Related papers: Topology meets Machine Learning: An Introduction u…
Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue.…
We investigate the knowledge graph entity typing task which aims at inferring plausible entity types. In this paper, we propose a novel Transformer-based Entity Typing (TET) approach, effectively encoding the content of neighbors of an…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
Persistence diagrams have been widely recognized as a compact descriptor for characterizing multiscale topological features in data. When many datasets are available, statistical features embedded in those persistence diagrams can be…
We present a novel attention-based mechanism to learn enhanced point features for point cloud processing tasks, e.g., classification and segmentation. Unlike prior works, which were trained to optimize the weights of a pre-selected set of…
Modeling object dynamics with a neural network is an important problem with numerous applications. Most recent work has been based on graph neural networks. However, physics happens in 3D space, where geometric information potentially plays…
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…
Epileptic seizure detection from EEG signals remains challenging due to the high dimensionality and nonlinear, potentially stochastic, dynamics of neural activity. In this work, we investigate whether features derived from topological data…
A suitable feature representation that can both preserve the data intrinsic information and reduce data complexity and dimensionality is key to the performance of machine learning models. Deeply rooted in algebraic topology, persistent…
Important advances have been made using convolutional neural network (CNN) approaches to solve complicated problems in areas that rely on grid structured data such as image processing and object classification. Recently, research on graph…
In low dimensional topology, we have some invariants defined by using solutions of some nonlinear elliptic operators. The invariants could be understood as Euler class or degree in the ordinary cohomology, in infinite dimensional setting.…
In this paper we present a deep neural network topology that incorporates a simple to implement transformation invariant pooling operator (TI-POOLING). This operator is able to efficiently handle prior knowledge on nuisance variations in…
Applying deep learning to investigate topological phase transitions (TPTs) becomes a useful method due to not only its ability to recognize patterns but also its statistical excellency to examine the amount of information carried by…
Methods for processing point cloud information have seen a great success in collider physics applications. One recent breakthrough in machine learning is the usage of Transformer networks to learn semantic relationships between sequences in…
Lots of neural network architectures have been proposed to deal with learning tasks on graph-structured data. However, most of these models concentrate on only node features during the learning process. The edge features, which usually play…
In recent years, topological data analysis has been utilized for a wide range of problems to deal with high dimensional noisy data. While text representations are often high dimensional and noisy, there are only a few work on the…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
Recovering point clouds involves the sequential process of sampling and restoration, yet existing methods struggle to effectively leverage both topological and geometric attributes. To address this, we propose an end-to-end architecture…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
Optimization for deep networks is currently a very active area of research. As neural networks become deeper, the ability in manually optimizing the network becomes harder. Mini-batch normalization, identification of effective respective…