mlsanityData to 7 Oct 2026

Fast BATLLNN: Fast Box Analysis of Two-Level Lattice Neural Networks

arXiv 2111.09293 ↗First posted 17 Nov 2021cs.LG cs.SY eess.SYcited by 8

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Abstract (arXiv)

In this paper, we present the tool Fast Box Analysis of Two-Level Lattice Neural Networks (Fast BATLLNN) as a fast verifier of box-like output constraints for Two-Level Lattice (TLL) Neural Networks (NNs). In particular, Fast BATLLNN can verify whether the output of a given TLL NN always lies within a specified hyper-rectangle whenever its input constrained to a specified convex polytope (not necessarily a hyper-rectangle). Fast BATLLNN uses the unique semantics of the TLL architecture and the decoupled nature of box-like output constraints to dramatically improve verification performance relative to known polynomial-time verification algorithms for TLLs with generic polytopic output constraints. In this paper, we evaluate the performance and scalability of Fast BATLLNN, both in its own right and compared to state-of-the-art NN verifiers applied to TLL NNs. Fast BATLLNN compares very favorably to even the fastest NN verifiers, completing our synthetic TLL test bench more than 400x faster than its nearest competitor.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 20 of its 38 references that are in the map. First posted on arXiv 17 Nov 2021.

Builds on

20 of 38 references.

References · 20

  1. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 739
  2. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
  3. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 290
  4. 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 241
  5. 2018Formal Security Analysis of Neural Networks using Symbolic Intervalscited by 185
  6. 2018Efficient Formal Safety Analysis of Neural Networkscited by 165
  7. 2019Branch and Bound for Piecewise Linear Neural Network Verificationcited by 138
  8. 2020NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systemscited by 128
  9. 2017An approach to reachability analysis for feed-forward ReLU neural networkscited by 126
  10. 2018A Dual Approach to Scalable Verification of Deep Networkscited by 125
  11. 2018Strong mixed-integer programming formulations for trained neural networkscited by 115
  12. 2017Maximum Resilience of Artificial Neural Networkscited by 97
8 more
  1. 2016Measuring Neural Net Robustness with Constraintscited by 90
  2. 2018Verisig: verifying safety properties of hybrid systems with neural network controllerscited by 83
  3. 2017Output Reachable Set Estimation and Verification for Multi-Layer Neural Networkscited by 79
  4. 2017Reachable Set Computation and Safety Verification for Neural Networks with ReLU Activationscited by 22
  5. 2019AReN: Assured ReLU NN Architecture for Model Predictive Control of LTI Systemscited by 9
  6. 2020Bounding the Complexity of Formally Verifying Neural Networks: A Geometric Approachcited by 6
  7. 2021Safe-by-Repair: A Convex Optimization Approach for Repairing Unsafe Two-Level Lattice Neural Network Controllerscited by 6
  8. 2020Two-Level Lattice Neural Network Architectures for Control of Nonlinear Systemscited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 2; 2024: 0; 2025: 1; 2026: 2.

8 papers.

  1. 2022The Third International Verification of Neural Networks Competition (VNN-COMP 2022): Summary and Resultscited by 39
  2. 2022NNLander-VeriF: A Neural Network Formal Verification Framework for Vision-Based Autonomous Aircraft Landingcited by 19
  3. 2023Towards a Certified Proof Checker for Deep Neural Network Verificationcited by 6
  4. 2026IoUCert: Robustness Verification for Anchor-based Object Detectorscited by 1
  5. 2022Polynomial-Time Reachability for LTI Systems with Two-Level Lattice Neural Network Controllerscited by 0
  6. 2023CGDTest: A Constrained Gradient Descent Algorithm for Testing Neural Networkscited by 0
  7. 2025Extracting Forward Invariant Sets from Neural Network-Based Control Barrier Functionscited by 0
  8. 2026NNV3: Expanding Neural Network Verification to New Architectures and Domainscited by 0