Lipschitz Neural Networks

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Overview

Lipschitz neural networks study ways to bound a model’s sensitivity to input changes, which matters for adversarial robustness, reliable prediction, and stable iterative systems such as image reconstruction. Common approaches constrain layer norms or use specially parameterized contractive, nonexpansive, and spectral-normalized layers; these ideas are also being adapted to Transformers, recurrent networks, audio models, and manifold-valued data. Researchers assess guarantees with certified bounds and exact or approximate Lipschitz-constant computation, alongside robustness and restoration benchmarks. A central tension is that tight guarantees can be costly to verify, while conservative bounds may limit accuracy or expressivity; the complexity of exact verification remains an important obstacle.

Latest papers

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24 papers1 paper in the last four weeks, down 67% on the four weeks before. 0.0% of all new papers.

  1. Lipschitz Thinking: Ten Years of Certifiable-by-Design Robust Neural Networks

    Oct 5, 2026Fabio Brau, Giorgio Piras, Maura Pintor +1Neural Network RobustnessCertified Robustness

    Department of Electrical and Electronic Engineering, University of Cagliari, Cagliari, Italy

  2. LipSSM: Structurally Lipschitz-Bounded Cascaded State-Space Model via Metric Transfer between Consecutive SSM Layers

    Sep 25, 2026Natsuki Yoshino, Ren Uchida, Kazuki Matsumoto +1Lipschitz Neural NetworksNeural Network Robustness

    Tokyo University of Agriculture and Technology (TUAT), Tokyo, Japan

  3. Stability-Constrained Approximation in Spline KANs: Exact Layer Balancing and Budget-Compatible Saturation

    Sep 14, 2026Aleksander TankmanFunction ApproximationNeural Network Approximation Theory

    Fivestar Europe OÜ, Tallinn, Estonia

  4. A Closed-Form Formula for Consistent Lipschitz Regression on Metric Spaces with Sparse Neural Network Realizations

    Sep 2, 2026Ruiyang Hong, Hrad Ghoukasian, Anastasis KratsiosNeural Network Approximation TheoryStatistical Learning Theory

  5. Parameterized Complexity of LpL_p-Lipschitz Constants for Input Convex Neural Networks and LpL_p-Norm Maximization over Zonotopes

    Aug 25, 2026Aritra Das, Vincent Froese, Moritz Grillo +6Lipschitz Neural NetworksParameterized Complexity

    Ashoka University, Truth Audit Labs · Technische Universität Berlin · Max Planck Institute for Mathematics in the Sciences +3

  6. LipsAM: Lipschitz-continuous Neural Networks for Convergent Plug-and-Play Audio Signal Recovery

    Aug 24, 2026Kazuki Matsumoto, Ren Uchida, Natsuki Yoshino +1Speech DereverberationLipschitz Neural Networks

    Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan

  7. LipCache: A Local Inference Proxy with Certified Caching for Edge Image Classification Service

    Aug 13, 2026Zhengzhe Xiang, Yinlin Chen, Fuli Ying +3Efficient Neural Network InferenceEdge Inference

  8. Trainable Nonexpansive Denoisers for Contractive Image Reconstruction

    Jul 25, 2026Arghya Sinha, Aditya Banerjee, Trishit Mukherjee +1Image ReconstructionLipschitz Neural Networks

    Indian Institute of Science, Bengaluru, India.

  9. 1-Lipschitz Neural Networks on Hadamard Manifolds

    Jul 21, 2026Davide Murari, Marta Ghirardelli, Ben Adcock +3Riemannian Neural NetworksNeural Network Robustness

    Department of Applied Mathematics and Theoretical Physics, University of Cambridge · Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU) · Department of Mathematics, Simon Fraser University

  10. A law of robustness for two-layer neural networks with arbitrary weights

    Jul 8, 2026Yitzchak ShmaloNeural Network MemorizationMultilayer Perceptrons

  11. LiST: Lipschitz Scaling Training for Robust and Calibrated Neural Networks

    Jul 8, 2026Arthur Chiron, Franck Mamalet, Thomas Massena +2Neural Network RobustnessAdversarial Robustness

    IRIT, EPE UT · IRIT · IRIT, DTIPG - SNCF, UT3 +6

  12. LipSSD: Lipschitz-Constrained Single-Shot Detection for Adversarially Robust Object Detection

    Jul 6, 2026Vincent Lébé, Yannick Prudent, Corentin Friedrich +3Adversarial RobustnessObject Detection

    IRIT, DTIPG - SNCF, UT3 · IRT Saint-Exup´ery · Alstom +2

  13. Convex training of Lipschitz-regularized shallow neural networks

    Jun 17, 2026Chao Yin, Antoine Lesage-LandryAdversarial TrainingShallow Neural Networks

    Polytechnique Montr´eal, GERAD & Mila, Montr´eal, QC, Canada, H3T 1J4.

  14. Architecture-agnostic Lipschitz-constant Bayesian header and its application to resolve semantically proximal classification errors with vision transformers

    May 7, 2026Frederik Schäfer, Luis Mandl, Lars Kälber +1Bayesian Neural NetworksVision Transformer

    Institute of Structural Mechanics and Dynamics in Aerospace Engineering, University of Stuttgart · Rockwell Collins Deutschland GmbH · Department of Hepatobiliary Surgery and Visceral Transplantation, University of Leipzig Medical Center

  15. Certified vs. Empirical Adversarial Robust-ness via Hybrid Convolutions with Attention Stochasticity

    May 2, 2026Joy Dhar, Song Xia, Manish Kumar Pandey +5Randomized SmoothingNeural Network Robustness

    1Indian Institute of Technology Ropar · 2Nanyang Technological University · 3RoentGen Health +5

  16. Layer-wise Lipschitz-Product Control for Deep Kolmogorov--Arnold Network Representations of Compositionally Structured Functions

    Apr 29, 2026Aleksander TankmanKolmogorov-Arnold NetworksNeural Network Approximation Theory

    Fivestar Europe OÜ, Tallinn, Estonia

  17. Demystifying Lipschitz verification: positive matrices, negative results

    Mar 30, 2026Simon Kuang, Yuezhu Xu, S. Sivaranjani +1Neural Network VerificationLipschitz Neural Networks

    Department of Mechanical and Aerospace Engineering University of California, Davis · Edwardson School of Industrial Engineering Purdue University

  18. Provably Contractive and High-Quality Denoisers for Convergent Restoration

    Mar 27, 2026Shubhi Shukla, Pravin NairImage RestorationImage Denoising

    Indian Institute of Technology Madras, India

  19. Layer-Specific Lipschitz Modulation for Fault-Tolerant Multimodal Representation Learning

    Mar 26, 2026Diyar Altinses, Andreas SchwungMultimodal LearningMultimodal Anomaly Detection

    Department of Automation Technology and Learning Systems, South Westphalia University of Applied Sciences, Soest, Germany

  20. LipsAM: Lipschitz-Continuous Amplitude Modifier for Audio Signal Processing and its Application to Plug-and-Play Dereverberation

    Mar 23, 2026Kazuki Matsumoto, Ren Uchida, Kohei YatabeSpeech DereverberationLipschitz Neural Networks

    Tokyo University of Agriculture and Technology, Tokyo, Japan

  21. Approximation Theory for Lipschitz Continuous Transformers

    Feb 17, 2026Takashi Furuya, Davide Murari, Carola-Bibiane SchönliebTransformerNeural Network Approximation Theory

    Faculty of Life and Medical Sciences, Department of Biomedical Engineering, Doshisha University, RIKEN AIP · Department of Applied Mathematics and Theoretical Physics, University of Cambridge

  22. ExLipBaB: Exact Lipschitz Constant Computation for Piecewise Linear Neural Networks

    Feb 17, 2026Tom A. SplittgerberLipschitz Neural Networks

    University of Bremen

  23. Optimal estimates for the ℓp\ell^p-Lipschitz constants of deep random ReLU neural networks

    Jun 24, 2025Sjoerd Dirksen, Patrick Finke, Paul Geuchen +2ReLU Neural NetworksLipschitz Neural Networks

  24. R2DN: Scalable Parameterization of Contracting and Lipschitz Recurrent Deep Networks

    Apr 1, 2025Nicholas H. Barbara, Ruigang Wang, Ian R. ManchesterNeural Network RobustnessRecurrent Neural Networks

    Australian Centre for Robotics (ACFR) and the School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Australia