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Graph neural networks (GNNs), as the de-facto model class for representation learning on graphs, are built upon the multi-layer perceptrons (MLP) architecture with additional message passing layers to allow features to flow across nodes.…

Machine Learning · Computer Science 2023-08-07 Chenxiao Yang , Qitian Wu , Jiahua Wang , Junchi Yan

The growing complexity of wireless systems has accelerated the move from traditional methods to learning-based solutions. Graph Neural Networks (GNNs) are especially well-suited here, since wireless networks can be naturally represented as…

Signal Processing · Electrical Eng. & Systems 2025-10-02 Romina Garcia Camargo , Zhiyang Wang , Alejandro Ribeiro

Graph Neural Networks (GNNs) are the dominant architecture for molecular machine learning, particularly for molecular property prediction and machine learning interatomic potentials (MLIPs). GNNs perform message passing on predefined graphs…

Machine Learning · Computer Science 2025-10-03 Tobias Kreiman , Yutong Bai , Fadi Atieh , Elizabeth Weaver , Eric Qu , Aditi S. Krishnapriyan

In one dimension, any disorder is traditionally believed to localize all states. We show that this paradigm breaks down under hyperuniform disorder, which suppresses long-wavelength fluctuations and interpolates between random and periodic…

Disordered Systems and Neural Networks · Physics 2025-09-30 Junmo Jeon , Harukuni Ikeda , Shiro Sakai

We show that standard Transformers without graph-specific modifications can lead to promising results in graph learning both in theory and practice. Given a graph, we simply treat all nodes and edges as independent tokens, augment them with…

Machine Learning · Computer Science 2022-10-25 Jinwoo Kim , Tien Dat Nguyen , Seonwoo Min , Sungjun Cho , Moontae Lee , Honglak Lee , Seunghoon Hong

We study the grokking phenomenon through the lens of topology. Using persistent homology on point clouds derived from the embedding matrices of a range of models trained on modular arithmetic with varying primes, we identify a clear and…

Machine Learning · Computer Science 2026-05-08 Yifan Tang , Qiquan Wang , Inés García-Redondo , Anthea Monod

We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…

Statistics Theory · Mathematics 2018-09-18 Steffen L. Lauritzen , Alessandro Rinaldo , Kayvan Sadeghi

The intersection of deep learning and symbolic mathematics has seen rapid progress in recent years, exemplified by the work of Lample and Charton. They demonstrated that effective training of machine learning models for solving mathematical…

Machine Learning · Computer Science 2025-04-18 Yuta Kambe , Yota Maeda , Tristan Vaccon

Generative modeling is typically framed as learning mapping rules, but from an observer's perspective without access to these rules, the task becomes disentangling the geometric support from the probability distribution. We propose that…

Machine Learning · Statistics 2025-12-04 Rui Tong

We prove bounds on the generalization error of convolutional networks. The bounds are in terms of the training loss, the number of parameters, the Lipschitz constant of the loss and the distance from the weights to the initial weights. They…

Machine Learning · Computer Science 2020-04-09 Philip M. Long , Hanie Sedghi

Transformers with self-attention modules as their core components have become an integral architecture in modern large language and foundation models. In this paper, we study the evolution of tokens in deep encoder-only transformers at…

Analysis of PDEs · Mathematics 2026-05-12 Albert Alcalde , Leon Bungert , Konstantin Riedl , Tim Roith

Neural networks that satisfy invariance with respect to input permutations have been widely studied in machine learning literature. However, in many applications, only a subset of all input permutations is of interest. For heterogeneous…

Machine Learning · Computer Science 2023-02-28 Dmitry Rybin , Ruoyu Sun , Zhi-Quan Luo

We introduce a Graph Transformer framework that serves as a general inverse physics engine on meshes, demonstrated through the challenging task of reconstructing aerodynamic flow fields from sparse surface measurements. While deep learning…

Machine Learning · Computer Science 2025-01-29 Gregory Duthé , Imad Abdallah , Eleni Chatzi

Will further scaling up of machine learning models continue to bring success? A significant challenge in answering this question lies in understanding generalization gap, which is the impact of overfitting. Understanding generalization gap…

Machine Learning · Statistics 2026-05-18 Atsushi Suzuki , Jing Wang

The versatility of self-attention mechanism earned transformers great success in almost all data modalities, with limitations on the quadratic complexity and difficulty of training. To apply transformers across different data modalities,…

Machine Learning · Computer Science 2024-08-20 Viet Anh Nguyen , Minh Lenhat , Khoa Nguyen , Duong Duc Hieu , Dao Huu Hung , Truong Son Hy

Symbolic regression algorithms search a space of mathematical expressions for formulas that explain given data. Transformer-based models have emerged as a promising, scalable approach shifting the expensive combinatorial search to a…

Machine Learning · Computer Science 2025-09-25 Henrik Voigt , Paul Kahlmeyer , Kai Lawonn , Michael Habeck , Joachim Giesen

This paper proves that robustness implies generalization via data-dependent generalization bounds. As a result, robustness and generalization are shown to be connected closely in a data-dependent manner. Our bounds improve previous bounds…

Machine Learning · Computer Science 2022-08-04 Kenji Kawaguchi , Zhun Deng , Kyle Luh , Jiaoyang Huang

We propose a theoretical framework for training Graph Neural Networks (GNNs) on large input graphs via training on small, fixed-size sampled subgraphs. This framework is applicable to a wide range of models, including popular sampling-based…

Machine Learning · Computer Science 2023-10-18 Yeganeh Alimohammadi , Luana Ruiz , Amin Saberi

We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its…

Probability · Mathematics 2017-11-22 Paola Bermolen , Matthieu Jonckheere , Jaron Sanders

In this paper, we establish novel data-dependent upper bounds on the generalization error through the lens of a "variable-size compressibility" framework that we introduce newly here. In this framework, the generalization error of an…

Machine Learning · Statistics 2024-06-12 Milad Sefidgaran , Abdellatif Zaidi