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The softmax function is a fundamental component in deep learning. This study delves into the often-overlooked parameter within the softmax function, known as "temperature," providing novel insights into the practical and theoretical aspects…

Machine Learning · Computer Science 2025-03-03 Hao Xuan , Bokai Yang , Xingyu Li

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…

Machine Learning · Computer Science 2025-06-03 Wojciech Masarczyk , Mateusz Ostaszewski , Tin Sum Cheng , Tomasz Trzciński , Aurelien Lucchi , Razvan Pascanu

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,…

Machine Learning · Computer Science 2020-10-16 Atish Agarwala , Jeffrey Pennington , Yann Dauphin , Sam Schoenholz

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…

Machine Learning · Computer Science 2022-10-19 Benjamin Chamand , Olivier Risser-Maroix , Camille Kurtz , Philippe Joly , Nicolas Loménie

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…

Computer Vision and Pattern Recognition · Computer Science 2019-06-11 Azadeh Sadat Mozafari , Hugo Siqueira Gomes , Wilson Leão , Christian Gagné

Estimating optimal dynamic policies from offline data is a fundamental problem in dynamic decision making. In the context of causal inference, the problem is known as estimating the optimal dynamic treatment regime. Even though there exists…

Econometrics · Economics 2023-12-15 Qizhao Chen , Morgane Austern , Vasilis Syrgkanis

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…

Machine Learning · Computer Science 2018-09-13 Xu Zhang , Felix Xinnan Yu , Svebor Karaman , Wei Zhang , Shih-Fu Chang

The sampling temperature, a critical hyperparameter in large language models (LLMs), modifies the logits before the softmax layer, thereby reshaping the distribution of output tokens. Recent studies have challenged the Stochastic Parrots…

Computation and Language · Computer Science 2025-06-10 Lujun Li , Lama Sleem , Niccolo' Gentile , Geoffrey Nichil , Radu State

Constructing confidence intervals for the value of an (unknown) optimal treatment policy is a fundamental problem in causal inference. Insight into the optimal policy value can guide the development of reward-maximizing, individualized…

Econometrics · Economics 2026-04-01 Justin Whitehouse , Qizhao Chen , Morgane Austern , Vasilis Syrgkanis

The temperature parameter plays a profound role during training and/or inference with large foundation models (LFMs) such as large language models (LLMs) and CLIP models. Particularly, it adjusts the logits in the softmax function in LLMs,…

Machine Learning · Computer Science 2024-06-18 Zi-Hao Qiu , Siqi Guo , Mao Xu , Tuo Zhao , Lijun Zhang , Tianbao Yang

We propose SimSC, a remarkably simple framework, to address the problem of semantic matching only based on the feature backbone. We discover that when fine-tuning ImageNet pre-trained backbone on the semantic matching task, L2 normalization…

Computer Vision and Pattern Recognition · Computer Science 2023-05-05 Xinghui Li , Kai Han , Xingchen Wan , Victor Adrian Prisacariu

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

The large variation of datasets is a huge barrier for image classification tasks. In this paper, we embraced this observation and introduce the finite temperature tensor network (FTTN), which imports the thermal perturbation into the matrix…

Machine Learning · Computer Science 2021-04-27 Haoxiang Lin , Shuqian Ye , Xi Zhu

Recently, there have been many works on the deep learning of statistical ensembles to determine the critical temperature of a possible phase transition. We analyze the detailed structure of an optimized deep learning machine and prove the…

Statistical Mechanics · Physics 2019-04-23 Ken-Ichi Aoki , Tatsuhiro Fujita , Tamao Kobayashi

The operation of machine tools often demands a highly accurate knowledge of the tool center point's (TCP) position. The displacement of the TCP over time can be inferred from thermal models, which comprise a set of geometrically coupled…

Numerical Analysis · Mathematics 2023-06-23 Alexandra Bünger , Roland Herzog , Andreas Naumann , Martin Stoll

Generative models of complex systems often require post-hoc parameter adjustments to produce useful outputs. For example, energy-based models for protein design are sampled at an artificially low ''temperature'' to generate novel,…

Quantitative Methods · Quantitative Biology 2025-12-11 Peter W Fields , Vudtiwat Ngampruetikorn , David J Schwab , Stephanie E Palmer

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…

Computation and Language · Computer Science 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…

Computer Vision and Pattern Recognition · Computer Science 2023-02-14 Xiang Zhou , Yuan Zeng , Yi Gong

The softmax function is widely used in artificial neural networks for the multiclass classification problems, where the softmax transformation enforces the output to be positive and sum to one, and the corresponding loss function allows to…

Machine Learning · Computer Science 2021-12-24 Shaoshi Sun , Zhenyuan Zhang , BoCheng Huang , Pengbin Lei , Jianlin Su , Shengfeng Pan , Jiarun Cao

Robust and non-destructive material classification is a challenging but crucial first-step in numerous vision applications. We propose a physics-guided material classification framework that relies on thermal properties of the object. Our…

Computer Vision and Pattern Recognition · Computer Science 2023-04-04 Aniket Dashpute , Vishwanath Saragadam , Emma Alexander , Florian Willomitzer , Aggelos Katsaggelos , Ashok Veeraraghavan , Oliver Cossairt
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