相关论文: Heat Kernel Goes Topological

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…

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…

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…

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…

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…

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…

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…

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…

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,…

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 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…

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…

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…

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…

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…

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…

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…

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…

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,…