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We discover restrained numerical instabilities in current training practices of deep networks with stochastic gradient descent (SGD), and its variants. We show numerical error (on the order of the smallest floating point bit and thus the…

Machine Learning · Computer Science 2024-06-13 Yuxin Sun , Dong Lao , Ganesh Sundaramoorthi , Anthony Yezzi

Deep neural networks (DNNs) have achieved remarkable success in computer vision tasks such as image classification, segmentation, and object detection. However, they are vulnerable to adversarial attacks, which can cause incorrect…

Computer Vision and Pattern Recognition · Computer Science 2025-11-03 Suklav Ghosh , Sonal Kumar , Arijit Sur

Deep learning models excel in stationary data but struggle in non-stationary environments due to a phenomenon known as loss of plasticity (LoP), the degradation of their ability to learn in the future. This work presents a first-principles…

Reinforcement learning (RL) policies deployed in real-world environments must remain reliable under adversarial perturbations. At the same time, modern deep RL agents are heavily over-parameterized, raising costs and fragility concerns.…

Machine Learning · Computer Science 2025-10-16 James Pedley , Benjamin Etheridge , Stephen J. Roberts , Francesco Quinzan

Due to their flexibility and predictive performance, machine-learning based regression methods have become an important tool for predictive modeling and forecasting. However, most methods focus on estimating the conditional mean or specific…

Machine Learning · Statistics 2019-03-15 Rui Li , Howard D. Bondell , Brian J. Reich

State-of-the-art pre-trained image models predominantly adopt a two-stage approach: initial unsupervised pre-training on large-scale datasets followed by task-specific fine-tuning using Cross-Entropy loss~(CE). However, it has been…

Computer Vision and Pattern Recognition · Computer Science 2024-11-18 Zijun Long , George Killick , Lipeng Zhuang , Gerardo Aragon-Camarasa , Zaiqiao Meng , Richard Mccreadie

Important insights towards the explainability of neural networks reside in the characteristics of their decision boundaries. In this work, we borrow tools from the field of adversarial robustness, and propose a new perspective that relates…

Machine Learning · Computer Science 2020-10-16 Guillermo Ortiz-Jimenez , Apostolos Modas , Seyed-Mohsen Moosavi-Dezfooli , Pascal Frossard

Time-dependent data-generating distributions have proven to be difficult for gradient-based training of neural networks, as the greedy updates result in catastrophic forgetting of previously learned knowledge. Despite the progress in the…

Machine Learning · Computer Science 2023-04-03 Matthias De Lange , Gido van de Ven , Tinne Tuytelaars

The highly non-linear nature of deep neural networks causes them to be susceptible to adversarial examples and have unstable gradients which hinders interpretability. However, existing methods to solve these issues, such as adversarial…

Machine Learning · Computer Science 2023-01-11 Suraj Srinivas , Kyle Matoba , Himabindu Lakkaraju , Francois Fleuret

The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhancing the stability of neural networks. We focus on a popular…

Numerical Analysis · Mathematics 2025-10-28 Matthias J. Ehrhardt , Davide Murari , Ferdia Sherry

Reinforcement learning (RL) has become a central component of post-training for large language models (LLMs), particularly for complex reasoning tasks that require stable optimization over long generation horizons. However, achieving…

Machine Learning · Computer Science 2026-02-17 Yuepeng Sheng , Yuwei Huang , Shuman Liu , Anxiang Zeng , Haibo Zhang

The existence of adversarial data examples has drawn significant attention in the deep-learning community; such data are seemingly minimally perturbed relative to the original data, but lead to very different outputs from a deep-learning…

Machine Learning · Computer Science 2019-11-12 Bai Li , Changyou Chen , Wenlin Wang , Lawrence Carin

The loss function is crucial to machine learning, especially in supervised learning frameworks. It is a fundamental component that controls the behavior and general efficacy of learning algorithms. However, despite their widespread use,…

Machine Learning · Computer Science 2026-02-09 Soumi Mahato , Lineesh M. C

This paper investigates the deep learning optimization problem with softmax cross-entropy loss. We propose a layer separation strategy to alleviate the strong nonconvexity encountered during training deep networks. For cross-entropy models…

Machine Learning · Computer Science 2026-04-28 Yaru Liu , Michael K. Ng , Yiqi Gu

Adversarial examples of deep neural networks are receiving ever increasing attention because they help in understanding and reducing the sensitivity to their input. This is natural given the increasing applications of deep neural networks…

Computer Vision and Pattern Recognition · Computer Science 2021-01-13 Hanwei Zhang , Yannis Avrithis , Teddy Furon , Laurent Amsaleg

Recent developments in AI have made it ubiquitous, every industry is trying to adopt some form of intelligent processing of their data. Despite so many advances in the field, AIs full capability is yet to be exploited by the industry.…

Machine Learning · Computer Science 2021-11-10 Vishal Rajput

We consider the sample complexity of learning with adversarial robustness. Most prior theoretical results for this problem have considered a setting where different classes in the data are close together or overlapping. Motivated by some…

Machine Learning · Computer Science 2023-01-19 Robi Bhattacharjee , Somesh Jha , Kamalika Chaudhuri

Cross-entropy loss is the standard metric used to train classification models in deep learning and gradient boosting. It is well-known that this loss function fails to account for similarities between the different values of the target. We…

Machine Learning · Statistics 2022-06-16 Brian Lucena

When humans learn a new concept, they might ignore examples that they cannot make sense of at first, and only later focus on such examples, when they are more useful for learning. We propose incorporating this idea of tunable sensitivity…

Machine Learning · Statistics 2016-11-24 Gil Keren , Sivan Sabato , Björn Schuller

Despite the significant advances in deep learning over the past decade, a major challenge that limits the wide-spread adoption of deep learning has been their fragility to adversarial attacks. This sensitivity to making erroneous…

Machine Learning · Computer Science 2021-06-21 Hossein Aboutalebi , Mohammad Javad Shafiee , Michelle Karg , Christian Scharfenberger , Alexander Wong