Related papers: Topology meets Machine Learning: An Introduction u…

Persistent homology (PH) -- the conventional method in topological data analysis -- is computationally expensive, requires further vectorization of its signatures before machine learning (ML) can be applied, and captures information along…

The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…

Recent advances in pretraining 3D point cloud encoders (e.g., Point-BERT, Point-MAE) have produced powerful models, whose abilities are typically evaluated on geometric or semantic tasks. At the same time, topological descriptors have been…

Neural network approaches have been applied to computational morphology with great success, improving the performance of most tasks by a large margin and providing new perspectives for modeling. This paper starts with a brief introduction…

Through the use of examples, we explain one way in which applied topology has evolved since the birth of persistent homology in the early 2000s. The first applications of topology to data emphasized the global shape of a dataset, such as…

Topological transforms are parametrized families of topological invariants, which, by analogy with transforms in signal processing, are much more discriminative than single measurements. The first two topological transforms to be defined…

This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral…

Topology optimization enables the design of highly efficient and complex structures, but conventional iterative methods, such as SIMP-based approaches, often suffer from high computational costs and sensitivity to initial conditions.…

Our work combines aspects of three promising paradigms in machine learning, namely, attention mechanism, energy-based models, and associative memory. Attention is the power-house driving modern deep learning successes, but it lacks clear…

The application of topology, a branch of mathematics, to the study of electronic states in crystalline materials has had a revolutionary impact on the field of condensed matter physics. For example, the development of topological band…

As both machine learning models and the datasets on which they are evaluated have grown in size and complexity, the practice of using a few summary statistics to understand model performance has become increasingly problematic. This is…

Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…

Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of…

The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…

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…

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

Topological deep learning is a formalism that is aimed at introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to formalize problems that arise in a generic deep learning…

Topology at the undergraduate level is often a theoretical mathematics course, introducing concepts from point-set topology or possibly algebraic topology. However, the last two decades have seen an explosion of growth in applied topology…

Methods from computational topology are becoming more and more popular in computer vision and have shown to improve the state-of-the-art in several tasks. In this paper, we investigate the applicability of topological descriptors in the…

Deep learning methods have achieved impressive performance for multi-class medical image segmentation. However, they are limited in their ability to encode topological interactions among different classes (e.g., containment and exclusion).…