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The ability to reason lies at the core of artificial intelligence (AI), and challenging problems usually call for deeper and longer reasoning to tackle. A crucial question about AI reasoning is whether models can extrapolate learned…

Machine Learning · Computer Science 2025-11-11 Yu Huang , Zixin Wen , Aarti Singh , Yuejie Chi , Yuxin Chen

Transformer models have advanced the state of the art in many Natural Language Processing (NLP) tasks. In this paper, we present a new Transformer architecture, Extended Transformer Construction (ETC), that addresses two key challenges of…

We show that a constant number of self-attention layers can efficiently simulate, and be simulated by, a constant number of communication rounds of Massively Parallel Computation. As a consequence, we show that logarithmic depth is…

Machine Learning · Computer Science 2024-02-15 Clayton Sanford , Daniel Hsu , Matus Telgarsky

Transformers were initially introduced for natural language processing (NLP) tasks, but fast they were adopted by most deep learning fields, including computer vision. They measure the relationships between pairs of input tokens (words in…

Computer Vision and Pattern Recognition · Computer Science 2023-03-22 Robin Courant , Maika Edberg , Nicolas Dufour , Vicky Kalogeiton

Depth-adaptive neural networks can dynamically adjust depths according to the hardness of input words, and thus improve efficiency. The main challenge is how to measure such hardness and decide the required depths (i.e., layers) to conduct.…

Computation and Language · Computer Science 2020-12-17 Yijin Liu , Fandong Meng , Jie Zhou , Yufeng Chen , Jinan Xu

Transformers have revolutionized machine learning with their simple yet effective architecture. Pre-training Transformers on massive text datasets from the Internet has led to unmatched generalization for natural language understanding…

The powerful modeling capabilities of all-attention-based transformer architectures often cause overfitting and - for natural language processing tasks - lead to an implicitly learned internal language model in the autoregressive…

Machine Learning · Computer Science 2022-09-21 Timo Lohrenz , Björn Möller , Zhengyang Li , Tim Fingscheidt

Transformers excel empirically on tasks that process well-formed inputs according to some grammar, such as natural language and code. However, it remains unclear how they can process grammatical syntax. In fact, under standard complexity…

Machine Learning · Computer Science 2026-02-09 Selim Jerad , Anej Svete , Sophie Hao , Ryan Cotterell , William Merrill

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

Attention matrices are fundamental to transformer research, supporting a broad range of applications including interpretability, visualization, manipulation, and distillation. Yet, most existing analyses focus on individual attention heads…

Machine Learning · Computer Science 2026-01-27 Ido Andrew Atad , Itamar Zimerman , Shahar Katz , Lior Wolf

Learning algorithms become more powerful, often at the cost of increased complexity. In response, the demand for algorithms to be transparent is growing. In NLP tasks, attention distributions learned by attention-based deep learning models…

Computation and Language · Computer Science 2019-07-09 Joris Baan , Maartje ter Hoeve , Marlies van der Wees , Anne Schuth , Maarten de Rijke

Existing expressivity results for transformers typically rely on hardmax attention, high precision, and other architectural modifications that disconnect them from the models used in practice. We bridge this gap by analyzing standard…

Machine Learning · Computer Science 2026-05-19 Moritz Brösamle , Stephan Eckstein

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

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

Transformers are widely used in natural language processing, where they consistently achieve state-of-the-art performance. This is mainly due to their attention-based architecture, which allows them to model rich linguistic relations…

Computation and Language · Computer Science 2022-11-29 Nikolaos Mylonas , Ioannis Mollas , Grigorios Tsoumakas

The Transformer translation model is based on the multi-head attention mechanism, which can be parallelized easily. The multi-head attention network performs the scaled dot-product attention function in parallel, empowering the model by…

Computation and Language · Computer Science 2021-09-13 Hongfei Xu , Qiuhui Liu , Josef van Genabith , Deyi Xiong

Understanding the internal circuits that language models use to solve tasks remains a central challenge in mechanistic interpretability. A crucial part of finding circuits is understanding why each attention head attends where it does. To…

Machine Learning · Computer Science 2026-05-15 Gabriel Franco , Lucas M. Tassis , Azalea Rohr , Mark Crovella

We investigate the complexity of uniform OR circuits and AND circuits of polynomial-size and depth. As their name suggests, OR circuits have OR gates as their computation gates, as well as the usual input, output and constant (0/1) gates.…

Computational Complexity · Computer Science 2013-09-06 Niall Murphy , Damien Woods

This document provides a brief introduction to the attention mechanism used in modern language models based on the Transformer architecture. We first illustrate how text is encoded as vectors and how the attention mechanism processes these…

Numerical Analysis · Mathematics 2026-04-02 Michel Fabrice Serret

Understanding the expressive power of transformers has recently attracted attention, as it offers insights into their abilities and limitations. Many studies analyze unique hard attention transformers, where attention selects a single…

Machine Learning · Computer Science 2025-11-14 Selim Jerad , Anej Svete , Jiaoda Li , Ryan Cotterell