mlsanityData to 14 Oct 2026

LDLT L-Lipschitz Network: Generalized Deep End-To-End Lipschitz Network Construction

arXiv 2512.05915 ↗First posted 5 Dec 2025cs.LG cs.SY eess.SYcited by 0

Not on the map. Why?

Abstract (arXiv)

Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz constant in neural networks has emerged as an essential area of research to enhance adversarial robustness and network certifiability. This paper presents a rigorous approach to the general design of L-Lipschitz deep residual networks using a Linear Matrix Inequality (LMI) framework. Initially, the ResNet architecture was reformulated as a cyclic tridiagonal LMI, and closed-form constraints on network parameters were derived to ensure L-Lipschitz continuity; however, using a new LDL^top decomposition approach for certifying LMI feasibility, we extend the construction of L-Lipchitz networks to any other nonlinear architecture. Our contributions include a provable parameterization methodology for constructing Lipschitz-constrained residual networks and other hierarchical architectures. Cholesky decomposition is also used for efficient parameterization. These findings enable robust network designs applicable to adversarial robustness, certified training, and control systems. The LDL^top formulation is shown to be a tight relaxation of the SDP-based network, maintaining full expressiveness and achieving 3%-13% accuracy gains over SLL Layers on 121 UCI data sets.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 39 of its 59 references that are in the map. First posted on arXiv 5 Dec 2025.

Builds on

39 of 59 references.

References · 39

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  3. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  4. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  5. 2017Squeeze-and-Excitation Networkscited by 4,789
  6. 2017MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applicationscited by 3,845
  7. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,611
  8. 2016Gaussian Error Linear Units (GELUs)cited by 3,502
  9. 2016Wide Residual Networkscited by 3,070
  10. 2016Aggregated Residual Transformations for Deep Neural Networkscited by 2,546
  11. 2019Searching for MobileNetV3cited by 1,994
  12. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,636
27 more
  1. 2016Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learningcited by 1,512
  2. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,070
  3. 2019An Introduction to Variational Autoencoderscited by 1,000
  4. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 950
  5. 2017Spectrally-normalized margin bounds for neural networkscited by 686
  6. 2017Self-Normalizing Neural Networkscited by 598
  7. 2015BinaryConnect: Training Deep Neural Networks with binary weights during propagationscited by 592
  8. 2015Empirical Evaluation of Rectified Activations in Convolutional Networkcited by 519
  9. 2018Regularisation of Neural Networks by Enforcing Lipschitz Continuitycited by 314
  10. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 293
  11. 2018Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networkscited by 195
  12. 2014Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech Recognitioncited by 111
  13. 2014Analysis and Design of Optimization Algorithms via Integral Quadratic Constraintscited by 105
  14. 2020Monotone operator equilibrium networkscited by 100
  15. 2017Continuously Differentiable Exponential Linear Unitscited by 73
  16. 2021A Dynamical System Perspective for Lipschitz Neural Networkscited by 60
  17. 2023A Unified Algebraic Perspective on Lipschitz Neural Networkscited by 60
  18. 2023Direct Parameterization of Lipschitz-Bounded Deep Networkscited by 51
  19. 2021Improved deterministic l2 robustness on CIFAR-10 and CIFAR-100cited by 47
  20. 2022Almost-Orthogonal Layers for Efficient General-Purpose Lipschitz Networkscited by 39
  21. 2020Deep Neural Networks with Trainable Activations and Controlled Lipschitz Constantcited by 25
  22. 2019Snooping Attacks on Deep Reinforcement Learningcited by 17
  23. 2024ECLipsE: Efficient Compositional Lipschitz Constant Estimation for Deep Neural Networkscited by 10
  24. 2024Rethinking Deep Thinking: Stable Learning of Algorithms using Lipschitz Constraintscited by 9
  25. 2019Sequential Synthesis of Distributed Controllers for Cascade Interconnected Systemscited by 5
  26. 2016Softplus Regressions and Convex Polytopescited by 4
  27. 20251-Lipschitz Network Initialization for Certifiably Robust Classification Applications: A Decay Problemcited by 2

Built on by

Not cited yet.