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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

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

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

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

Non-local (NL) block is a popular module that demonstrates the capability to model global contexts. However, NL block generally has heavy computation and memory costs, so it is impractical to apply the block to high-resolution feature maps.…

Computer Vision and Pattern Recognition · Computer Science 2022-07-28 Yooshin Cho , Youngsoo Kim , Hanbyel Cho , Jaesung Ahn , Hyeong Gwon Hong , Junmo Kim

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

Softmax is widely used in deep learning to map some representation to a probability distribution. As it is based on exp/log functions that are relatively expensive in multi-party computation, Mohassel and Zhang (2017) proposed a simpler…

Machine Learning · Computer Science 2021-07-07 Marcel Keller , Ke Sun

While transformer models exhibit strong in-context learning (ICL) abilities, they often fail to generalize under simple distribution shifts. We analyze these failures and identify Softmax, the scoring function in the attention mechanism, as…

Computation and Language · Computer Science 2026-05-12 Omar Naim , Swarnadeep Bhar , Jérôme Bolte , Nicholas Asher

As the performance gains from accelerating quantized matrix multiplication plateau, the softmax operation becomes the critical bottleneck in Transformer inference. This bottleneck stems from two hardware limitations: (1) limited data…

Machine Learning · Computer Science 2026-02-03 Zisheng Ye , Xiaoyu He , Maoyuan Song , Guoliang Qiu , Chao Liao , Chen Wu , Yonggang Sun , Zhichun Li , Xiaoru Xie , Yuanyong Luo , Hu Liu , Pinyan Lu , Heng Liao

Transformers have achieved remarkable successes across a wide range of applications, yet the theoretical foundation of their model efficiency remains underexplored. In this work, we investigate how the model parameters -- mainly attention…

Machine Learning · Computer Science 2025-10-07 Ruoxi Yu , Haotian Jiang , Jingpu Cheng , Penghao Yu , Qianxiao Li , Zhong Li

Since its introduction, softmax attention has become the backbone of modern transformer architectures due to its expressiveness and scalability across a wide range of tasks. However, the main drawback of softmax attention is the quadratic…

Machine Learning · Computer Science 2026-02-20 Gabriel Mongaras , Eric C. Larson

Attention is a key part of the transformer architecture. It is a sequence-to-sequence mapping that transforms each sequence element into a weighted sum of values. The weights are typically obtained as the softmax of dot products between…

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

Transformer model architectures have garnered immense interest lately due to their effectiveness across a range of domains like language, vision and reinforcement learning. In the field of natural language processing for example,…

Machine Learning · Computer Science 2022-03-15 Yi Tay , Mostafa Dehghani , Dara Bahri , Donald Metzler

Existing analyses of the expressive capacity of Transformer models have required excessively deep layers for data memorization, leading to a discrepancy with the Transformers actually used in practice. This is primarily due to the…

Machine Learning · Computer Science 2024-01-30 Tokio Kajitsuka , Issei Sato

Transformers are central to recent successes in natural language processing and computer vision. Transformers have a mostly uniform backbone where layers alternate between feed-forward and self-attention in order to build a deep network.…

Transformer-based speech enhancement models yield impressive results. However, their heterogeneous and complex structure restricts model compression potential, resulting in greater complexity and reduced hardware efficiency. Additionally,…

Hardware Architecture · Computer Science 2025-03-28 Ci-Hao Wu , Tian-Sheuan Chang

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

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

Transformers have excelled in many tasks including vision. However, efficient deployment of transformer models in low-latency or high-throughput applications is hindered by the computation in the attention mechanism which involves expensive…

Computer Vision and Pattern Recognition · Computer Science 2024-06-12 John Yang , Le An , Su Inn Park