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Learned optimizers -- neural networks that are trained to act as optimizers -- have the potential to dramatically accelerate training of machine learning models. However, even when meta-trained across thousands of tasks at huge…

Machine Learning · Computer Science 2022-09-23 James Harrison , Luke Metz , Jascha Sohl-Dickstein

We propose a general framework for increasing local stability of Artificial Neural Nets (ANNs) using Robust Optimization (RO). We achieve this through an alternating minimization-maximization procedure, in which the loss of the network is…

Machine Learning · Statistics 2018-05-07 Uri Shaham , Yutaro Yamada , Sahand Negahban

Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…

Machine Learning · Computer Science 2026-01-13 Chutian Huang , Chang Ma , Kaibo Wang , Yang Xiang

In this paper we address the issue of output instability of deep neural networks: small perturbations in the visual input can significantly distort the feature embeddings and output of a neural network. Such instability affects many deep…

Computer Vision and Pattern Recognition · Computer Science 2016-04-18 Stephan Zheng , Yang Song , Thomas Leung , Ian Goodfellow

Deep learning systems achieve remarkable empirical performance, yet the stability of the training process itself remains poorly understood. Training unfolds as a high-dimensional dynamical system in which small perturbations to…

Machine Learning · Computer Science 2026-01-21 Zhipeng Zhang , Zhenjie Yao , Kai Li , Lei Yang

Deep Neural Networks (DNNs) are becoming integral components of real world services relied upon by millions of users. Unfortunately, architects of these systems can find it difficult to ensure reliable performance as irrelevant details like…

Machine Learning · Computer Science 2023-05-22 Arghya Datta , Subhrangshu Nandi , Jingcheng Xu , Greg Ver Steeg , He Xie , Anoop Kumar , Aram Galstyan

Maintaining numerical stability in machine learning models is crucial for their reliability and performance. One approach to maintain stability of a network layer is to integrate the condition number of the weight matrix as a regularizing…

Machine Learning · Computer Science 2024-10-02 Rossen Nenov , Daniel Haider , Peter Balazs

We consider the problem of retraining machine learning (ML) models when new batches of data become available. Existing approaches greedily optimize for predictive power independently at each batch, without considering the stability of the…

Machine Learning · Computer Science 2025-02-05 Dimitris Bertsimas , Vassilis Digalakis , Yu Ma , Phevos Paschalidis

The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…

Machine Learning · Computer Science 2024-04-10 Kaloyan Danovski , Miguel C. Soriano , Lucas Lacasa

Spiking neural networks (SNNs) are gaining popularity in deep learning due to their low energy budget on neuromorphic hardware. However, they still face challenges in lacking sufficient robustness to guard safety-critical applications such…

Neural and Evolutionary Computing · Computer Science 2024-06-03 Jianhao Ding , Zhiyu Pan , Yujia Liu , Zhaofei Yu , Tiejun Huang

We examine the stability of loss-minimizing training processes that are used for deep neural networks (DNN) and other classifiers. While a classifier is optimized during training through a so-called loss function, the performance of…

Analysis of PDEs · Mathematics 2020-10-05 Leonid Berlyand , Pierre-Emmanuel Jabin , C. Alex Safsten

The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…

Numerical Analysis · Mathematics 2024-02-08 Davide Evangelista , James Nagy , Elena Morotti , Elena Loli Piccolomini

We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization…

Optimization and Control · Mathematics 2025-10-07 Rajiv Sambharya , Jinho Bok , Nikolai Matni , George Pappas

Current reconfiguration techniques are based on starting the system in a consistent configuration, in which all participating entities are in their initial state. Starting from that state, the system must preserve consistency as long as a…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-12-07 Shlomi Dolev , Chryssis Georgiou , Ioannis Marcoullis , Elad M. Schiller

Reinforcement learning is a general methodology of adaptive optimal control that has attracted much attention in various fields ranging from video game industry to robot manipulators. Despite its remarkable performance demonstrations, plain…

Dynamical Systems · Mathematics 2022-06-14 Pavel Osinenko , Grigory Yaremenko , Ilya Osokin

We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…

Data Structures and Algorithms · Computer Science 2025-03-10 Wouter Meulemans , Bettina Speckmann , Kevin Verbeek , Jules Wulms

In this paper, a robust optimization framework is developed to train shallow neural networks based on reachability analysis of neural networks. To characterize noises of input data, the input training data is disturbed in the description of…

Machine Learning · Computer Science 2021-07-28 Yejiang Yang , Weiming Xiang

There is an emerging trend in applying deep learning methods to control complex nonlinear systems. This paper considers enhancing the runtime safety of nonlinear systems controlled by neural networks in the presence of disturbance and…

Systems and Control · Electrical Eng. & Systems 2024-03-26 Jianglin Lan , Siyuan Zhan , Ron Patton , Xianxian Zhao

Optimization is an integral part of modern deep learning. Recently, the concept of learned optimizers has emerged as a way to accelerate this optimization process by replacing traditional, hand-crafted algorithms with meta-learned…

Machine Learning · Computer Science 2023-12-13 Jan Sobotka , Petr Šimánek , Daniel Vašata

While existing work in robust deep learning has focused on small pixel-level norm-based perturbations, this may not account for perturbations encountered in several real-world settings. In many such cases although test data might not be…

Computer Vision and Pattern Recognition · Computer Science 2021-04-09 Tejas Gokhale , Rushil Anirudh , Bhavya Kailkhura , Jayaraman J. Thiagarajan , Chitta Baral , Yezhou Yang
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