LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layers

[2410.22258] LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layers Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2410.22258 (cs) [Submitted on 29 Oct 2024 ( v1 ), last revised 9 Apr 2026 (this version, v2)] Title: LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layers Authors: Patricia Pauli , Ruigang Wang , Ian Manchester , Frank Allgöwer View a PDF of the paper titled LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layers, by Patricia Pauli and 2 other authors View PDF HTML (experimental) Abstract: We propose a novel layer-wise parameterization for convolutional neural networks (CNNs) that includes built-in robustness guarantees by enforcing a prescribed Lipschitz bound. Each layer in our parameterization is designed to satisfy a linear matrix inequality (LMI), which in turn implies dissipativity with respect to a specific supply rate. Collectively, these layer-wise LMIs ensure Lipschitz boundedness for the input-output mapping of the neural network, yielding a more expressive parameterization than through spectral bounds or orthogonal layers. Our new method LipKernel directly parameterizes dissipative convolution kernels using a 2-D Roesser-type state space model. This means that the convolutional layers are given in standard form after training and can be evaluated without computational overhead. In numerical experiments, we show that the run-time using our method is orders of magnitude faster than state-of-the-art Lipschitz-bounded networks that parameterize convolutions in the Fourier domain, making our approach particularly attractive for improving the robustness of learning-based real-time perception or control in robotics, autonomous vehicles, or automation systems. We focus on CNNs, and in contrast to previous works, our approach accommodates a wide variety of layers typically used in CNNs, including 1-D and 2-D convolutional layers, maximum and average pooling layers, as well as strided and dilated convolutions and zero padding. However, our approach naturally extends beyond CNNs as we can incorporate any layer that is incrementally dissipative. Subjects: Machine Learning (cs.LG) ; Image and Video Processing (eess.IV); Systems and Control (eess.SY); Machine Learning (stat.ML) Cite as: arXiv:2410.22258 [cs.LG] (or arXiv:2410.22258v2 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2410.22258 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Automatica 188 (2026): 112959 Related DOI : https://doi.org/10.1016/j.automatica.2026.112959 Focus to learn more DOI(s) linking to related resources Submission history From: Patricia Pauli [ view email ] [v1] Tue, 29 Oct 2024 17:20:14 UTC (220 KB) [v2] Thu, 9 Apr 2026 07:45:10 UTC (2,172 KB) Full-text links: Access Paper: View a PDF of the paper titled LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layers, by Patricia Pauli and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2024-10 Change to browse by: cs cs.SY eess eess.IV eess.SY stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Accelerating Ordinary Differential Equations Through Physics-Preserving Neural Networks#291217
• TOWARDS DATA-EFFICIENT DEEP LEARNING#254778
• OD3: Optimization-free Dataset Distillation for Object Detection#1062772
• Adaptive activation functions accelerate convergence in deep and physics-informed neural networks#19810
• Layerwise Decoupling for Stable Structured Sparsification of Fully Connected Layers#1035095