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Neural networks trained to minimize the logistic (a.k.a. cross-entropy) loss with gradient-based methods are observed to perform well in many supervised classification tasks. Towards understanding this phenomenon, we analyze the training…

Optimization and Control · Mathematics 2020-06-23 Lenaic Chizat , Francis Bach

A loss function measures the discrepancy between the true values and their estimated fits, for a given instance of data. In classification problems, a loss function is said to be proper if a minimizer of the expected loss is the true…

Information Theory · Computer Science 2020-01-03 Amichai Painsky , Gregory W. Wornell

Increasing diversity in language models is a challenging yet essential objective. A common approach is to raise the decoding temperature. In this work, we investigate this approach through a simplistic yet common case to provide insights…

Computation and Language · Computer Science 2025-08-14 Alexandre Verine , Florian Le Bronnec , Kunhao Zheng , Alexandre Allauzen , Yann Chevaleyre , Benjamin Negrevergne

We propose an extended generalization of the pseudo Huber loss formulation. We show that using the log-exp transform together with the logistic function, we can create a loss which combines the desirable properties of the strictly convex…

Machine Learning · Statistics 2022-02-24 Kaan Gokcesu , Hakan Gokcesu

All machine learning algorithms use a loss, cost, utility or reward function to encode the learning objective and oversee the learning process. This function that supervises learning is a frequently unrecognized hyperparameter that…

Neural and Evolutionary Computing · Computer Science 2024-11-06 Mathew Mithra Noel , Arindam Banerjee , Yug Oswal , Geraldine Bessie Amali D , Venkataraman Muthiah-Nakarajan

Estimating the ratio of two probability densities from a finite number of observations is a central machine learning problem. A common approach is to construct estimators using binary classifiers that distinguish observations from the two…

Machine Learning · Computer Science 2025-01-28 Werner Zellinger

Policy-gradient approaches to reinforcement learning have two common and undesirable overhead procedures, namely warm-start training and sample variance reduction. In this paper, we describe a reinforcement learning method based on a…

Machine Learning · Computer Science 2017-10-17 Nan Ding , Radu Soricut

When training neural networks with custom objectives, such as ranking losses and shortest-path losses, a common problem is that they are, per se, non-differentiable. A popular approach is to continuously relax the objectives to provide…

Machine Learning · Computer Science 2024-10-28 Felix Petersen , Christian Borgelt , Tobias Sutter , Hilde Kuehne , Oliver Deussen , Stefano Ermon

We propose a computationally-friendly adaptive learning rate schedule, "AdaLoss", which directly uses the information of the loss function to adjust the stepsize in gradient descent methods. We prove that this schedule enjoys linear…

Machine Learning · Statistics 2021-09-20 Xiaoxia Wu , Yuege Xie , Simon Du , Rachel Ward

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

Regularization in modern machine learning is crucial, and it can take various forms in algorithmic design: training set, model family, error function, regularization terms, and optimizations. In particular, the learning rate, which can be…

Machine Learning · Computer Science 2023-12-04 Yefan Zhou , Tianyu Pang , Keqin Liu , Charles H. Martin , Michael W. Mahoney , Yaoqing Yang

There is a growing need for models that are interpretable and have reduced energy and computational cost (e.g., in health care analytics and federated learning). Examples of algorithms to train such models include logistic regression and…

Machine Learning · Computer Science 2023-02-21 Tyler Sypherd , Nathan Stromberg , Richard Nock , Visar Berisha , Lalitha Sankar

Multi-task learning (MTL) trains deep neural networks to optimize several objectives simultaneously using a shared backbone, which leads to reduced computational costs, improved data efficiency, and enhanced performance through cross-task…

Machine Learning · Computer Science 2025-09-30 Hoang Phan , Lam Tran , Quyen Tran , Ngoc N. Tran , Tuan Truong , Qi Lei , Nhat Ho , Dinh Phung , Trung Le

Person re-identification is a challenging task because of the high intra-class variance induced by the unrestricted nuisance factors of variations such as pose, illumination, viewpoint, background, and sensor noise. Recent approaches…

Computer Vision and Pattern Recognition · Computer Science 2023-01-02 Sinan Sabri , Zaigham Randhawa , Gianfranco Doretto

Softmax Loss (SL) is widely applied in recommender systems (RS) and has demonstrated effectiveness. This work analyzes SL from a pairwise perspective, revealing two significant limitations: 1) the relationship between SL and conventional…

Machine Learning · Computer Science 2025-08-05 Weiqin Yang , Jiawei Chen , Xin Xin , Sheng Zhou , Binbin Hu , Yan Feng , Chun Chen , Can Wang

Although recent works have brought some insights into the performance improvement of techniques used in state-of-the-art deep-learning models, more work is needed to understand their generalization properties. We shed light on this matter…

Machine Learning · Computer Science 2020-07-31 Mahsa Forouzesh , Farnood Salehi , Patrick Thiran

Optimal decision making requires that classifiers produce uncertainty estimates consistent with their empirical accuracy. However, deep neural networks are often under- or over-confident in their predictions. Consequently, methods have been…

Training neural networks with high certified accuracy against adversarial examples remains an open challenge despite significant efforts. While certification methods can effectively leverage tight convex relaxations for bound computation,…

Machine Learning · Computer Science 2025-07-16 Stefan Balauca , Mark Niklas Müller , Yuhao Mao , Maximilian Baader , Marc Fischer , Martin Vechev

Proper losses such as cross-entropy incentivize classifiers to produce class probabilities that are well-calibrated on the training data. Due to the generalization gap, these classifiers tend to become overconfident on the test data,…

Machine Learning · Computer Science 2025-08-27 Viacheslav Komisarenko , Meelis Kull

Orthogonal statistical learning and double machine learning have emerged as general frameworks for two-stage statistical prediction in the presence of a nuisance component. We establish non-asymptotic bounds on the excess risk of orthogonal…

Machine Learning · Statistics 2022-06-22 Lang Liu , Carlos Cinelli , Zaid Harchaoui