mlsanityData to 7 Oct 2026

BDD4BNN: A BDD-based Quantitative Analysis Framework for Binarized Neural Networks

arXiv 2103.07224 ↗First posted 12 Mar 2021cs.LG cs.AI cs.LOcited by 17

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Abstract (arXiv)

Verifying and explaining the behavior of neural networks is becoming increasingly important, especially when they are deployed in safety-critical applications. In this paper, we study verification problems for Binarized Neural Networks (BNNs), the 1-bit quantization of general real-numbered neural networks. Our approach is to encode BNNs into Binary Decision Diagrams (BDDs), which is done by exploiting the internal structure of the BNNs. In particular, we translate the input-output relation of blocks in BNNs to cardinality constraints which are then encoded by BDDs. Based on the encoding, we develop a quantitative verification framework for BNNs where precise and comprehensive analysis of BNNs can be performed. We demonstrate the application of our framework by providing quantitative robustness analysis and interpretability for BNNs. We implement a prototype tool BDD4BNN and carry out extensive experiments which confirm the effectiveness and efficiency of our approach.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). Builds on 45 of its 80 references that are in the map. First posted on arXiv 12 Mar 2021.

Builds on

45 of 80 references.

References · 45

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33 more
  1. 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 241
  2. 2017Distilling a Neural Network Into a Soft Decision Treecited by 230
  3. 2018Formal Security Analysis of Neural Networks using Symbolic Intervalscited by 185
  4. 2017Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulationcited by 182
  5. 2019Branch and Bound for Piecewise Linear Neural Network Verificationcited by 138
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  11. 2017Output Reachable Set Estimation and Verification for Multi-Layer Neural Networkscited by 79
  12. 2017Verifying Properties of Binarized Deep Neural Networkscited by 77
  13. 2020Verification of Deep Convolutional Neural Networks Using ImageStarscited by 75
  14. 2019An Abstraction-Based Framework for Neural Network Verificationcited by 68
  15. 2017Extracting Automata from Recurrent Neural Networks Using Queries and Counterexamplescited by 66
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 5; 2023: 5; 2024: 2; 2025: 2; 2026: 1.

17 papers.

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  1. 2023Logic for Explainable AIcited by 23
  2. 2023The #DNN-Verification Problem: Counting Unsafe Inputs for Deep Neural Networkscited by 19
  3. 2025RvLLM: LLM Runtime Verification with Domain Knowledgecited by 15
  4. 2021Attack as Defense: Characterizing Adversarial Examples using Robustnesscited by 14
  5. 2022QVIP: An ILP-based Formal Verification Approach for Quantized Neural Networkscited by 12
  6. 2022Abstraction and Refinement: Towards Scalable and Exact Verification of Neural Networkscited by 11
  7. 2022AS2T: Arbitrary Source-To-Target Adversarial Attack on Speaker Recognition Systemscited by 10
  8. 2022QEBVerif: Quantization Error Bound Verification of Neural Networkscited by 9
  9. 2022A Scalable, Interpretable, Verifiable & Differentiable Logic Gate Convolutional Neural Network Architecture From Truth Tablescited by 4
  10. 2021Adversarial Attacks on ML Defense Models Competitioncited by 3
  11. 2025Verification of Bit-Flip Attacks against Quantized Neural Networkscited by 2
  12. 2023gRoMA: a Tool for Measuring the Global Robustness of Deep Neural Networkscited by 1
5 more
  1. 2023Scaling #DNN-Verification Tools with Efficient Bound Propagation and Parallel Computingcited by 1
  2. 2024Verifying Properties of Binary Neural Networks Using Sparse Polynomial Optimizationcited by 1
  3. 2024Training Verification-Friendly Neural Networks via Neuron Behavior Consistencycited by 1
  4. 2023An Automata-Theoretic Approach to Synthesizing Binarized Neural Networkscited by 0
  5. 2026Eventizing Traditionally Opaque Binary Neural Networks as 1-safe Petri net Modelscited by 0