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This paper analyzes three formal models of Transformer encoders that differ in the form of their self-attention mechanism: unique hard attention (UHAT); generalized unique hard attention (GUHAT), which generalizes UHAT; and averaging hard…

Computational Complexity · Computer Science 2022-04-15 Yiding Hao , Dana Angluin , Robert Frank

We contribute to the study of formal languages that can be recognized by transformer encoders. We focus on two self-attention mechanisms: (1) UHAT (Unique Hard Attention Transformers) and (2) AHAT (Average Hard Attention Transformers). UHAT…

Formal Languages and Automata Theory · Computer Science 2023-10-09 Pablo Barcelo , Alexander Kozachinskiy , Anthony Widjaja Lin , Vladimir Podolskii

Formal language theory has recently been successfully employed to unravel the power of transformer encoders. This setting is primarily applicable in Natural Language Processing (NLP), as a token embedding function (where a bounded number of…

Formal Languages and Automata Theory · Computer Science 2024-11-13 Pascal Bergsträßer , Chris Köcher , Anthony Widjaja Lin , Georg Zetzsche

Transformers have emerged as a widely used neural network model for various natural language processing tasks. Previous research explored their relationship with constant-depth threshold circuits, making two assumptions: average-hard…

Computation and Language · Computer Science 2023-08-23 Lena Strobl

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

Image captioning involves generating textual descriptions from input images, bridging the gap between computer vision and natural language processing. Recent advancements in transformer-based models have significantly improved caption…

Computer Vision and Pattern Recognition · Computer Science 2025-06-09 Israa A. Albadarneh , Bassam H. Hammo , Omar S. Al-Kadi

Transformer architecture has become ubiquitous in the natural language processing field. To interpret the Transformer-based models, their attention patterns have been extensively analyzed. However, the Transformer architecture is not only…

Computation and Language · Computer Science 2021-09-16 Goro Kobayashi , Tatsuki Kuribayashi , Sho Yokoi , Kentaro Inui

One of the crucial challenges taken in document analysis is mathematical expression recognition. Unlike text recognition which only focuses on one-dimensional structure images, mathematical expression recognition is a much more complicated…

Computer Vision and Pattern Recognition · Computer Science 2026-03-10 Anh Duy Le , Van Linh Pham , Vinh Loi Ly , Nam Quan Nguyen , Huu Thang Nguyen , Tuan Anh Tran

Characterizing neural networks in terms of better-understood formal systems has the potential to yield new insights into the power and limitations of these networks. Doing so for transformers remains an active area of research. Bhattamishra…

Machine Learning · Computer Science 2023-11-14 David Chiang , Peter Cholak , Anand Pillay

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

Transformers serve as the foundation of most modern large language models. To mitigate the quadratic complexity of standard full attention, various efficient attention mechanisms, such as linear and hybrid attention, have been developed. A…

Machine Learning · Computer Science 2026-02-03 Xiaowei Ye , Xiaoyu He , Chao Liao , Chen Wu , Pinyan Lu

Previous work on the learnability of transformers \textemdash\ focused primarily on examining their ability to approximate specific algorithmic patterns through training \textemdash\ has largely been data-driven, offering only probabilistic…

Machine Learning · Computer Science 2026-04-23 Debanjan Dutta , Anish Chakrabarty , Faizanuddin Ansari , Swagatam Das

Recent studies on the analysis of the multilingual representations focus on identifying whether there is an emergence of language-independent representations, or whether a multilingual model partitions its weights among different languages.…

Computation and Language · Computer Science 2021-06-01 Zae Myung Kim , Laurent Besacier , Vassilina Nikoulina , Didier Schwab

Cross-lingual image captioning is a challenging task that requires addressing both cross-lingual and cross-modal obstacles in multimedia analysis. The crucial issue in this task is to model the global and the local matching between the…

Computer Vision and Pattern Recognition · Computer Science 2024-04-08 Zijie Song , Zhenzhen Hu , Yuanen Zhou , Ye Zhao , Richang Hong , Meng Wang

We study conditions under which transformers using soft attention can simulate hard attention, that is, effectively focus all attention on a subset of positions. First, we examine several subclasses of languages recognized by hard-attention…

Machine Learning · Computer Science 2025-06-27 Andy Yang , Lena Strobl , David Chiang , Dana Angluin

Language and vision-language models have shown impressive performance across a wide range of tasks, but their internal mechanisms remain only partly understood. In this work, we study how individual attention heads in text-generative models…

Computer Vision and Pattern Recognition · Computer Science 2026-01-15 Lorenzo Basile , Valentino Maiorca , Diego Doimo , Francesco Locatello , Alberto Cazzaniga

The expressive power of transformers over inputs of unbounded size can be studied through their ability to recognize classes of formal languages. In this paper, we establish exact characterizations of transformers with hard attention (in…

Formal Languages and Automata Theory · Computer Science 2024-10-31 Andy Yang , David Chiang , Dana Angluin

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

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

We give a novel logical characterization of encoder-decoder transformers, the foundational architecture for LLMs that also sees use in various settings that benefit from cross-attention. We study such transformers over text in the practical…

Logic in Computer Science · Computer Science 2026-05-11 Veeti Ahvonen , Damian Heiman , Antti Kuusisto , Miguel Moreno , Matias Selin
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