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While kernel methods and Graph Neural Networks offer complementary strengths, integrating the two has posed challenges in efficiency and scalability. The Graph Neural Tangent Kernel provides a theoretical bridge by interpreting GNNs through…

Machine Learning · Computer Science 2025-07-17 Lin Wang , Shijie Wang , Sirui Huang , Qing Li

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

Capsule Networks attempt to represent patterns in images in a way that preserves hierarchical spatial relationships. Additionally, research has demonstrated that these techniques may be robust against adversarial perturbations. We present…

Machine Learning · Statistics 2019-06-10 Taylor Killian , Justin Goodwin , Olivia Brown , Sung-Hyun Son

Smoothing a signal based on local neighborhoods is a core operation in machine learning and geometry processing. On well-structured domains such as vector spaces and manifolds, the Laplace operator derived from differential geometry offers…

Computer Vision and Pattern Recognition · Computer Science 2025-07-09 Nathan Kessler , Robin Magnet , Jean Feydy

In this paper, we develop a new graph kernel, namely the Hierarchical Transitive-Aligned kernel, by transitively aligning the vertices between graphs through a family of hierarchical prototype graphs. Comparing to most existing…

Social and Information Networks · Computer Science 2020-02-12 Lu Bai , Lixin Cui , Edwin R. Hancock

Head pose estimation is a crucial problem for many tasks, such as driver attention, fatigue detection, and human behaviour analysis. It is well known that neural networks are better at handling classification problems than regression…

Computer Vision and Pattern Recognition · Computer Science 2020-05-26 Zhongxu Hu , Yang Xing , Chen Lv , Peng Hang , Jie Liu

We introduce the Hierarchically Interacting Particle Neural Network (HIP-NN) to model molecular properties from datasets of quantum calculations. Inspired by a many-body expansion, HIP-NN decomposes properties, such as energy, as a sum over…

Machine Learning · Statistics 2018-04-04 Nicholas Lubbers , Justin S. Smith , Kipton Barros

Graph convolutional networks (GCNs) are powerful tools for graph-structured data. However, they have been recently shown to be vulnerable to topological attacks. To enhance adversarial robustness, we go beyond spectral graph theory to…

Machine Learning · Computer Science 2021-09-22 Ming Jin , Heng Chang , Wenwu Zhu , Somayeh Sojoudi

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

Computer Vision and Pattern Recognition · Computer Science 2018-02-19 Christoph Hofer , Roland Kwitt , Marc Niethammer , Andreas Uhl

Topological deep learning (TDL) is a rapidly growing field that seeks to leverage topological structure in data and facilitate learning from data supported on topological objects, ranging from molecules to 3D shapes. Most TDL architectures…

Machine Learning · Computer Science 2025-02-13 Yam Eitan , Yoav Gelberg , Guy Bar-Shalom , Fabrizio Frasca , Michael Bronstein , Haggai Maron

Machine learning potential (MLP) has been a popular topic in recent years for its potential to replace expensive first-principles calculations in some large systems. Meanwhile, message passing networks have gained significant attention due…

Computational Physics · Physics 2024-09-04 Junjie Wang , Yong Wang , Haoting Zhang , Ziyang Yang , Zhixin Liang , Jiuyang Shi , Hui-Tian Wang , Dingyu Xing , Jian Sun

Autonomous individuals establish a structural complex system through pairwise connections and interactions. Notably, the evolution reflects the dynamic nature of each complex system since it recodes a series of temporal changes from the…

Machine Learning · Computer Science 2023-06-27 Xue Liu , Dan Sun , Wei Wei , Zhiming Zheng

Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the…

Machine Learning · Computer Science 2024-05-14 Xin Liu , Weiqi Wang , Jiaxin Bai , Yangqiu Song

This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and…

Machine Learning · Computer Science 2020-04-01 Yiquan Zhang , Bo Peng , Xiaoyi Zhou , Cheng Xiang , Dalei Wang

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…

We introduce a novel class of explicit feature maps based on topological indices that represent each graph by a compact feature vector, enabling fast and interpretable graph classification. Using radial basis function kernels on these…

Machine Learning · Computer Science 2025-09-23 Adam Wesołowski , Ronin Wu , Karim Essafi

Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be…

Machine Learning · Computer Science 2025-01-17 Zuoyu Yan , Qi Zhao , Ze Ye , Tengfei Ma , Liangcai Gao , Zhi Tang , Yusu Wang , Chao Chen

Graph neural networks (GNNs) have demonstrated great success in representation learning for graph-structured data. The layer-wise graph convolution in GNNs is shown to be powerful at capturing graph topology. During this process, GNNs are…

Machine Learning · Computer Science 2021-12-10 Mingxuan Ju , Shifu Hou , Yujie Fan , Jianan Zhao , Liang Zhao , Yanfang Ye

We introduce the first graph kernels for metric graphs via tropical algebraic geometry. In contrast to conventional graph kernels based on graph combinatorics such as nodes, edges, and subgraphs, our metric graph kernels are purely based on…

Machine Learning · Computer Science 2026-01-30 Yueqi Cao , Anthea Monod

Many state-of-the-art trackers usually resort to the pretrained convolutional neural network (CNN) model for correlation filtering, in which deep features could usually be redundant, noisy and less discriminative for some certain instances,…

Computer Vision and Pattern Recognition · Computer Science 2019-08-06 Chenglong Li , Yan Huang , Liang Wang , Jin Tang , Liang Lin