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Softmax is an output activation function for modeling categorical probability distributions in many applications of deep learning. However, a recent study revealed that softmax can be a bottleneck of representational capacity of neural…

Machine Learning · Statistics 2018-05-29 Sekitoshi Kanai , Yasuhiro Fujiwara , Yuki Yamanaka , Shuichi Adachi

Every person speaks or writes their own flavor of their native language, influenced by a number of factors: the content they tend to talk about, their gender, their social status, or their geographical origin. When attempting to perform…

Computation and Language · Computer Science 2018-05-07 Paul Michel , Graham Neubig

While linear attention reduces the quadratic complexity of standard Transformers to linear time, it often lags behind in expressivity due to the removal of softmax normalization. This omission eliminates \emph{global competition}, a…

Machine Learning · Computer Science 2026-02-03 Mingwei Xu , Xuan Lin , Xinnan Guo , Wanqing Xu , Wanyun Cui

Sequence-to-sequence models are a powerful workhorse of NLP. Most variants employ a softmax transformation in both their attention mechanism and output layer, leading to dense alignments and strictly positive output probabilities. This…

Computation and Language · Computer Science 2019-06-14 Ben Peters , Vlad Niculae , André F. T. Martins

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

This short paper discusses an efficient implementation of \emph{sampled softmax loss} for Tensorflow. The speedup over the default implementation is achieved due to simplification of the graph for the forward and backward passes.

Machine Learning · Computer Science 2020-04-14 Maciej Skorski

Noisy labels pose a common challenge for training accurate deep neural networks. To mitigate label noise, prior studies have proposed various robust loss functions to achieve noise tolerance in the presence of label noise, particularly…

Machine Learning · Computer Science 2025-08-05 Jialiang Wang , Xiong Zhou , Deming Zhai , Junjun Jiang , Xiangyang Ji , Xianming Liu

The self-attention mechanism distinguishes transformer-based large language models (LLMs) apart from convolutional and recurrent neural networks. Despite the performance improvement, achieving real-time LLM inference on silicon remains…

Hardware Architecture · Computer Science 2024-11-18 Shiwei Liu , Guanchen Tao , Yifei Zou , Derek Chow , Zichen Fan , Kauna Lei , Bangfei Pan , Dennis Sylvester , Gregory Kielian , Mehdi Saligane

Current benchmark tasks for natural language processing contain text that is qualitatively different from the text used in informal day to day digital communication. This discrepancy has led to severe performance degradation of…

Computation and Language · Computer Science 2021-10-13 Ana-Maria Bucur , Adrian Cosma , Liviu P. Dinu

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

Classifiers in natural language processing (NLP) often have a large number of output classes. For example, neural language models (LMs) and machine translation (MT) models both predict tokens from a vocabulary of thousands. The Softmax…

Machine Learning · Computer Science 2022-03-22 Andreas Grivas , Nikolay Bogoychev , Adam Lopez

Mixture of Softmaxes (MoS) has been shown to be effective at addressing the expressiveness limitation of Softmax-based models. Despite the known advantage, MoS is practically sealed by its large consumption of memory and computational time…

Computation and Language · Computer Science 2019-06-27 Xiang Kong , Qizhe Xie , Zihang Dai , Eduard Hovy

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

Normalization is a vital process for any machine learning task as it controls the properties of data and affects model performance at large. The impact of particular forms of normalization, however, has so far been investigated in limited…

Machine Learning · Computer Science 2022-06-22 Chintan Trivedi , Konstantinos Makantasis , Antonios Liapis , Georgios N. Yannakakis

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

In a multi-class classification problem, it is standard to model the output of a neural network as a categorical distribution conditioned on the inputs. The output must therefore be positive and sum to one, which is traditionally enforced…

Neural and Evolutionary Computing · Computer Science 2016-03-01 Alexandre de Brébisson , Pascal Vincent

Large language models (LLMs) have made transformed changes for human society. One of the key computation in LLMs is the softmax unit. This operation is important in LLMs because it allows the model to generate a distribution over possible…

Machine Learning · Computer Science 2023-04-27 Yichuan Deng , Zhihang Li , Zhao Song

Replicated Softmax model, a well-known undirected topic model, is powerful in extracting semantic representations of documents. Traditional learning strategies such as Contrastive Divergence are very inefficient. This paper provides a novel…

Machine Learning · Computer Science 2015-06-25 Jiatao Gu , Victor O. K. Li

Transformer networks have emerged as the state-of-the-art approach for natural language processing tasks and are gaining popularity in other domains such as computer vision and audio processing. However, the efficient hardware acceleration…

Hardware Architecture · Computer Science 2024-07-29 Gamze İslamoğlu , Moritz Scherer , Gianna Paulin , Tim Fischer , Victor J. B. Jung , Angelo Garofalo , Luca Benini

The maximum element of the vector output by the Softmax function approaches zero as the input vector size increases. Transformer-based language models rely on Softmax to compute attention scores, causing the attention distribution to…

Computation and Language · Computer Science 2025-02-03 Ken M. Nakanishi