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Related papers: The Counting Power of Transformers

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Deriving formal bounds on the expressivity of transformers, as well as studying transformers that are constructed to implement known algorithms, are both effective methods for better understanding the computational power of transformers.…

Logic in Computer Science · Computer Science 2024-12-03 Andy Yang , David Chiang

While transformers have proven enormously successful in a range of tasks, their fundamental properties as models of computation are not well understood. This paper contributes to the study of the expressive capacity of transformers,…

Machine Learning · Computer Science 2025-03-31 Lena Strobl , Dana Angluin , Robert Frank

Transformers are being used extensively across several sequence modeling tasks. Significant research effort has been devoted to experimentally probe the inner workings of Transformers. However, our conceptual and theoretical understanding…

Machine Learning · Computer Science 2020-10-13 Satwik Bhattamishra , Arkil Patel , Navin Goyal

The study on the expressive power of transformers shows that transformers are permutation equivariant, and they can approximate all permutation-equivariant continuous functions on a compact domain. However, these results are derived under…

Machine Learning · Computer Science 2026-01-26 Sejun Park , Yeachan Park , Geonho Hwang

The ability to perform arithmetic tasks is a remarkable trait of human intelligence and might form a critical component of more complex reasoning tasks. In this work, we investigate if the surface form of a number has any influence on how…

Computation and Language · Computer Science 2021-04-14 Rodrigo Nogueira , Zhiying Jiang , Jimmy Lin

We study the sequence-to-sequence mapping capacity of transformers by relating them to finite transducers, and find that they can express surprisingly large classes of transductions. We do so using variants of RASP, a programming language…

Formal Languages and Automata Theory · Computer Science 2024-11-07 Lena Strobl , Dana Angluin , David Chiang , Jonathan Rawski , Ashish Sabharwal

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

Transformers have become pivotal in Natural Language Processing, demonstrating remarkable success in applications like Machine Translation and Summarization. Given their widespread adoption, several works have attempted to analyze the…

Machine Learning · Computer Science 2024-09-02 Swaroop Nath , Harshad Khadilkar , Pushpak Bhattacharyya

We conduct a systematic study of the approximation properties of Transformer for sequence modeling with long, sparse and complicated memory. We investigate the mechanisms through which different components of Transformer, such as the…

Machine Learning · Computer Science 2024-10-31 Mingze Wang , Weinan E

Empirical studies have identified a range of learnability biases and limitations of transformers, such as a persistent difficulty in learning to compute simple formal languages such as PARITY, and a bias towards low-degree functions.…

Machine Learning · Computer Science 2024-05-28 Michael Hahn , Mark Rofin

Despite the great success of Transformer networks in various applications such as natural language processing and computer vision, their theoretical aspects are not well understood. In this paper, we study the approximation and estimation…

Machine Learning · Computer Science 2024-03-26 Shokichi Takakura , Taiji Suzuki

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

Humans can often count unfamiliar objects by observing visual repetition and composition, rather than relying only on object categories. However, many exemplar-free counting models struggle in such situations and may overcount when objects…

Computer Vision and Pattern Recognition · Computer Science 2026-03-10 Md Tanvir Hossain , Akif Islam , Mohd Ruhul Ameen

Transformers are a type of neural network that have demonstrated remarkable performance across various domains, particularly in natural language processing tasks. Motivated by this success, research on the theoretical understanding of…

Machine Learning · Computer Science 2025-02-18 Naoki Takeshita , Masaaki Imaizumi

Attention layers, as commonly used in transformers, form the backbone of modern deep learning, yet there is no mathematical description of their benefits and deficiencies as compared with other architectures. In this work we establish both…

Machine Learning · Computer Science 2023-11-17 Clayton Sanford , Daniel Hsu , Matus Telgarsky

When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…

Computation and Language · Computer Science 2022-11-07 Shikhar Murty , Pratyusha Sharma , Jacob Andreas , Christopher D. Manning

As transformers have gained prominence in natural language processing, some researchers have investigated theoretically what problems they can and cannot solve, by treating problems as formal languages. Exploring such questions can help…

Machine Learning · Computer Science 2024-09-05 Lena Strobl , William Merrill , Gail Weiss , David Chiang , Dana Angluin

It has been observed that transformers with greater depth (that is, more layers) have more capabilities, but can we establish formally which capabilities are gained? We answer this question with a theoretical proof followed by an empirical…

Computation and Language · Computer Science 2026-01-21 Andy Yang , Michaël Cadilhac , David Chiang

Transformers are extremely successful machine learning models whose mathematical properties remain poorly understood. Here, we rigorously characterize the behavior of transformers with hardmax self-attention and normalization sublayers as…

Computation and Language · Computer Science 2026-05-14 Albert Alcalde , Giovanni Fantuzzi , Enrique Zuazua

Transformers have revolutionized machine learning across diverse domains, yet understanding their behavior remains crucial, particularly in high-stakes applications. This paper introduces the contextual counting task, a novel toy problem…

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