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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…

Machine Learning · Computer Science 2025-06-03 Petar Veličković , Christos Perivolaropoulos , Federico Barbero , Razvan Pascanu

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

Transformers have had tremendous impact for several sequence related tasks, largely due to their ability to retrieve from any part of the sequence via softmax based dot-product attention. This mechanism plays a crucial role in Transformer's…

Machine Learning · Computer Science 2025-07-15 Sai Surya Duvvuri , Inderjit S. Dhillon

Large language models (LLMs) have played a pivotal role in revolutionizing various facets of our daily existence. Solving attention regression is a fundamental task in optimizing LLMs. In this work, we focus on giving a provable guarantee…

Data Structures and Algorithms · Computer Science 2023-09-15 Yeqi Gao , Zhao Song , Weixin Wang , Junze Yin

The softmax representation of probabilities for categorical variables plays a prominent role in modern machine learning with numerous applications in areas such as large scale classification, neural language modeling and recommendation…

Machine Learning · Statistics 2016-11-01 Michalis K. Titsias

Training large language models (LLMs) is computationally expensive, partly because the loss exhibits slow power-law convergence whose origin remains debatable. Through systematic analysis of toy models and empirical evaluation of LLMs, we…

Machine Learning · Computer Science 2026-02-04 Yizhou Liu , Ziming Liu , Cengiz Pehlevan , Jeff Gore

There has been a rapid advance of custom hardware (HW) for accelerating the inference speed of deep neural networks (DNNs). Previously, the softmax layer was not a main concern of DNN accelerating HW, because its portion is relatively small…

Machine Learning · Computer Science 2021-11-23 Ihor Vasyltsov , Wooseok Chang

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

The input method is an essential service on every mobile and desktop devices that provides text suggestions. It converts sequential keyboard inputs to the characters in its target language, which is indispensable for Japanese and Chinese…

Computation and Language · Computer Science 2018-10-23 Jiali Yao , Raphael Shu , Xinjian Li , Katsutoshi Ohtsuki , Hideki Nakayama

Learning of low-rank matrices is fundamental to many machine learning applications. A state-of-the-art algorithm is the rank-one matrix pursuit (R1MP). However, it can only be used in matrix completion problems with the square loss. In this…

Machine Learning · Computer Science 2016-07-28 Quanming Yao , James T. Kwok

Language Models (LMs) assign significant attention to the first token, even if it is not semantically important, which is known as attention sink. This phenomenon has been widely adopted in applications such as streaming/long context…

Computation and Language · Computer Science 2025-03-04 Xiangming Gu , Tianyu Pang , Chao Du , Qian Liu , Fengzhuo Zhang , Cunxiao Du , Ye Wang , Min Lin

The softmax function is a widely used activation function in the output layers of neural networks, responsible for converting raw scores into class probabilities while introducing essential non-linearity. Implementing Softmax efficiently…

Recently, fully-connected and convolutional neural networks have been trained to achieve state-of-the-art performance on a wide variety of tasks such as speech recognition, image classification, natural language processing, and…

Machine Learning · Computer Science 2015-02-24 Yichuan Tang

Nowadays artificial neural network models achieve remarkable results in many disciplines. Functions mapping the representation provided by the model to the probability distribution are the inseparable aspect of deep learning solutions.…

Machine Learning · Computer Science 2023-04-24 Klaudia Bałazy , Łukasz Struski , Marek Śmieja , Jacek Tabor

Recent advances in language modeling consist in pretraining highly parameterized neural networks on extremely large web-mined text corpora. Training and inference with such models can be costly in practice, which incentivizes the use of…

Computation and Language · Computer Science 2024-04-12 Nathan Godey , Éric de la Clergerie , Benoît Sagot

The effectiveness of large language models (LLMs) is often hindered by duplicated data in their extensive pre-training datasets. Current approaches primarily focus on detecting and removing duplicates, which risks the loss of valuable…

Computation and Language · Computer Science 2024-07-10 Nan He , Weichen Xiong , Hanwen Liu , Yi Liao , Lei Ding , Kai Zhang , Guohua Tang , Xiao Han , Wei Yang

The learning objective plays a fundamental role to build a recommender system. Most methods routinely adopt either pointwise or pairwise loss to train the model parameters, while rarely pay attention to softmax loss due to its computational…

Information Retrieval · Computer Science 2023-12-20 Jiancan Wu , Xiang Wang , Xingyu Gao , Jiawei Chen , Hongcheng Fu , Tianyu Qiu

Large Language Models (LLMs) with billions of parameters are known for their impressive predicting capabilities but require lots of resources to run. With their massive rise in popularity, even a small reduction in required resources could…

Computation and Language · Computer Science 2024-07-30 Domas Grigaliūnas , Mantas Lukoševičius

Understanding the reasons behind the exceptional success of transformers requires a better analysis of why attention layers are suitable for NLP tasks. In particular, such tasks require predictive models to capture contextual meaning which…

Machine Learning · Statistics 2024-05-20 Simone Bombari , Marco Mondelli

Attention mechanisms have become ubiquitous in NLP. Recent architectures, notably the Transformer, learn powerful context-aware word representations through layered, multi-headed attention. The multiple heads learn diverse types of word…

Computation and Language · Computer Science 2019-09-09 Gonçalo M. Correia , Vlad Niculae , André F. T. Martins