相关论文: A Persistent Homology Design Space for 3D Point Cl…

The inner representation of deep neural networks (DNNs) is indecipherable, which makes it difficult to tune DNN models, control their training process, and interpret their outputs. In this paper, we propose a novel approach to investigate…

Recent years have witnessed a fast growth in mathematical artificial intelligence (AI). One of the most successful mathematical AI approaches is topological data analysis (TDA) via persistent homology (PH) that provides explainable AI (xAI)…

In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…

Two-dimensional (2D) particle systems, such as magnetic skyrmions, exhibit topological phase transitions between unique 2D phases. However, a simple and computationally efficient methodology to capture lattice configurational properties and…

Persistent homology (PH) is a popular tool for topological data analysis that has found applications across diverse areas of research. It provides a rigorous method to compute robust topological features in discrete experimental…

Building upon [2308.02636], we investigate the constraining power of persistent homology on cosmological parameters and primordial non-Gaussianity in a likelihood-free inference pipeline utilizing machine learning. We evaluate the ability…

Persistent homology has been widely used to discover hidden topological structures in data across various applications, including music data. To apply persistent homology, a distance or metric must be defined between points in a point cloud…

Deep learning models have achieved remarkable success across various domains, yet their learned representations and decision-making processes remain largely opaque and hard to interpret. This work introduces HOLE (Homological Observation of…

Persistence diagrams (PDs) provide a powerful tool for understanding the topology of the underlying shape of a point cloud. However, identifying which points in PDs encode genuine signals remains challenging. This challenge directly hinders…

This research uses deep learning to estimate the topology of manifolds represented by sparse, unordered point cloud scenes in 3D. A new labelled dataset was synthesised to train neural networks and evaluate their ability to estimate the…

Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short…

Exploring contextual information in the local region is important for shape understanding and analysis. Existing studies often employ hand-crafted or explicit ways to encode contextual information of local regions. However, it is hard to…

Controlling structural complexity, particularly the number of holes, remains a fundamental challenge in topology optimization, with significant implications for both theoretical analysis and manufacturability. Most existing approaches rely…

Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…

Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…

We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics…

Machine learning has emerged as a powerful approach in materials discovery. Its major challenge is selecting features that create interpretable representations of materials, useful across multiple prediction tasks. We introduce an…

Contemporary deep neural networks offer state-of-the-art results when applied to visual reasoning, e.g., in the context of 3D point cloud data. Point clouds are important datatype for precise modeling of three-dimensional environments, but…

Recent investigations on rotation invariance for 3D point clouds have been devoted to devising rotation-invariant feature descriptors or learning canonical spaces where objects are semantically aligned. Examinations of learning frameworks…

Topological Data Analysis (TDA) combines computational topology and data science to extract and analyze intrinsic topological and geometric structures in data set in a metric space. While the persistent homology (PH), a widely used tool in…