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Related papers: A Mathematical Explanation of Transformers

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Despite the popularity of transformers in practice, their architectures are empirically designed and neither mathematically justified nor interpretable. Moreover, as indicated by many empirical studies, some components of transformer…

Machine Learning · Computer Science 2025-06-05 Peng Wang , Yifu Lu , Yaodong Yu , Druv Pai , Qing Qu , Yi Ma

Recent advancements in large language models (LLMs) based on transformer architectures have sparked significant interest in understanding their inner workings. In this paper, we introduce a novel approach to modeling transformer…

Machine Learning · Computer Science 2025-04-17 Anh Tong , Thanh Nguyen-Tang , Dongeun Lee , Duc Nguyen , Toan Tran , David Hall , Cheongwoong Kang , Jaesik Choi

Understanding the transformer architecture and its workings is essential for machine learning (ML) engineers. However, truly understanding the transformer architecture can be demanding, even if you have a solid background in machine…

Machine Learning · Computer Science 2025-02-28 Joni-Kristian Kämäräinen

The Transformer architecture has significantly advanced deep learning, particularly in natural language processing, by effectively managing long-range dependencies. However, as the demand for understanding complex relationships grows,…

Computation and Language · Computer Science 2024-06-18 Qian Chen , Wen Wang , Qinglin Zhang , Siqi Zheng , Shiliang Zhang , Chong Deng , Hai Yu , Jiaqing Liu , Yukun Ma , Chong Zhang

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

Data-driven learning of partial differential equations' solution operators has recently emerged as a promising paradigm for approximating the underlying solutions. The solution operators are usually parameterized by deep learning models…

Machine Learning · Computer Science 2023-05-01 Zijie Li , Kazem Meidani , Amir Barati Farimani

Transformers play a central role in the inner workings of large language models. We develop a mathematical framework for analyzing Transformers based on their interpretation as interacting particle systems, which reveals that clusters…

Machine Learning · Computer Science 2025-08-22 Borjan Geshkovski , Cyril Letrouit , Yury Polyanskiy , Philippe Rigollet

Transformer-based deep learning models have achieved state-of-the-art performance across numerous language and vision tasks. While the self-attention mechanism, a core component of transformers, has proven capable of handling complex data…

Machine Learning · Computer Science 2025-08-05 Laziz Abdullaev , Tan M. Nguyen

Deep learning models such as the Transformer are often constructed by heuristics and experience. To provide a complementary foundation, in this work we study the following problem: Is it possible to find an energy function underlying the…

Machine Learning · Computer Science 2023-02-28 Yongyi Yang , Zengfeng Huang , David Wipf

The introduction of Transformers architecture has brought about significant breakthroughs in Deep Learning (DL), particularly within Natural Language Processing (NLP). Since their inception, Transformers have outperformed many traditional…

Robotics · Computer Science 2024-12-17 Nikunj Sanghai , Nik Bear Brown

Transformer-based language models exhibit complex and distributed behavior, yet their internal computations remain poorly understood. Existing mechanistic interpretability methods typically treat attention heads and multilayer perceptron…

Machine Learning · Computer Science 2025-11-26 Areeb Ahmad , Abhinav Joshi , Ashutosh Modi

One of the main challenges of Topological Data Analysis (TDA) is to extract features from persistent diagrams directly usable by machine learning algorithms. Indeed, persistence diagrams are intrinsically (multi-)sets of points in…

Machine Learning · Computer Science 2022-09-27 Raphael Reinauer , Matteo Caorsi , Nicolas Berkouk

Transformer networks have seen great success in natural language processing and machine vision, where task objectives such as next word prediction and image classification benefit from nuanced context sensitivity across high-dimensional…

Machine Learning · Computer Science 2022-12-13 Yuxuan Li , James L. McClelland

The Transformer architecture has gained growing attention in graph representation learning recently, as it naturally overcomes several limitations of graph neural networks (GNNs) by avoiding their strict structural inductive biases and…

Machine Learning · Statistics 2022-06-14 Dexiong Chen , Leslie O'Bray , Karsten Borgwardt

The process by which Large Language Models (LLMs) acquire complex capabilities during training remains a key open question in mechanistic interpretability. This project investigates whether these learning dynamics can be characterized…

Machine Learning · Computer Science 2025-09-22 Elisabetta Rocchetti

Hyperbolic geometry have shown significant potential in modeling complex structured data, particularly those with underlying tree-like and hierarchical structures. Despite the impressive performance of various hyperbolic neural networks…

Machine Learning · Computer Science 2025-08-26 Menglin Yang , Harshit Verma , Delvin Ce Zhang , Jiahong Liu , Irwin King , Rex Ying

Transformers have revolutionized Computer Vision (CV) through self-attention mechanisms. However, their complexity makes latent token representations difficult to interpret. We introduce ULTra, a framework for interpreting Transformer…

Computer Vision and Pattern Recognition · Computer Science 2026-01-06 Hesam Hosseini , Ghazal Hosseini Mighan , Amirabbas Afzali , Sajjad Amini , Amir Houmansadr

While the successes of transformers across many domains are indisputable, accurate understanding of the learning mechanics is still largely lacking. Their capabilities have been probed on benchmarks which include a variety of structured and…

Machine Learning · Computer Science 2023-07-25 Yuchen Li , Yuanzhi Li , Andrej Risteski

Modern neural network architectures can leverage large amounts of data to generalize well within the training distribution. However, they are less capable of systematic generalization to data drawn from unseen but related distributions, a…

Transformers are one of the most successful architectures of modern neural networks. At their core there is the so-called attention mechanism, which recently interested the physics community as it can be written as the derivative of an…

Machine Learning · Computer Science 2024-09-25 Francesco D'Amico , Matteo Negri