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We examine the impact of learning Lipschitz continuous models in the context of model-based reinforcement learning. We provide a novel bound on multi-step prediction error of Lipschitz models where we quantify the error using the…

Machine Learning · Computer Science 2018-07-30 Kavosh Asadi , Dipendra Misra , Michael L. Littman

This paper presents a study of robust policy networks in deep reinforcement learning. We investigate the benefits of policy parameterizations that naturally satisfy constraints on their Lipschitz bound, analyzing their empirical performance…

Machine Learning · Computer Science 2025-02-07 Nicholas H. Barbara , Ruigang Wang , Ian R. Manchester

Neural networks are getting better accuracy with higher energy and computational cost. After quantization, the cost can be greatly saved, and the quantized models are more hardware friendly with acceptable accuracy loss. On the other hand,…

Machine Learning · Computer Science 2021-10-26 Chang Song , Riya Ranjan , Hai Li

Neural Machine Translation (NMT) is resource intensive. We design a quantization procedure to compress NMT models better for devices with limited hardware capability. Because most neural network parameters are near zero, we employ…

Computation and Language · Computer Science 2019-09-23 Alham Fikri Aji , Kenneth Heafield

Empirical scaling laws prescribe how to allocate parameters, data, and compute, while maximal-update parameterization ($\mu$P) enables learning-rate transfer across widths by equalizing early-time update magnitudes. However, in modern…

Machine Learning · Computer Science 2025-10-20 Zhiyuan Fan , Yifeng Liu , Qingyue Zhao , Angela Yuan , Quanquan Gu

Modern language-model training is increasingly exposed to instability, degraded runs, and wasted compute, especially under aggressive learning-rate, scale, and runtime-stress conditions. This paper introduces Learn-by-Wire Guard…

Artificial Intelligence · Computer Science 2026-05-20 Anis Radianis

The robustness of neural networks against input perturbations with bounded magnitude represents a serious concern in the deployment of deep learning models in safety-critical systems. Recently, the scientific community has focused on…

Machine Learning · Computer Science 2023-11-29 Bernd Prach , Fabio Brau , Giorgio Buttazzo , Christoph H. Lampert

Lipschitz constants of neural networks have been explored in various contexts in deep learning, such as provable adversarial robustness, estimating Wasserstein distance, stabilising training of GANs, and formulating invertible neural…

Machine Learning · Statistics 2021-06-10 Hyunjik Kim , George Papamakarios , Andriy Mnih

Lipschitz-constrained neural networks have several advantages over unconstrained ones and can be applied to a variety of problems, making them a topic of attention in the deep learning community. Unfortunately, it has been shown both…

Machine Learning · Computer Science 2023-12-20 Stanislas Ducotterd , Alexis Goujon , Pakshal Bohra , Dimitris Perdios , Sebastian Neumayer , Michael Unser

Open weight models, which are ubiquitous, rarely provide access to their training data or loss function. This makes modifying such models for tasks such as pruning or unlearning, which are constrained by this unavailability, an active area…

Machine Learning · Computer Science 2026-01-19 Dhruva Kashyap , Chaitanya Murti , Pranav K Nayak , Tanay Narshana , Chiranjib Bhattacharyya

Deep learning has achieved remarkable success across a wide range of tasks, but its models often suffer from instability and vulnerability: small changes to the input may drastically affect predictions, while optimization can be hindered by…

Machine Learning · Computer Science 2025-10-30 Blaise Delattre

Motivated by classical work on the numerical integration of ordinary differential equations we present a ResNet-styled neural network architecture that encodes non-expansive (1-Lipschitz) operators, as long as the spectral norms of the…

We propose a novel multi-layer neural network architecture that gives a promising neural network empowered optimization approach to the image restoration problem. The proposed architecture is motivated by the recent study of monotone…

Optimization and Control · Mathematics 2025-10-27 Haruya Shimizu , Masahiro Yukawa

Despite the widespread success of Transformers across various domains, their optimization guarantees in large-scale model settings are not well-understood. This paper rigorously analyzes the convergence properties of gradient flow in…

Machine Learning · Statistics 2024-11-01 Cheng Gao , Yuan Cao , Zihao Li , Yihan He , Mengdi Wang , Han Liu , Jason Matthew Klusowski , Jianqing Fan

A crucial property for achieving secure, trustworthy and interpretable deep learning systems is their robustness: small changes to a system's inputs should not result in large changes to its outputs. Mathematically, this means one strives…

Machine Learning · Computer Science 2024-06-04 Bernd Prach , Christoph H. Lampert

The state of the art in machine translation (MT) is governed by neural approaches, which typically provide superior translation accuracy over statistical approaches. However, on the closely related task of word alignment, traditional…

Computation and Language · Computer Science 2019-09-06 Sarthak Garg , Stephan Peitz , Udhyakumar Nallasamy , Matthias Paulik

Convergence and convergence rate analyses of adaptive methods, such as Adaptive Moment Estimation (Adam) and its variants, have been widely studied for nonconvex optimization. The analyses are based on assumptions that the expected or…

Machine Learning · Computer Science 2022-06-28 Hideaki Iiduka

For a given stable recurrent neural network (RNN) that is trained to perform a classification task using sequential inputs, we quantify explicit robustness bounds as a function of trainable weight matrices. The sequential inputs can be…

Machine Learning · Computer Science 2022-03-11 Guangyi Liu , Arash Amini , Martin Takac , Nader Motee

Large models recently are widely applied in artificial intelligence, so efficient training of large models has received widespread attention. More recently, a useful Muon optimizer is specifically designed for matrix-structured parameters…

Machine Learning · Computer Science 2025-09-22 Feihu Huang , Yuning Luo , Songcan Chen

Understanding and evaluating the robustness of neural networks under adversarial settings is a subject of growing interest. Attacks proposed in the literature usually work with models trained to minimize cross-entropy loss and output…

Machine Learning · Computer Science 2020-03-09 Sean Saito , Sujoy Roy
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