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Multi-head attention empowers the recent success of transformers, the state-of-the-art models that have achieved remarkable success in sequence modeling and beyond. These attention mechanisms compute the pairwise dot products between the…

Machine Learning · Computer Science 2022-06-02 Tan Nguyen , Minh Pham , Tam Nguyen , Khai Nguyen , Stanley J. Osher , Nhat Ho

Understanding the training dynamics of transformers is important to explain the impressive capabilities behind large language models. In this work, we study the dynamics of training a shallow transformer on a task of recognizing…

Machine Learning · Computer Science 2024-10-15 Hongru Yang , Bhavya Kailkhura , Zhangyang Wang , Yingbin Liang

Pairwise dot product-based attention allows Transformers to exchange information between tokens in an input-dependent way, and is key to their success across diverse applications in language and vision. However, a typical Transformer model…

Most expressivity results for transformers treat them as language recognizers -- devices that accept or reject strings -- rather than as they are used in practice: as language models that generate strings autoregressively and…

Computation and Language · Computer Science 2026-05-26 Andy Yang , Anej Svete , Jiaoda Li , Anthony Widjaja Lin , Jonathan Rawski , Ryan Cotterell , David Chiang

The debate around the interpretability of attention mechanisms is centered on whether attention scores can be used as a proxy for the relative amounts of signal carried by sub-components of data. We propose to study the interpretability of…

Machine Learning · Computer Science 2022-07-27 Jonathan Haab , Nicolas Deutschmann , Maria Rodríguez Martínez

Transformers are built upon multi-head scaled dot-product attention and positional encoding, which aim to learn the feature representations and token dependencies. In this work, we focus on enhancing the distinctive representation by…

Computer Vision and Pattern Recognition · Computer Science 2022-07-12 Litao Yu , Jian Zhang

The success of Transformer-based Language Models (LMs) stems from their attention mechanism. While this mechanism has been extensively studied in explainability research, particularly through the attention values obtained during the forward…

Computation and Language · Computer Science 2024-12-24 Shahar Katz , Lior Wolf

Layer Normalization (LayerNorm) is an inherent component in all Transformer-based models. In this paper, we show that LayerNorm is crucial to the expressivity of the multi-head attention layer that follows it. This is in contrast to the…

Machine Learning · Computer Science 2023-05-12 Shaked Brody , Uri Alon , Eran Yahav

Transformers are widely used for their ability to capture data relations in sequence processing, with great success for a wide range of static tasks. However, the computational and memory footprint of their main component, i.e., the Scaled…

Computer Vision and Pattern Recognition · Computer Science 2025-07-29 Ginés Carreto Picón , Illia Oleksiienko , Lukas Hedegaard , Arian Bakhtiarnia , Alexandros Iosifidis

Phase transitions mark qualitative reorganizations of collective behavior, yet identifying their boundaries remains challenging whenever analytic solutions are absent and conventional simulations fail. Here we introduce learnability as a…

Materials Science · Physics 2025-10-10 Şener Özönder

Transformers are increasingly dominating multi-modal reasoning tasks, such as visual question answering, achieving state-of-the-art results thanks to their ability to contextualize information using the self-attention and co-attention…

Computer Vision and Pattern Recognition · Computer Science 2021-03-30 Hila Chefer , Shir Gur , Lior Wolf

Recent generalizations of the Hopfield model of associative memories are able to store a number $P$ of random patterns that grows exponentially with the number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity, another…

Disordered Systems and Neural Networks · Physics 2024-02-14 Carlo Lucibello , Marc Mézard

Transformer-based models have demonstrated exceptional performance across diverse domains, becoming the state-of-the-art solution for addressing sequential machine learning problems. Even though we have a general understanding of the…

Disordered Systems and Neural Networks · Physics 2024-06-12 Ángel Poc-López , Miguel Aguilera

Analogy is a central faculty of human intelligence, enabling abstract patterns discovered in one domain to be applied to another. Despite its central role in cognition, the mechanisms by which Transformers acquire and implement analogical…

Artificial Intelligence · Computer Science 2026-05-28 Gouki Minegishi , Jingyuan Feng , Hiroki Furuta , Takeshi Kojima , Yusuke Iwasawa , Yutaka Matsuo

When training transformers on graph-structured data, incorporating information about the underlying topology is crucial for good performance. Topological masking, a type of relative position encoding, achieves this by upweighting or…

Linear layers in neural networks (NNs) trained by gradient descent can be expressed as a key-value memory system which stores all training datapoints and the initial weights, and produces outputs using unnormalised dot attention over the…

Machine Learning · Computer Science 2022-06-20 Kazuki Irie , Róbert Csordás , Jürgen Schmidhuber

We incorporate Tensor-Product Representations within the Transformer in order to better support the explicit representation of relation structure. Our Tensor-Product Transformer (TP-Transformer) sets a new state of the art on the…

Machine Learning · Computer Science 2020-11-05 Imanol Schlag , Paul Smolensky , Roland Fernandez , Nebojsa Jojic , Jürgen Schmidhuber , Jianfeng Gao

Transformer-based models have achieved remarkable success across a wide range of domains, yet our understanding of their training dynamics remains limited. In this work, we identify a recurrent focus-dilution cycle in attention learning and…

Machine Learning · Computer Science 2026-05-05 Zheng-An Chen , Pengxiao Lin , Zhi-Qin John Xu , Tao Luo

The usage of transformers has grown from learning about language semantics to forming meaningful visiolinguistic representations. These architectures are often over-parametrized, requiring large amounts of computation. In this work, we…

Computation and Language · Computer Science 2020-07-09 Prajjwal Bhargava

Attention mechanisms have played a crucial role in the development of complex architectures such as Transformers in natural language processing. However, Transformers remain hard to interpret and are considered as black-boxes. This paper…

Machine Learning · Computer Science 2023-03-28 Milan Bhan , Nina Achache , Victor Legrand , Annabelle Blangero , Nicolas Chesneau