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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 paper questions whether the strong performance of softmax attention in transformers stems from producing a probability distribution over inputs. Instead, we argue that softmax's effectiveness lies in its implicit regularization of the…

Machine Learning · Computer Science 2026-03-16 Hemanth Saratchandran , Jianqiao Zheng , Yiping Ji , Wenbo Zhang , Simon Lucey

The softmax (also called softargmax) function is widely used in machine learning models to normalize real-valued scores into a probability distribution. To avoid floating-point overflow, the softmax function is conventionally implemented in…

Performance · Computer Science 2020-01-14 Marat Dukhan , Artsiom Ablavatski

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

In neural machine translation (NMT), the computational cost at the output layer increases with the size of the target-side vocabulary. Using a limited-size vocabulary instead may cause a significant decrease in translation quality. This…

Computation and Language · Computer Science 2018-07-31 Katsuki Chousa , Katsuhito Sudoh , Satoshi Nakamura

Homomorphic encryption is one of the main solutions for building secure and privacy-preserving solutions for Machine Learning as a Service. This motivates the development of homomorphic algorithms for the main building blocks of AI,…

Cryptography and Security · Computer Science 2024-10-16 Wonhee Cho , Guillaume Hanrot , Taeseong Kim , Minje Park , Damien Stehlé

To mitigate the problem of having to traverse over the full vocabulary in the softmax normalization of a neural language model, sampling-based training criteria are proposed and investigated in the context of large vocabulary word-based…

Computation and Language · Computer Science 2022-06-20 Zijian Yang , Yingbo Gao , Alexander Gerstenberger , Jintao Jiang , Ralf Schlüter , Hermann Ney

Neural models for text generation require a softmax layer with proper token embeddings during the decoding phase. Most existing approaches adopt single point embedding for each token. However, a word may have multiple senses according to…

Computation and Language · Computer Science 2019-11-04 Ning Miao , Hao Zhou , Chengqi Zhao , Wenxian Shi , Lei Li

Large Language Models (LLMs) excel in English, but their performance degrades significantly on low-resource languages (LRLs) due to English-centric training. While methods like LangBridge align LLMs with multilingual encoders such as the…

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

Neural Machine Translation (NMT) is a new approach to machine translation that has made great progress in recent years. However, recent studies show that NMT generally produces fluent but inadequate translations (Tu et al. 2016b; Tu et al.…

Computation and Language · Computer Science 2017-01-02 Xing Wang , Zhengdong Lu , Zhaopeng Tu , Hang Li , Deyi Xiong , Min Zhang

Prompting method is regarded as one of the crucial progress for few-shot nature language processing. Recent research on prompting moves from discrete tokens based ``hard prompts'' to continuous ``soft prompts'', which employ learnable…

Computation and Language · Computer Science 2023-02-06 Yutai Hou , Hongyuan Dong , Xinghao Wang , Bohan Li , Wanxiang Che

Despite being the standard loss function to train multi-class neural networks, the log-softmax has two potential limitations. First, it involves computations that scale linearly with the number of output classes, which can restrict the size…

Machine Learning · Computer Science 2016-05-30 Alexandre de Brébisson , Pascal Vincent

Lemmatization of standard languages is concerned with (i) abstracting over morphological differences and (ii) resolving token-lemma ambiguities of inflected words in order to map them to a dictionary headword. In the present paper we aim to…

Computation and Language · Computer Science 2019-03-19 Enrique Manjavacas , Ákos Kádár , Mike Kestemont

In Transformer models, non-GEMM (non-General Matrix Multiplication) operations -- especially Softmax and Layer Normalization (LayerNorm) -- often dominate hardware cost due to their nonlinear nature. To address this, previous approximation…

Hardware Architecture · Computer Science 2026-04-28 Dawon Choi , Hana Kim , Ji-Hoon Kim

Low-resource language translation is a challenging but socially valuable NLP task. Building on recent work adapting the Transformer's normalization to this setting, we propose QKNorm, a normalization technique that modifies the attention…

Computation and Language · Computer Science 2020-10-12 Alex Henry , Prudhvi Raj Dachapally , Shubham Pawar , Yuxuan Chen

Neural machine translation is a recently proposed approach to machine translation. Unlike the traditional statistical machine translation, the neural machine translation aims at building a single neural network that can be jointly tuned to…

Computation and Language · Computer Science 2016-05-23 Dzmitry Bahdanau , Kyunghyun Cho , Yoshua Bengio

RNN-Transducer has been one of promising architectures for end-to-end automatic speech recognition. Although RNN-Transducer has many advantages including its strong accuracy and streaming-friendly property, its high memory consumption…

Audio and Speech Processing · Electrical Eng. & Systems 2022-04-01 Jaesong Lee , Lukas Lee , Shinji Watanabe

The softmax attention mechanism has emerged as a noteworthy development in the field of Artificial Intelligence research, building on the successes of Transformer-based architectures. However, their ever increasing sizes necessitate ever…

Computation and Language · Computer Science 2023-05-19 Luca Herranz-Celotti , Ermal Rrapaj

Softmax is widely used in neural networks for multiclass classification, gate structure and attention mechanisms. The statistical assumption that the input is normal distributed supports the gradient stability of Softmax. However, when used…

Computer Vision and Pattern Recognition · Computer Science 2021-08-17 Shulun Wang , Bin Liu , Feng Liu
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