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The softmax function is a fundamental building block of deep neural networks, commonly used to define output distributions in classification tasks or attention weights in transformer architectures. Despite its widespread use and proven…

In deep learning-based classification tasks, the softmax function's temperature parameter $T$ critically influences the output distribution and overall performance. This study presents a novel theoretical insight that the optimal…

机器学习 · 计算机科学 2026-04-24 Tatsuhito Hasegawa , Shunsuke Sakai

The softmax function combined with a cross-entropy loss is a principled approach to modeling probability distributions that has become ubiquitous in deep learning. The softmax function is defined by a lone hyperparameter, the temperature,…

机器学习 · 计算机科学 2020-10-16 Atish Agarwala , Jeffrey Pennington , Yann Dauphin , Sam Schoenholz

Even before deep learning architectures became the de facto models for complex computer vision tasks, the softmax function was, given its elegant properties, already used to analyze the predictions of feedforward neural networks. Nowadays,…

机器学习 · 计算机科学 2018-11-22 Utku Ozbulak , Wesley De Neve , Arnout Van Messem

Cosine similarity is the common choice for measuring the distance between the feature representations in contrastive visual-textual alignment learning. However, empirically a learnable softmax temperature parameter is required when learning…

计算机视觉与模式识别 · 计算机科学 2023-10-10 Zhun Sun

A key property of reasoning systems is the ability to make sharp decisions on their input data. For contemporary AI systems, a key carrier of sharp behaviour is the softmax function, with its capability to perform differentiable query-key…

机器学习 · 计算机科学 2025-06-03 Petar Veličković , Christos Perivolaropoulos , Federico Barbero , Razvan Pascanu

Metric learning aims at learning a distance which is consistent with the semantic meaning of the samples. The problem is generally solved by learning an embedding for each sample such that the embeddings of samples of the same category are…

机器学习 · 计算机科学 2018-09-13 Xu Zhang , Felix Xinnan Yu , Svebor Karaman , Wei Zhang , Shih-Fu Chang

Despite the impressive generalization capabilities of deep neural networks, they have been repeatedly shown to be overconfident when they are wrong. Fixing this issue is known as model calibration, and has consequently received much…

机器学习 · 计算机科学 2024-02-15 Muthu Chidambaram , Rong Ge

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…

机器学习 · 计算机科学 2017-10-17 Nan Ding , Radu Soricut

Recently, the robustness of deep learning models has received widespread attention, and various methods for improving model robustness have been proposed, including adversarial training, model architecture modification, design of loss…

机器学习 · 计算机科学 2023-03-23 Hao Wang , Chen Li , Jinzhe Jiang , Xin Zhang , Yaqian Zhao , Weifeng Gong

Data uncertainty is commonly observed in the images for face recognition (FR). However, deep learning algorithms often make predictions with high confidence even for uncertain or irrelevant inputs. Intuitively, FR algorithms can benefit…

计算机视觉与模式识别 · 计算机科学 2022-12-05 Lei Shang , Mouxiao Huang , Wu Shi , Yuchen Liu , Yang Liu , Fei Wang , Baigui Sun , Xuansong Xie , Yu Qiao

Attention is a core component of transformer architecture, whether encoder-only, decoder-only, or encoder-decoder model. However, the standard softmax attention often produces noisy probability distribution, which can impair effective…

计算与语言 · 计算机科学 2025-11-11 Dhananjay Ram , Wei Xia , Stefano Soatto

Recent advances in deep generative adversarial networks (GAN) and self-attention mechanism have led to significant improvements in the challenging task of inpainting large missing regions in an image. These methods integrate self-attention…

计算机视觉与模式识别 · 计算机科学 2023-02-14 Xiang Zhou , Yuan Zeng , Yi Gong

Temperature scaling is a simple method that allows to control the uncertainty of probabilistic models. It is mostly used in two contexts: improving the calibration of classifiers and tuning the stochasticity of large language models (LLMs).…

机器学习 · 统计学 2026-05-28 Pierre-Alexandre Mattei , Bruno Loureiro

The great performances of deep learning are undeniable, with impressive results over a wide range of tasks. However, the output confidence of these models is usually not well-calibrated, which can be an issue for applications where…

计算机视觉与模式识别 · 计算机科学 2019-06-11 Azadeh Sadat Mozafari , Hugo Siqueira Gomes , Wilson Leão , Christian Gagné

Training a classifier over a large number of classes, known as 'extreme classification', has become a topic of major interest with applications in technology, science, and e-commerce. Traditional softmax regression induces a gradient cost…

机器学习 · 统计学 2020-02-18 Robert Bamler , Stephan Mandt

In this paper, we utilize results from convex analysis and monotone operator theory to derive additional properties of the softmax function that have not yet been covered in the existing literature. In particular, we show that the softmax…

最优化与控制 · 数学 2018-08-23 Bolin Gao , Lacra Pavel

Temperature is a widely used hyperparameter in various tasks involving neural networks, such as classification or metric learning, whose choice can have a direct impact on the model performance. Most of existing works select its value using…

机器学习 · 计算机科学 2022-10-19 Benjamin Chamand , Olivier Risser-Maroix , Camille Kurtz , Philippe Joly , Nicolas Loménie

The extraction of useful deep features is important for many computer vision tasks. Deep features extracted from classification networks have proved to perform well in those tasks. To obtain features of greater usefulness, end-to-end…

计算机视觉与模式识别 · 计算机科学 2023-05-26 Shota Horiguchi , Daiki Ikami , Kiyoharu Aizawa

Deep learning-based Natural Language Processing (NLP) models are vulnerable to adversarial attacks, where small perturbations can cause a model to misclassify. Adversarial Training (AT) is often used to increase model robustness. However,…

计算与语言 · 计算机科学 2024-10-15 Vyas Raina , Samson Tan , Volkan Cevher , Aditya Rawal , Sheng Zha , George Karypis
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