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Sampling-based methods, e.g., Deep Ensembles and Bayesian Neural Nets have become promising approaches to improve the quality of uncertainty estimation and robust generalization. However, they suffer from a large model size and high latency…

Machine Learning · Computer Science 2024-05-29 Ha Manh Bui , Anqi Liu

Neural networks utilize the softmax as a building block in classification tasks, which contains an overconfidence problem and lacks an uncertainty representation ability. As a Bayesian alternative to the softmax, we consider a random…

Machine Learning · Computer Science 2020-06-30 Taejong Joo , Uijung Chung , Min-Gwan Seo

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…

Machine Learning · Computer Science 2023-03-23 Hao Wang , Chen Li , Jinzhe Jiang , Xin Zhang , Yaqian Zhao , Weifeng Gong

Despite achieving state-of-the-art results in nearly all Natural Language Processing applications, fine-tuning Transformer-based language models still requires a significant amount of labeled data to work. A well known technique to reduce…

Machine Learning · Computer Science 2025-03-13 Julius Gonsior , Christian Falkenberg , Silvio Magino , Anja Reusch , Maik Thiele , Wolfgang Lehner

Is the output softmax layer, which is adopted by most language models (LMs), always the best way to compute the next word probability? Given so many attention layers in a modern transformer-based LM, are the pointer networks redundant…

Computation and Language · Computer Science 2023-05-23 Haw-Shiuan Chang , Zonghai Yao , Alolika Gon , Hong Yu , Andrew McCallum

Large language models rely on attention mechanisms with a softmax activation. Yet the dominance of softmax over alternatives (e.g., component-wise or linear) remains poorly understood, and many theoretical works have focused on the…

Machine Learning · Computer Science 2026-02-27 O. Duranthon , P. Marion , C. Boyer , B. Loureiro , L. Zdeborová

Transformers have transformed the field of natural language processing. This performance is largely attributed to the use of stacked self-attention layers, each of which consists of matrix multiplies as well as softmax operations. As a…

Hardware Architecture · Computer Science 2021-03-18 Jacob R. Stevens , Rangharajan Venkatesan , Steve Dai , Brucek Khailany , Anand Raghunathan

Softmax is the de facto standard in modern neural networks for language processing when it comes to normalizing logits. However, by producing a dense probability distribution each token in the vocabulary has a nonzero chance of being…

Computation and Language · Computer Science 2022-05-20 Maxat Tezekbayev , Vassilina Nikoulina , Matthias Gallé , Zhenisbek Assylbekov

Softmax is the most commonly used output function for multiclass problems and is widely used in areas such as vision, natural language processing, and recommendation. A softmax model has linear costs in the number of classes which makes it…

Machine Learning · Computer Science 2018-08-03 Guy Blanc , Steffen Rendle

This study presents a comparative analysis of two objective functions, Mean Squared Error (MSE) and Softmax Cross-Entropy (SCE) for neural network classification tasks. While SCE combined with softmax activation is the conventional choice…

Machine Learning · Computer Science 2024-11-19 Kanishka Tyagi , Chinmay Rane , Ketaki Vaidya , Jeshwanth Challgundla , Soumitro Swapan Auddy , Michael Manry

The Softmax activation layer is a very popular Deep Neural Network (DNN) component when dealing with multi-class prediction problems. However, in DNN accelerator implementations it creates additional complexities due to the need for…

Hardware Architecture · Computer Science 2022-01-13 Raghuram S

Typically, Softmax is used in the final layer of a neural network to get a probability distribution for output classes. But the main problem with Softmax is that it is computationally expensive for large scale data sets with large number of…

Machine Learning · Computer Science 2018-12-17 Abdul Arfat Mohammed , Venkatesh Umaashankar

Latent categorical variables are frequently found in deep learning architectures. They can model actions in discrete reinforcement-learning environments, represent categories in latent-variable models, or express relations in graph neural…

Machine Learning · Computer Science 2026-05-14 Alessandro Manenti , Cesare Alippi

The softmax function is a cornerstone of multi-class classification, integral to a wide range of machine learning applications, from large-scale retrieval and ranking models to advanced large language models. However, its computational cost…

Machine Learning · Computer Science 2025-01-16 Jin Chen , Jin Zhang , Xu huang , Yi Yang , Defu Lian , Enhong Chen

To encourage intra-class compactness and inter-class separability among trainable feature vectors, large-margin softmax methods are developed and widely applied in the face recognition community. The introduction of the large-margin concept…

Audio and Speech Processing · Electrical Eng. & Systems 2021-04-22 Jingjing Huo , Yingbo Gao , Weiyue Wang , Ralf Schlüter , Hermann Ney

Weakly supervised semantic segmentation produces pixel-level localization from class labels; however, a classifier trained on such labels is likely to focus on a small discriminative region of the target object. We interpret this phenomenon…

Computer Vision and Pattern Recognition · Computer Science 2021-10-14 Jungbeom Lee , Jooyoung Choi , Jisoo Mok , Sungroh Yoon

We propose a new self-organizing hierarchical softmax formulation for neural-network-based language models over large vocabularies. Instead of using a predefined hierarchical structure, our approach is capable of learning word clusters with…

Computation and Language · Computer Science 2017-07-29 Yikang Shen , Shawn Tan , Chrisopher Pal , Aaron Courville

In recent years, the softmax model and its fast approximations have become the de-facto loss functions for deep neural networks when dealing with multi-class prediction. This loss has been extended to language modeling and recommendation,…

Machine Learning · Statistics 2019-09-19 Ugo Tanielian , Flavian Vasile

Softmax is popular normalization method used in machine learning. Deep learning solutions like Transformer or BERT use the softmax function intensively, so it is worthwhile to optimize its performance. This article presents our methodology…

Mathematical Software · Computer Science 2019-05-28 Jacek Czaja , Michal Gallus , Tomasz Patejko , Jian Tang

In this work, we show that saturating output activation functions, such as the softmax, impede learning on a number of standard classification tasks. Moreover, we present results showing that the utility of softmax does not stem from the…

Machine Learning · Computer Science 2017-07-14 Anders Oland , Aayush Bansal , Roger B. Dannenberg , Bhiksha Raj