mlsanityData to 7 Oct 2026

Zonotope Domains for Lagrangian Neural Network Verification

arXiv 2210.08069 ↗First posted 14 Oct 2022cs.LG stat.MLcited by 5

Not on the map. Why?

Abstract (arXiv)

Neural network verification aims to provide provable bounds for the output of a neural network for a given input range. Notable prior works in this domain have either generated bounds using abstract domains, which preserve some dependency between intermediate neurons in the network; or framed verification as an optimization problem and solved a relaxation using Lagrangian methods. A key drawback of the latter technique is that each neuron is treated independently, thereby ignoring important neuron interactions. We provide an approach that merges these two threads and uses zonotopes within a Lagrangian decomposition. Crucially, we can decompose the problem of verifying a deep neural network into the verification of many 2-layer neural networks. While each of these problems is provably hard, we provide efficient relaxation methods that are amenable to efficient dual ascent procedures. Our technique yields bounds that improve upon both linear programming and Lagrangian-based verification techniques in both time and bound tightness.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 25 of its 47 references that are in the map. First posted on arXiv 14 Oct 2022.

Builds on

25 of 47 references.

References · 25

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13 more
  1. 2018Efficient Formal Safety Analysis of Neural Networkscited by 165
  2. 2018A Dual Approach to Scalable Verification of Deep Networkscited by 125
  3. 2019A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networkscited by 124
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  5. 2020Exactly Computing the Local Lipschitz Constant of ReLU Networkscited by 102
  6. 2020Enabling certification of verification-agnostic networks via memory-efficient semidefinite programmingcited by 65
  7. 2019Neural Network Branching for Neural Network Verificationcited by 45
  8. 2021Improved Branch and Bound for Neural Network Verification via Lagrangian Decompositioncited by 44
  9. 2020Lagrangian Decomposition for Neural Network Verificationcited by 35
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Built on by

Cited by year (2026 to 7 Oct)

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

5 papers.

  1. 2023On the Robustness of Removal-Based Feature Attributionscited by 18
  2. 2025Parameterized Hardness of Zonotope Containment and Neural Network Verificationcited by 4
  3. 2024Learning from Uncertain Data: From Possible Worlds to Possible Modelscited by 0
  4. 2026Hybrid Robustness Verification for Spatio-Temporal Neural Networkscited by 0
  5. 2026Matrix Zonotopic Attention: A Context-Adaptive Value Projection for Set Transformerscited by 0