mlsanityData to 14 Oct 2026

DISCO Verification: Division of Input Space into COnvex polytopes for neural network verification

arXiv 2105.07776 ↗First posted 17 May 2021cs.AI cs.NE cs.PFcited by 1

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Abstract (arXiv)

The impressive results of modern neural networks partly come from their non linear behaviour. Unfortunately, this property makes it very difficult to apply formal verification tools, even if we restrict ourselves to networks with a piecewise linear structure. However, such networks yields subregions that are linear and thus simpler to analyse independently. In this paper, we propose a method to simplify the verification problem by operating a partitionning into multiple linear subproblems. To evaluate the feasibility of such an approach, we perform an empirical analysis of neural networks to estimate the number of linear regions, and compare them to the bounds currently known. We also present the impact of a technique aiming at reducing the number of linear regions during training.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 15 of its 29 references that are in the map. First posted on arXiv 17 May 2021.

Builds on

15 of 29 references.

References · 15

  1. 2016Membership Inference Attacks against Machine Learning Modelscited by 2,281
  2. 2018Robustness May Be at Odds with Accuracycited by 880
  3. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 744
  4. 2016Stealing Machine Learning Models via Prediction APIscited by 619
  5. 2016Transferability in Machine Learning: from Phenomena to Black-Box Attacks using Adversarial Samplescited by 446
  6. 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 242
  7. 2018Formal Security Analysis of Neural Networks using Symbolic Intervalscited by 185
  8. 2019Complexity of Linear Regions in Deep Networkscited by 167
  9. 2017Bounding and Counting Linear Regions of Deep Neural Networkscited by 161
  10. 2019Deep ReLU Networks Have Surprisingly Few Activation Patternscited by 161
  11. 2018ShapeShifter: Robust Physical Adversarial Attack on Faster R-CNN Object Detectorcited by 159
  12. 2019Imperceptible, Robust, and Targeted Adversarial Examples for Automatic Speech Recognitioncited by 124
3 more
  1. 2018Provable Robustness of ReLU networks via Maximization of Linear Regionscited by 51
  2. 2018CNN-Cert: An Efficient Framework for Certifying Robustness of Convolutional Neural Networkscited by 50
  3. 2019Universal Approximation with Certified Networkscited by 9

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Cited by year

Citing papers per year: 2021: 1.

1 paper.

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