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Understanding what graph neural networks can learn, especially their ability to learn to execute algorithms, remains a central theoretical challenge. In this work, we prove exact learnability results for graph algorithms under…

Machine Learning · Computer Science 2026-02-02 Muhammad Fetrat Qharabagh , Artur Back de Luca , George Giapitzakis , Kimon Fountoulakis

Fine-grained recognition involves the classification of images from subordinate macro-categories, and it is challenging due to small inter-class differences. To overcome this, most methods perform discriminative feature selection enabled by…

Computer Vision and Pattern Recognition · Computer Science 2024-07-19 Edwin Arkel Rios , Min-Chun Hu , Bo-Cheng Lai

The convolution operator at the core of many modern neural architectures can effectively be seen as performing a dot product between an input matrix and a filter. While this is readily applicable to data such as images, which can be…

Machine Learning · Computer Science 2025-11-26 Luca Cosmo , Giorgia Minello , Alessandro Bicciato , Michael Bronstein , Emanuele Rodolà , Luca Rossi , Andrea Torsello

Mechanistic interpretability aims to reverse-engineer transformer computations by identifying causal circuits through activation patching. However, scaling these interventions across diverse prompts and task families produces…

Artificial Intelligence · Computer Science 2026-05-08 Ruben Fernandez-Boullon , David N. Olivieri

Graph convolutional networks are a new promising learning approach to deal with data on irregular domains. They are predestined to overcome certain limitations of conventional grid-based architectures and will enable efficient handling of…

Computer Vision and Pattern Recognition · Computer Science 2018-09-17 Lasse Hansen , Jasper Diesel , Mattias P. Heinrich

Graph neural networks (GNNs) achieve remarkable performance in graph machine learning tasks but can be hard to train on large-graph data, where their learning dynamics are not well understood. We investigate the training dynamics of…

Machine Learning · Computer Science 2023-06-02 Sanjukta Krishnagopal , Luana Ruiz

While lifting map has significantly enhanced the expressivity of graph neural networks, extending this paradigm to hypergraphs remains fragmented. To address this, we introduce the categorical Weisfeiler-Lehman framework, which formalizes…

Machine Learning · Computer Science 2026-02-09 Seongjin Choi , Gahee Kim , Se-Young Yun

Applying machine learning to molecules is challenging because of their natural representation as graphs rather than vectors.Several architectures have been recently proposed for deep learning from molecular graphs, but they suffer from…

Machine Learning · Statistics 2020-09-15 Jaak Simm , Adam Arany , Edward De Brouwer , Yves Moreau

Graph embeddings play a critical role in graph representation learning, allowing machine learning models to explore and interpret graph-structured data. However, existing methods often rely on opaque, high-dimensional embeddings, limiting…

Machine Learning · Computer Science 2025-11-26 Astrit Tola , Funmilola Mary Taiwo , Cuneyt Gurcan Akcora , Baris Coskunuzer

The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…

Social and Information Networks · Computer Science 2016-10-21 Cheng Li , Xiaoxiao Guo , Qiaozhu Mei

Graph signals are widely used to describe vertex attributes or features in graph-structured data, with applications spanning the internet, social media, transportation, sensor networks, and biomedicine. Graph signal processing (GSP) has…

Signal Processing · Electrical Eng. & Systems 2025-05-22 Yu Zhang , Linyu Peng , Bing-Zhao Li

Spectral graph convolutional neural networks (GCNNs) have been producing encouraging results in graph classification tasks. However, most spectral GCNNs utilize fixed graphs when aggregating node features, while omitting edge feature…

Computer Vision and Pattern Recognition · Computer Science 2022-10-06 Yang Yi , Xuequan Lu , Shang Gao , Antonio Robles-Kelly , Yuejie Zhang

Graph Convolutional Networks (GCNs) have emerged as powerful tools for learning on network structured data. Although empirically successful, GCNs exhibit certain behaviour that has no rigorous explanation -- for instance, the performance of…

Machine Learning · Computer Science 2023-11-07 Mahalakshmi Sabanayagam , Pascal Esser , Debarghya Ghoshdastidar

We extend the quantum-feature kernel framework, which relies on measurements of graph-dependent observables, along three directions. First, leveraging neutral-atom quantum processing units (QPUs), we introduce a scheme that incorporates…

Quantum Physics · Physics 2026-03-20 Mehdi Djellabi , Matthias Hecker , Shaheen Acheche

Kernels on discrete structures evaluate pairwise similarities between objects which capture semantics and inherent topology information. Existing kernels on discrete structures are only developed by topology information(such as adjacency…

Machine Learning · Computer Science 2022-11-01 Fuyang Li , Jiying Zhang , Xi Xiao , Bin Zhang , Dijun Luo

Prediction and discovery of new materials with desired properties are at the forefront of quantum science and technology research. A major bottleneck in this field is the computational resources and time complexity related to finding new…

Nowadays, the coupling of electronic structure and machine learning techniques serves as a powerful tool to predict chemical and physical properties of a broad range of systems. With the aim of improving the accuracy of predictions, a large…

Sparse autoencoders (SAEs) have become central to mechanistic interpretability, decomposing transformer activations into monosemantic features. Yet existing analyses characterise features almost exclusively through top-activating token…

Artificial Intelligence · Computer Science 2026-05-08 Ruben Fernandez-Boullon , Pablo Magariños-Docampo , Javier Perez-Robles

Large language models show great potential in unstructured data understanding, but still face significant challenges with graphs due to their structural hallucination. Existing approaches mainly either verbalize graphs into natural…

Computation and Language · Computer Science 2026-02-03 Jingyao Wu , Bin Lu , Zijun Di , Xiaoying Gan , Meng Jin , Luoyi Fu , Xinbing Wang , Chenghu Zhou

Recent papers have formulated the problem of learning graphs from data as an inverse covariance estimation with graph Laplacian constraints. While such problems are convex, existing methods cannot guarantee that solutions will have specific…

Machine Learning · Statistics 2018-05-09 Eduardo Pavez , Hilmi E. Egilmez , Antonio Ortega