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Computational efficiency and robustness are essential in process modeling, optimization, and control for real-world engineering applications. While neural network-based approaches have gained significant attention in recent years,…

Machine Learning · Computer Science 2026-03-17 Zihao Wang , Yuhan Li , Yao Shi , Zhe Wu

This paper presents a framework for bounding the approximation error in imitation model predictive controllers utilizing neural networks. Leveraging the Lipschitz properties of these neural networks, we derive a bound that guides dataset…

Systems and Control · Electrical Eng. & Systems 2026-03-27 Hendrik Alsmeier , Lukas Theiner , Anton Savchenko , Ali Mesbah , Rolf Findeisen

This paper introduces new parameterizations of equilibrium neural networks, i.e. networks defined by implicit equations. This model class includes standard multilayer and residual networks as special cases. The new parameterization admits a…

Machine Learning · Computer Science 2020-10-06 Max Revay , Ruigang Wang , Ian R. Manchester

Lipschitz continuity of algorithms, introduced by Kumabe and Yoshida (FOCS'23), measures the stability of an algorithm against small input perturbations. Algorithms with small Lipschitz continuity are desirable, as they ensure reliable…

Data Structures and Algorithms · Computer Science 2025-07-01 Tatsuya Gima , Soh Kumabe , Yuichi Yoshida

We consider the problem of distributionally robust multimodal machine learning. Existing approaches often rely on merging modalities on the feature level (early fusion) or heuristic uncertainty modeling, which downplays modality-aware…

Machine Learning · Computer Science 2025-11-11 Peilin Yang , Yu Ma

Gradient Descent (GD) is a powerful workhorse of modern machine learning thanks to its scalability and efficiency in high-dimensional spaces. Its ability to find local minimisers is only guaranteed for losses with Lipschitz gradients, where…

Machine Learning · Computer Science 2023-07-27 Lei Chen , Joan Bruna

Neural Ordinary Differential Equations (NODEs) probed the usage of numerical solvers to solve the differential equation characterized by a Neural Network (NN), therefore initiating a new paradigm of deep learning models with infinite depth.…

Machine Learning · Computer Science 2023-05-17 Vishal Purohit

We investigate the problems and challenges of evaluating the robustness of Differential Equation-based (DE) networks against synthetic distribution shifts. We propose a novel and simple accuracy metric which can be used to evaluate…

Machine Learning · Computer Science 2022-06-17 Martin Gonzalez , Hatem Hajri , Loic Cantat , Mihaly Petreczky

Despite significant advances, deep networks remain highly susceptible to adversarial attack. One fundamental challenge is that small input perturbations can often produce large movements in the network's final-layer feature space. In this…

Machine Learning · Computer Science 2023-04-20 Maria-Florina Balcan , Avrim Blum , Dravyansh Sharma , Hongyang Zhang

Predictive uncertainty estimation is essential for deploying Deep Neural Networks in real-world autonomous systems. However, most successful approaches are computationally intensive. In this work, we attempt to address these challenges in…

Computer Vision and Pattern Recognition · Computer Science 2022-07-22 Gianni Franchi , Xuanlong Yu , Andrei Bursuc , Emanuel Aldea , Severine Dubuisson , David Filliat

Most prior results on differentially private stochastic gradient descent (DP-SGD) are derived under the simplistic assumption of uniform Lipschitzness, i.e., the per-sample gradients are uniformly bounded. We generalize uniform…

Machine Learning · Computer Science 2023-06-07 Rudrajit Das , Satyen Kale , Zheng Xu , Tong Zhang , Sujay Sanghavi

We propose an algorithm to enhance certified robustness of a deep model ensemble by optimally weighting each base model. Unlike previous works on using ensembles to empirically improve robustness, our algorithm is based on optimizing a…

Machine Learning · Statistics 2019-11-01 Huan Zhang , Minhao Cheng , Cho-Jui Hsieh

Deriving sharp and computable upper bounds of the Lipschitz constant of deep neural networks is crucial to formally guarantee the robustness of neural-network based models. We analyse three existing upper bounds written for the $l^2$ norm.…

Machine Learning · Computer Science 2024-10-29 Moreno Pintore , Bruno Després

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 bound in neural…

Machine Learning · Computer Science 2025-03-03 Marius F. R. Juston , William R. Norris , Dustin Nottage , Ahmet Soylemezoglu

Diffusion models, which employ stochastic differential equations to sample images through integrals, have emerged as a dominant class of generative models. However, the rationality of the diffusion process itself receives limited attention,…

Computer Vision and Pattern Recognition · Computer Science 2024-12-17 Zhantao Yang , Ruili Feng , Han Zhang , Yujun Shen , Kai Zhu , Lianghua Huang , Yifei Zhang , Yu Liu , Deli Zhao , Jingren Zhou , Fan Cheng

Lipschitz constants of neural networks allow for guarantees of robustness in image classification, safety in controller design, and generalizability beyond the training data. As calculating Lipschitz constants is NP-hard, techniques for…

Machine Learning · Computer Science 2024-01-09 Anton Xue , Lars Lindemann , Alexander Robey , Hamed Hassani , George J. Pappas , Rajeev Alur

Feature attributions are a popular tool for explaining the behavior of Deep Neural Networks (DNNs), but have recently been shown to be vulnerable to attacks that produce divergent explanations for nearby inputs. This lack of robustness is…

Machine Learning · Computer Science 2020-10-23 Zifan Wang , Haofan Wang , Shakul Ramkumar , Matt Fredrikson , Piotr Mardziel , Anupam Datta

A standard technique for understanding underlying dependency structures among a set of variables posits a shared conditional probability distribution for the variables measured on individuals within a group. This approach is often referred…

Machine Learning · Statistics 2014-05-13 Elham Azizi , James E. Galagan , Edoardo M. Airoldi

We propose an Adaptive MPC framework for uncertain linear systems to achieve robust satisfaction of state and input constraints. The uncertainty in the system is assumed additive, state dependent, and globally Lipschitz with a known…

Systems and Control · Electrical Eng. & Systems 2020-02-18 Monimoy Bujarbaruah , Siddharth H. Nair , Francesco Borrelli

We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…

Optimization and Control · Mathematics 2025-10-20 Simon Michalowsky , Carsten Scherer , Christian Ebenbauer