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The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…

Artificial Intelligence · Computer Science 2021-03-22 Lukas Harsch , Johannes Burgbacher , Stefan Riedelbauch

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

Despite their widespread use, training deep Transformers can be unstable. Layer normalization, a standard component, improves training stability, but its placement has often been ad-hoc. In this paper, we conduct a principled study on the…

Machine Learning · Computer Science 2025-10-14 Kelvin Kan , Xingjian Li , Benjamin J. Zhang , Tuhin Sahai , Stanley Osher , Krishna Kumar , Markos A. Katsoulakis

The introduction of the transformer architecture in 2017 marked the most striking advancement in natural language processing. The transformer is a model architecture relying entirely on an attention mechanism to draw global dependencies…

Machine Learning · Computer Science 2025-07-23 Zeqian Chen

Real-world data generation often involves complex inter-dependencies among instances, violating the IID-data hypothesis of standard learning paradigms and posing a challenge for uncovering the geometric structures for learning desired…

Machine Learning · Computer Science 2023-05-30 Qitian Wu , Chenxiao Yang , Wentao Zhao , Yixuan He , David Wipf , Junchi Yan

Structured prediction tasks pose a fundamental trade-off between the need for model complexity to increase predictive power and the limited computational resources for inference in the exponentially-sized output spaces such models require.…

Machine Learning · Statistics 2012-08-17 David Weiss , Benjamin Sapp , Ben Taskar

Neural networks often have identifiable computational structures - components of the network which perform an interpretable algorithm or task - but the mechanisms by which these emerge and the best methods for detecting these structures are…

Machine Learning · Computer Science 2025-04-17 Rohan Hitchcock , Gary W. Delaney , Jonathan H. Manton , Richard Scalzo , Jingge Zhu

A convolutional encoder-decoder-based transformer model is proposed for autoregressively training on spatio-temporal data of turbulent flows. The prediction of future fluid flow fields is based on the previously predicted fluid flow field…

Fluid Dynamics · Physics 2023-03-31 Aakash Patil , Jonathan Viquerat , Elie Hachem

We investigate how embedding dimension affects the emergence of an internal "world model" in a transformer trained with reinforcement learning to perform bubble-sort-style adjacent swaps. Models achieve high accuracy even with very small…

Machine Learning · Computer Science 2025-10-22 Brady Bhalla , Honglu Fan , Nancy Chen , Tony Yue YU

Learning representations for structured data with certain geometries (e.g., observed or unobserved) is a fundamental challenge, wherein message passing neural networks (MPNNs) have become a de facto class of model solutions. In this paper,…

Machine Learning · Computer Science 2025-07-02 Qitian Wu , David Wipf , Junchi Yan

Autoregressive language models have demonstrated a remarkable ability to extract latent structure from text. The embeddings from large language models have been shown to capture aspects of the syntax and semantics of language. But what…

Machine Learning · Computer Science 2026-01-09 Liyi Zhang , Michael Y. Li , R. Thomas McCoy , Theodore R. Sumers , Jian-Qiao Zhu , Thomas L. Griffiths

A foundation model like GPT elicits many emergent abilities, owing to the pre-training with broad inclusion of data and the use of the powerful Transformer architecture. While foundation models in natural languages are prevalent, can we…

Machine Learning · Computer Science 2025-06-18 Ziyuan Tang , Jie Chen

This paper proposes a transformer over transformer framework, called Transformer$^2$, to perform neural text segmentation. It consists of two components: bottom-level sentence encoders using pre-trained transformers, and an upper-level…

Computation and Language · Computer Science 2021-10-15 Kelvin Lo , Yuan Jin , Weicong Tan , Ming Liu , Lan Du , Wray Buntine

When agents interact with a complex environment, they must form and maintain beliefs about the relevant aspects of that environment. We propose a way to efficiently train expressive generative models in complex environments. We show that a…

Machine Learning · Computer Science 2019-06-25 Karol Gregor , Danilo Jimenez Rezende , Frederic Besse , Yan Wu , Hamza Merzic , Aaron van den Oord

Large language models are remarkably capable, yet how computation propagates through their layers remains poorly understood. A growing line of work treats depth as discrete time and the residual stream as a dynamical system, where each…

Machine Learning · Computer Science 2026-05-15 Jesseba Fernando , Grigori Guitchounts

Trajectory planning in autonomous driving is highly dependent on predicting the emergent behavior of other road users. Learning-based methods are currently showing impressive results in simulation-based challenges, with transformer-based…

Machine Learning · Computer Science 2024-08-08 Lars Ullrich , Alex McMaster , Knut Graichen

Given a sequence of tokens, such as words, the task of next-token prediction is to predict the next-token conditional probability distribution. Decoder-only transformers have become effective models for this task, but their properties are…

Machine Learning · Computer Science 2025-11-25 Liam Madden , Curtis Fox , Christos Thrampoulidis

We investigate the capacity of transformers to learn algorithms involving their context while solely being trained using next token prediction. We set up Markov chains with random transition matrices and we train transformers to predict the…

Machine Learning · Computer Science 2025-08-07 Simon Lepage , Jeremie Mary , David Picard

The emergence of deep learning has yielded noteworthy advancements in time series forecasting (TSF). Transformer architectures, in particular, have witnessed broad utilization and adoption in TSF tasks. Transformers have proven to be the…

Machine Learning · Computer Science 2023-11-01 Liyilei Su , Xumin Zuo , Rui Li , Xin Wang , Heng Zhao , Bingding Huang

Digital AI systems spanning large language models, vision models, and generative architectures that operate primarily in symbolic, linguistic, or pixel domains. They have achieved striking progress, but almost all of this progress lives in…

Machine Learning · Computer Science 2026-01-07 Tao Xu , Zhixin Hu , Li Luo , Momiao Xiong