mlsanityData to 14 Oct 2026

The inverse problem for neural networks

arXiv 2308.14093 ↗First posted 27 Aug 2023cs.LG cs.AI cs.LOcited by 0

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Abstract (arXiv)

We study the problem of computing the preimage of a set under a neural network with piecewise-affine activation functions. We recall an old result that the preimage of a polyhedral set is again a union of polyhedral sets and can be effectively computed. We show several applications of computing the preimage for analysis and interpretability of neural networks.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 17 of its 31 references that are in the map. First posted on arXiv 27 Aug 2023.

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17 of 31 references.

References · 17

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  2. 2013Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Mapscited by 2,371
  3. 2013Visualizing and Understanding Convolutional Networkscited by 2,290
  4. 2014Understanding Deep Image Representations by Inverting Themcited by 403
  5. 2014On the Number of Linear Regions of Deep Neural Networkscited by 381
  6. 2018Formal Security Analysis of Neural Networks using Symbolic Intervalscited by 185
  7. 2019When Explanations Lie: Why Many Modified BP Attributions Failcited by 92
  8. 2023Provably Bounding Neural Network Preimagescited by 29
  9. 2019JuliaReach: a Toolbox for Set-Based Reachabilitycited by 28
  10. 2021Verification of Neural-Network Control Systems by Integrating Taylor Models and Zonotopescited by 26
  11. 2022Open- and Closed-Loop Neural Network Verification using Polynomial Zonotopescited by 24
  12. 2021SyReNN: A Tool for Analyzing Deep Neural Networkscited by 10
5 more
  1. 2022Backward Reachability Analysis for Neural Feedback Loopscited by 9
  2. 2022Neural Network Compression of ACAS Xu Early Prototype is Unsafe: Closed-Loop Verification through Quantized State Backreachabilitycited by 8
  3. 2022A Hybrid Partitioning Strategy for Backward Reachability of Neural Feedback Loopscited by 6
  4. 2022DRIP: Domain Refinement Iteration with Polytopes for Backward Reachability Analysis of Neural Feedback Loopscited by 6
  5. 2021LazySets.jl: Scalable Symbolic-Numeric Set Computationscited by 4

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