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Many deep learning-based speech enhancement algorithms are designed to minimize the mean-square error (MSE) in some transform domain between a predicted and a target speech signal. However, optimizing for MSE does not necessarily guarantee…

Sound · Computer Science 2020-01-31 Morten Kolbæk , Zheng-Hua Tan , Søren Holdt Jensen , Jesper Jensen

The Softmax bottleneck was first identified in language modeling as a theoretical limit on the expressivity of Softmax-based models. Being one of the most widely-used methods to output probability, Softmax-based models have found a wide…

Machine Learning · Computer Science 2021-10-12 Ying-Chen Lin

The Softmax loss is one of the most widely employed surrogate objectives for classification and ranking tasks. To elucidate its theoretical properties, the Fenchel-Young framework situates it as a canonical instance within a broad family of…

Machine Learning · Computer Science 2026-02-02 Yuanhao Pu , Defu Lian , Enhong Chen

In the field of pattern classification, the training of deep learning classifiers is mostly end-to-end learning, and the loss function is the constraint on the final output (posterior probability) of the network, so the existence of Softmax…

Computer Vision and Pattern Recognition · Computer Science 2022-10-24 Qiuyu Zhu , Xuewen Zu

Large language models (LLMs) have gained much attention in the recommendation community; some studies have observed that LLMs, fine-tuned by the cross-entropy loss with a full softmax, could achieve state-of-the-art performance already.…

Information Retrieval · Computer Science 2024-02-23 Cong Xu , Zhangchi Zhu , Jun Wang , Jianyong Wang , Wei Zhang

Ranking tasks constitute fundamental components of extreme similarity learning frameworks, where extremely large corpora of objects are modeled through relative similarity relationships adhering to predefined ordinal structures. Among…

Machine Learning · Computer Science 2025-06-12 Yuanhao Pu , Defu Lian , Xiaolong Chen , Xu Huang , Jin Chen , Enhong Chen

In the domain of machine learning, the significance of the loss function is paramount, especially in supervised learning tasks. It serves as a fundamental pillar that profoundly influences the behavior and efficacy of supervised learning…

Machine Learning · Computer Science 2024-09-23 Mushir Akhtar , M. Tanveer , Mohd. Arshad

Large language models (LLMs) have made transformed changes for human society. One of the key computation in LLMs is the softmax unit. This operation is important in LLMs because it allows the model to generate a distribution over possible…

Machine Learning · Computer Science 2023-04-27 Yichuan Deng , Zhihang Li , Zhao Song

Distance metric learning (DML) is to learn the embeddings where examples from the same class are closer than examples from different classes. It can be cast as an optimization problem with triplet constraints. Due to the vast number of…

Computer Vision and Pattern Recognition · Computer Science 2020-04-16 Qi Qian , Lei Shang , Baigui Sun , Juhua Hu , Hao Li , Rong Jin

A soft-max function has two main efficiency measures: (1) approximation - which corresponds to how well it approximates the maximum function, (2) smoothness - which shows how sensitive it is to changes of its input. Our goal is to identify…

Machine Learning · Computer Science 2026-01-01 Alessandro Epasto , Mohammad Mahdian , Vahab Mirrokni , Manolis Zampetakis

The use of contrastive loss for representation learning has become prominent in computer vision, and it is now getting attention in Natural Language Processing (NLP). Here, we explore the idea of using a batch-softmax contrastive loss when…

Computation and Language · Computer Science 2021-11-01 Anton Chernyavskiy , Dmitry Ilvovsky , Pavel Kalinin , Preslav Nakov

We consider learning a probabilistic classifier from partially-labelled supervision (inputs denoted with multiple possibilities) using standard neural architectures with a softmax as the final layer. We identify a bias phenomenon that can…

Machine Learning · Computer Science 2023-07-04 Zsolt Zombori , Agapi Rissaki , Kristóf Szabó , Wolfgang Gatterbauer , Michael Benedikt

We consider training decision trees using noisily labeled data, focusing on loss functions that can lead to robust learning algorithms. Our contributions are threefold. First, we offer novel theoretical insights on the robustness of many…

Machine Learning · Computer Science 2024-01-24 Jonathan Wilton , Nan Ye

Batch size scheduling (BSS) plays a critical role in large-scale deep learning training, influencing both optimization dynamics and computational efficiency. Yet, its theoretical foundations remain poorly understood. In this work, we show…

Machine Learning · Computer Science 2026-02-24 Jinbo Wang , Binghui Li , Zhanpeng Zhou , Mingze Wang , Yuxuan Sun , Jiaqi Zhang , Xunliang Cai , Lei Wu

Nowadays, deep learning is the standard approach for a wide range of problems, including biometrics, such as face recognition and speech recognition, etc. Biometric problems often use deep learning models to extract features from images,…

Computer Vision and Pattern Recognition · Computer Science 2022-02-14 Pedro Silva , Gladston Moreira , Vander Freitas , Rodrigo Silva , David Menotti , Eduardo Luz

Normalization methods improve both optimization and generalization of ConvNets. To further boost performance, the recently-proposed switchable normalization (SN) provides a new perspective for deep learning: it learns to select different…

Computer Vision and Pattern Recognition · Computer Science 2019-03-12 Wenqi Shao , Tianjian Meng , Jingyu Li , Ruimao Zhang , Yudian Li , Xiaogang Wang , Ping Luo

This paper illustrates the central role of loss functions in data-driven decision making, providing a comprehensive survey on their influence in cost-sensitive classification (CSC) and reinforcement learning (RL). We demonstrate how…

Machine Learning · Statistics 2025-04-07 Kaiwen Wang , Nathan Kallus , Wen Sun

Designing an effective loss function plays a crucial role in training deep recommender systems. Most existing works often leverage a predefined and fixed loss function that could lead to suboptimal recommendation quality and training…

Information Retrieval · Computer Science 2021-06-15 Xiangyu Zhao , Haochen Liu , Wenqi Fan , Hui Liu , Jiliang Tang , Chong Wang

Evaluating the log-sum-exp function or the softmax function is a key step in many modern data science algorithms, notably in inference and classification. Because of the exponentials that these functions contain, the evaluation is prone to…

Numerical Analysis · Mathematics 2019-09-10 Pierre Blanchard , Desmond J. Higham , Nicholas J. Higham

Normalization is a vital process for any machine learning task as it controls the properties of data and affects model performance at large. The impact of particular forms of normalization, however, has so far been investigated in limited…

Machine Learning · Computer Science 2022-06-22 Chintan Trivedi , Konstantinos Makantasis , Antonios Liapis , Georgios N. Yannakakis