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We study Transformers through the perspective of optimal control theory, using tools from continuous-time formulations to derive actionable insights into training and architecture design. This framework improves the performance of existing…

Machine Learning · Computer Science 2025-10-27 Kelvin Kan , Xingjian Li , Benjamin J. Zhang , Tuhin Sahai , Stanley Osher , Markos A. Katsoulakis

Transformers have become the dominant architecture for sequence modeling tasks such as natural language processing or audio processing, and they are now even considered for tasks that are not naturally sequential such as image…

Machine Learning · Computer Science 2024-03-05 Jorg Bornschein , Yazhe Li , Amal Rannen-Triki

Classical Bayesian persuasion assumes that senders fully understand how receivers form beliefs and make decisions--an assumption that rarely holds when receivers possess private information or exhibit non-Bayesian behavior. In this paper,…

Systems and Control · Electrical Eng. & Systems 2025-11-11 Heeseung Bang , Andreas A. Malikopoulos

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

Language exhibits inherent structures, a property that explains both language acquisition and language change. Given this characteristic, we expect language models to manifest their own internal structures as well. While interpretability…

Computation and Language · Computer Science 2026-05-19 Haruki Sakajo , Frederikus Hudi , Yusuke Sakai , Hidetaka Kamigaito , Taro Watanabe

Astounding results from Transformer models on natural language tasks have intrigued the vision community to study their application to computer vision problems. Among their salient benefits, Transformers enable modeling long dependencies…

Computer Vision and Pattern Recognition · Computer Science 2022-01-20 Salman Khan , Muzammal Naseer , Munawar Hayat , Syed Waqas Zamir , Fahad Shahbaz Khan , Mubarak Shah

We introduce dense vision transformers, an architecture that leverages vision transformers in place of convolutional networks as a backbone for dense prediction tasks. We assemble tokens from various stages of the vision transformer into…

Computer Vision and Pattern Recognition · Computer Science 2021-03-26 René Ranftl , Alexey Bochkovskiy , Vladlen Koltun

Transformer architectures show significant promise for natural language processing. Given that a single pretrained model can be fine-tuned to perform well on many different tasks, these networks appear to extract generally useful linguistic…

Machine Learning · Computer Science 2019-10-29 Andy Coenen , Emily Reif , Ann Yuan , Been Kim , Adam Pearce , Fernanda Viégas , Martin Wattenberg

Large language models are capable of in-context learning, the ability to perform new tasks at test time using a handful of input-output examples, without parameter updates. We develop a universal approximation theory to elucidate how…

Machine Learning · Computer Science 2025-08-29 Gen Li , Yuchen Jiao , Yu Huang , Yuting Wei , Yuxin Chen

Transformers deliver outstanding performance across a wide range of tasks and are now a dominant backbone architecture for large language models (LLMs). Their task-solving performance is improved by increasing parameter size, as shown in…

Computation and Language · Computer Science 2025-06-10 Hidetaka Kamigaito , Ying Zhang , Jingun Kwon , Katsuhiko Hayashi , Manabu Okumura , Taro Watanabe

Understanding the learning process and the embedded computation in transformers is becoming a central goal for the development of interpretable AI. In the present study, we introduce a hierarchical filtering procedure for data models of…

Machine Learning · Computer Science 2025-06-11 Jerome Garnier-Brun , Marc Mézard , Emanuele Moscato , Luca Saglietti

A recent body of work has demonstrated that Transformer embeddings can be linearly decomposed into well-defined sums of factors, that can in turn be related to specific network inputs or components. There is however still a dearth of work…

Computation and Language · Computer Science 2023-10-12 Timothee Mickus , Raúl Vázquez

Transformer-based encoder-decoder models produce a fused token-wise representation after every encoder layer. We investigate the effects of allowing the encoder to preserve and explore alternative hypotheses, combined at the end of the…

Computation and Language · Computer Science 2021-07-23 Mikhail Burtsev , Anna Rumshisky

The transformer architecture has shown remarkable success in various domains, such as natural language processing and computer vision. When it comes to graph learning, transformers are required not only to capture the interactions between…

Machine Learning · Computer Science 2024-01-30 Van Thuy Hoang , O-Joun Lee

Data augmentation is widely recognized for improving generalization in deep networks, yet its impact on the geometry of learned representations remains poorly understood. In this work, we characterize how different data augmentation…

Machine Learning · Computer Science 2026-05-18 Tianxiao He , Alex H. Williams , Sarah E. Harvey

Large scale neural models show impressive performance across a wide array of linguistic tasks. Despite this they remain, largely, black-boxes - inducing vector-representations of their input that prove difficult to interpret. This limits…

Computation and Language · Computer Science 2024-06-05 Henry Conklin , Kenny Smith

Transformer-based large language models have remarkable potential to accelerate design optimization for applications such as drug development and materials discovery. Self-supervised pretraining of transformer models requires large-scale…

Machine Learning · Computer Science 2023-10-27 Pei Zhang , Logan Kearney , Debsindhu Bhowmik , Zachary Fox , Amit K. Naskar , John Gounley

Transformers underpin modern large language models (LLMs) and are commonly assumed to be behaviorally unstructured at random initialization, with all meaningful preferences emerging only through large-scale training. We challenge this…

Machine Learning · Statistics 2026-02-06 Siquan Li , Yao Tong , Haonan Wang , Tianyang Hu

Neural networks with self-attention (a.k.a. Transformers) like ViT and Swin have emerged as a better alternative to traditional convolutional neural networks (CNNs). However, our understanding of how the new architecture works is still…

Computer Vision and Pattern Recognition · Computer Science 2023-12-15 Juyeop Kim , Junha Park , Songkuk Kim , Jong-Seok Lee

While there is much recent interest in studying why Transformer-based large language models make predictions the way they do, the complex computations performed within each layer have made their behavior somewhat opaque. To mitigate this…

Computation and Language · Computer Science 2023-06-06 Byung-Doh Oh , William Schuler
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