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Next-token prediction with the logarithmic loss is a cornerstone of autoregressive sequence modeling, but, in practice, suffers from error amplification, where errors in the model compound and generation quality degrades as sequence length…

Machine Learning · Computer Science 2025-02-19 Dhruv Rohatgi , Adam Block , Audrey Huang , Akshay Krishnamurthy , Dylan J. Foster

We present a detailed study of cardinality-aware top-$k$ classification, a novel approach that aims to learn an accurate top-$k$ set predictor while maintaining a low cardinality. We introduce a new target loss function tailored to this…

Machine Learning · Computer Science 2024-07-12 Corinna Cortes , Anqi Mao , Christopher Mohri , Mehryar Mohri , Yutao Zhong

Cross Entropy (CE) has an important role in machine learning and, in particular, in neural networks. It is commonly used in neural networks as the cost between the known distribution of the label and the Softmax/Sigmoid output. In this…

Machine Learning · Computer Science 2020-07-17 Ron Shoham , Haim Permuter

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

Cross-entropy (CE) loss is the de-facto standard for training deep neural networks to perform classification. However, CE-trained deep neural networks struggle with robustness and generalisation issues. To alleviate these issues, we propose…

Machine Learning · Computer Science 2025-01-22 Michael W. Spratling , Heiko H. Schütt

In Sequential Recommendation Systems (SRecsys), traditional training approaches that rely on Cross-Entropy (CE) loss often prioritize accuracy but fail to align well with user satisfaction metrics. CE loss focuses on maximizing the…

Information Retrieval · Computer Science 2025-02-21 Chen Wang , Fangxin Wang , Ruocheng Guo , Yueqing Liang , Philip S. Yu

In many large-scale classification problems, classes are organized in a known hierarchy, typically represented as a tree expressing the inclusion of classes in superclasses. We introduce a loss for this type of supervised hierarchical…

Computer Vision and Pattern Recognition · Computer Science 2024-11-26 Nicolas Urbani , Sylvain Rousseau , Yves Grandvalet , Leonardo Tanzi

In classification, the de facto method for aggregating individual losses is the average loss. When the actual metric of interest is 0-1 loss, it is common to minimize the average surrogate loss for some well-behaved (e.g. convex) surrogate.…

Machine Learning · Computer Science 2018-11-06 Bryan He , James Zou

Conformal prediction (CP) provides a comprehensive framework to produce statistically rigorous uncertainty sets for black-box machine learning models. To further improve the efficiency of CP, conformal correction is proposed to fine-tune or…

Machine Learning · Computer Science 2025-12-03 Senrong Xu , Tianyu Wang , Zenan Li , Yuan Yao , Taolue Chen , Feng Xu , Xiaoxing Ma

Stochastic optimization often involves calculating the expected value of a first-order max or min function, known as a first-order loss function. In this context, loss functions are frequently approximated using piecewise linear functions.…

Optimization and Control · Mathematics 2023-09-26 Yotaro Takazawa

Two things seem to be indisputable in the contemporary deep learning discourse: 1. The categorical cross-entropy loss after softmax activation is the method of choice for classification. 2. Training a CNN classifier from scratch on small…

Machine Learning · Computer Science 2019-12-12 Björn Barz , Joachim Denzler

When it is ethical and legal to use a sensitive attribute (such as gender or race) in machine learning systems, the question remains how to do so. We show that the naive application of machine learning algorithms using sensitive features…

Machine Learning · Computer Science 2017-07-21 Cynthia Dwork , Nicole Immorlica , Adam Tauman Kalai , Max Leiserson

In this work, we introduce the {\em average top-$k$} (\atk) loss as a new aggregate loss for supervised learning, which is the average over the $k$ largest individual losses over a training dataset. We show that the \atk loss is a natural…

Machine Learning · Statistics 2017-12-21 Yanbo Fan , Siwei Lyu , Yiming Ying , Bao-Gang Hu

As deep neural networks are more commonly deployed in high-stakes domains, their black-box nature makes uncertainty quantification challenging. We investigate the presentation of conformal prediction sets--a distribution-free class of…

Human-Computer Interaction · Computer Science 2024-04-29 Dongping Zhang , Angelos Chatzimparmpas , Negar Kamali , Jessica Hullman

Understanding the confidence with which a machine learning model classifies an input datum is an important, and perhaps under-investigated, concept. In this paper, we propose a new calibration metric, the Entropic Calibration Difference…

Machine Learning · Computer Science 2025-02-21 Daniel James Sumler , Lee Devlin , Simon Maskell , Richard O. Lane

In extreme classification problems, learning algorithms are required to map instances to labels from an extremely large label set. We build on a recent extreme classification framework with logarithmic time and space, and on a general…

Machine Learning · Computer Science 2018-12-13 Itay Evron , Edward Moroshko , Koby Crammer

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

By searching for shared inductive biases across tasks, meta-learning promises to accelerate learning on novel tasks, but with the cost of solving a complex bilevel optimization problem. We introduce and rigorously define the trade-off…

Machine Learning · Computer Science 2021-04-15 Katelyn Gao , Ozan Sener

This paper analyzes Cross-Entropy (CE) loss in knowledge distillation (KD) for recommender systems. KD for recommender systems targets at distilling rankings, especially among items most likely to be preferred, and can only be computed on a…

Information Retrieval · Computer Science 2026-03-03 Zhangchi Zhu , Wei Zhang

In this paper, we examine the CE method in the broad context of Monte Carlo Optimization (MCO) and Parametric Learning (PL), a type of machine learning. A well-known overarching principle used to improve the performance of many PL…

Numerical Analysis · Computer Science 2008-10-07 Dev Rajnarayan , David Wolpert