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We offer a theoretical mathematical background through Lagrangian optimization on the unit hyperspherical manifold and its tangential collection with application to the Transformer and its token space. Our methods are catered to the…

Machine Learning · Computer Science 2026-01-27 Andrew Gracyk

Transformers have become the dominant architecture in modern machine learning, yet the theoretical understanding of their training dynamics remains limited. This paper develops a rigorous mathematical framework for analyzing gradient-based…

Optimization and Control · Mathematics 2026-05-19 Raphaël Barboni , Maarten V. de Hoop , Takashi Furuya , Gabriel Peyré

We propose a novel self-attention mechanism that can learn its optimal attention span. This allows us to extend significantly the maximum context size used in Transformer, while maintaining control over their memory footprint and…

Machine Learning · Computer Science 2019-08-09 Sainbayar Sukhbaatar , Edouard Grave , Piotr Bojanowski , Armand Joulin

Transformer-based models have brought a radical change to neural machine translation. A key feature of the Transformer architecture is the so-called multi-head attention mechanism, which allows the model to focus simultaneously on different…

Computation and Language · Computer Science 2020-10-06 Alessandro Raganato , Yves Scherrer , Jörg Tiedemann

Transformers have demonstrated remarkable success across vision, language, and video. Yet, increasing task complexity has led to larger models and more tokens, raising the quadratic cost of self-attention and the overhead of GPU memory…

Computer Vision and Pattern Recognition · Computer Science 2025-08-04 Joonmyung Choi , Sanghyeok Lee , Byungoh Ko , Eunseo Kim , Jihyung Kil , Hyunwoo J. Kim

Standard transformer architectures apply a single attention mechanism uniformly across all tokens and sequence positions, irrespective of local context or computational budget. We propose Meta-Attention, a framework that dynamically routes…

Machine Learning · Computer Science 2026-05-28 Alan Ferrari

This study aims to enhance the quality of music generation using Transformers by incorporating meta-information. While Transformer-based approaches are effective at capturing long-term dependencies in musical compositions, the music they…

Sound · Computer Science 2026-05-21 Shinnosuke Taksuka , Hideo Mukai

Whereas deep neural networks were first mostly used for classification tasks, they are rapidly expanding in the realm of structured output problems, where the observed target is composed of multiple random variables that have a rich joint…

Neural and Evolutionary Computing · Computer Science 2016-11-15 Kyunghyun Cho , Aaron Courville , Yoshua Bengio

Attention-based architectures have become ubiquitous in machine learning, yet our understanding of the reasons for their effectiveness remains limited. This work proposes a new way to understand self-attention networks: we show that their…

Machine Learning · Computer Science 2023-08-02 Yihe Dong , Jean-Baptiste Cordonnier , Andreas Loukas

Computational fluid dynamics (CFD) simulations of complex fluid flows in energy systems are prohibitively expensive due to strong nonlinearities and multiscale-multiphysics interactions. In this work, we present a transformer-based modeling…

Fluid Dynamics · Physics 2026-04-06 Kiran Yalamanchi , Shivam Barwey , Ibrahim Jarrah , Pinaki Pal

In this dissertation, we analyze the computational properties of game-theoretic centrality measures. The key idea behind game-theoretic approach to network analysis is to treat nodes as players in a cooperative game, where the value of each…

Computer Science and Game Theory · Computer Science 2015-12-08 Piotr Lech Szczepański

It is well known that deep generative models have a rich latent space, and that it is possible to smoothly manipulate their outputs by traversing this latent space. Recently, architectures have emerged that allow for more complex…

Machine Learning · Computer Science 2019-12-06 Andrew Gambardella , Atılım Güneş Baydin , Philip H. S. Torr

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

Much of recent Deep Reinforcement Learning success is owed to the neural architecture's potential to learn and use effective internal representations of the world. While many current algorithms access a simulator to train with a large…

Artificial Intelligence · Computer Science 2022-02-03 Amir Ardalan Kalantari , Mohammad Amini , Sarath Chandar , Doina Precup

An attention matrix of a transformer self-attention sublayer can provably be decomposed into two components and only one of them (effective attention) contributes to the model output. This leads us to ask whether visualizing effective…

Computation and Language · Computer Science 2021-05-20 Kaiser Sun , Ana Marasović

Transformer is the backbone of modern NLP models. In this paper, we propose RealFormer, a simple and generic technique to create Residual Attention Layer Transformer networks that significantly outperform the canonical Transformer and its…

Machine Learning · Computer Science 2021-09-14 Ruining He , Anirudh Ravula , Bhargav Kanagal , Joshua Ainslie

Transformers and their attention mechanism have been revolutionary in the field of Machine Learning. While originally proposed for the language data, they quickly found their way to the image, video, graph, etc. data modalities with various…

Machine Learning · Computer Science 2025-09-22 Saeed Amizadeh , Sara Abdali , Yinheng Li , Kazuhito Koishida

Despite the significant progress made by transformer models in machine reading comprehension tasks, they still fall short in handling complex reasoning tasks due to the absence of explicit knowledge in the input sequence. To address this…

Computation and Language · Computer Science 2024-01-17 Shima Foolad , Kourosh Kiani

The Transformer model is widely used in natural language processing for sentence representation. However, the previous Transformer-based models focus on function words that have limited meaning in most cases and could merely extract…

Computation and Language · Computer Science 2021-07-05 Yu Shi

Transformers have reshaped machine learning by utilizing attention mechanisms to capture complex patterns in large datasets, leading to significant improvements in performance. This success has contributed to the belief that "bigger means…

Machine Learning · Computer Science 2025-05-28 Hemanth Saratchandran , Damien Teney , Simon Lucey
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