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We formulate language modeling as a matrix factorization problem, and show that the expressiveness of Softmax-based models (including the majority of neural language models) is limited by a Softmax bottleneck. Given that natural language is…

Computation and Language · Computer Science 2018-03-06 Zhilin Yang , Zihang Dai , Ruslan Salakhutdinov , William W. Cohen

An essential component of modern recurrent sequence models is the forget gate. While Transformers do not have an explicit recurrent form, we show that a forget gate can be naturally incorporated into Transformers by down-weighting the…

Machine Learning · Computer Science 2025-04-02 Zhixuan Lin , Evgenii Nikishin , Xu Owen He , Aaron Courville

The softmax activation function plays a crucial role in the success of large language models (LLMs), particularly in the self-attention mechanism of the widely adopted Transformer architecture. However, the underlying learning dynamics that…

Machine Learning · Computer Science 2026-01-27 Yang Cao , Yingyu Liang , Zhenmei Shi , Zhao Song

Multitask learning poses significant challenges due to the highly multimodal and diverse nature of robot action distributions. However, effectively fitting policies to these complex task distributions is often difficult, and existing…

Robotics · Computer Science 2026-04-27 Chaoqi Liu , Haonan Chen , Sigmund H. Høeg , Shaoxiong Yao , Yunzhu Li , Kris Hauser , Yilun Du

Mixture-of-experts (MoE) model incorporates the power of multiple submodels via gating functions to achieve greater performance in numerous regression and classification applications. From a theoretical perspective, while there have been…

Machine Learning · Statistics 2024-06-25 Huy Nguyen , Pedram Akbarian , TrungTin Nguyen , Nhat Ho

We study two mixed robust/average-case submodular partitioning problems that we collectively call Submodular Partitioning. These problems generalize both purely robust instances of the problem (namely max-min submodular fair allocation…

Data Structures and Algorithms · Computer Science 2016-08-17 Kai Wei , Rishabh Iyer , Shengjie Wang , Wenruo Bai , Jeff Bilmes

Memory networks are neural networks with an explicit memory component that can be both read and written to by the network. The memory is often addressed in a soft way using a softmax function, making end-to-end training with backpropagation…

Machine Learning · Statistics 2016-05-25 Sarath Chandar , Sungjin Ahn , Hugo Larochelle , Pascal Vincent , Gerald Tesauro , Yoshua Bengio

Recent advances in efficient Transformers have exploited either the sparsity or low-rank properties of attention matrices to reduce the computational and memory bottlenecks of modeling long sequences. However, it is still challenging to…

Machine Learning · Computer Science 2021-10-29 Beidi Chen , Tri Dao , Eric Winsor , Zhao Song , Atri Rudra , Christopher Ré

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

While sparse attention mitigates the computational bottleneck of long-context LLM training, its distributed training process exhibits extreme heterogeneity in both \textit{1)} sequence length and \textit{2)} sparsity sensitivity, leading to…

Machine Learning · Computer Science 2026-04-27 Hongtao Xu , Jianchao Tan , Yuxuan Hu , Pengju Lu , Hongyu Wang , Pingwei Sun , Yerui Sun , Yuchen Xie , Xunliang Cai , Mingzhen Li , Weile Jia

The growing demand for long-context inference capabilities in Large Language Models (LLMs) has intensified the computational and memory bottlenecks inherent to the self-attention mechanism. To address this challenge, we introduce BLASST, a…

Loss functions steer the optimization direction of recommendation models and are critical to model performance, but have received relatively little attention in recent recommendation research. Among various losses, we find Softmax loss (SL)…

Machine Learning · Computer Science 2023-12-21 Junkang Wu , Jiawei Chen , Jiancan Wu , Wentao Shi , Jizhi Zhang , Xiang Wang

Recently, speech recognition with ad-hoc microphone arrays has received much attention. It is known that channel selection is an important problem of ad-hoc microphone arrays, however, this topic seems far from explored in speech…

Audio and Speech Processing · Electrical Eng. & Systems 2022-02-15 Junqi Chen , Xiao-Lei Zhang

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

We explore clustering the softmax predictions of deep neural networks and introduce a novel probabilistic clustering method, referred to as k-sBetas. In the general context of clustering discrete distributions, the existing methods focused…

Computer Vision and Pattern Recognition · Computer Science 2024-07-02 Florent Chiaroni , Malik Boudiaf , Amar Mitiche , Ismail Ben Ayed

In this thesis we discuss machine learning methods performing automated variable selection for learning sparse predictive models. There are multiple reasons for promoting sparsity in the predictive models. By relying on a limited set of…

Machine Learning · Computer Science 2019-03-27 Magda Gregorova

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

Optimization and Control · Mathematics 2025-05-20 Laurent Condat , Elnur Gasanov , Peter Richtárik

Online continual learning is a challenging problem where models must learn from a non-stationary data stream while avoiding catastrophic forgetting. Inter-class imbalance during training has been identified as a major cause of forgetting,…

Machine Learning · Computer Science 2024-10-01 Zhehao Huang , Tao Li , Chenhe Yuan , Yingwen Wu , Xiaolin Huang

Softmax-based losses have achieved state-of-the-art performances on various tasks such as face recognition and re-identification. However, these methods highly relied on clean datasets with global labels, which limits their usage in many…

Computer Vision and Pattern Recognition · Computer Science 2022-01-25 Qiang Meng , Xinqian Gu , Xiaqing Xu , Feng Zhou

Modern deep neural networks can achieve high accuracy when the training distribution and test distribution are identically distributed, but this assumption is frequently violated in practice. When the train and test distributions are…

Machine Learning · Statistics 2020-02-18 Dan Hendrycks , Norman Mu , Ekin D. Cubuk , Barret Zoph , Justin Gilmer , Balaji Lakshminarayanan