1
  14. 2023Expediting Neural Network Verification via Network Reductioncited by 1
  15. 2021Permutation Invariance of Deep Neural Networks with ReLUscited by 0
  16. 2022A Domain-Theoretic Framework for Robustness Analysis of Neural Networkscited by 0
  17. 2022Towards Global Neural Network Abstractions with Locally-Exact Reconstructioncited by 0
  18. 2022Efficiently Finding Adversarial Examples with DNN Preprocessingcited by 0
  19. 2023CGDTest: A Constrained Gradient Descent Algorithm for Testing Neural Networkscited by 0
  20. 2023Syntactic vs Semantic Linear Abstraction and Refinement of Neural Networkscited by 0
  21. 2023Verification of Neural Networks Local Differential Classification Privacycited by 0
  22. 2026NNV3: Expanding Neural Network Verification to New Architectures and Domainscited by 0