Related papers: Predicting Euler Characteristics and Constructing …

In common real-world robotic operations, action and state spaces can be vast and sometimes unknown, and observations are often relatively sparse. How do we learn the full topology of action and state spaces when given only few and sparse…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

A closed form formula (generating function) for the Euler characteristic of the configuration space of $\scriptstyle n$ particles in a simplicial complex is given.

Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation…

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…

The observation and description of collective excitations in solids is a fundamental issue when seeking to understand the physics of a many-body system. Analysis of these excitations is usually carried out by measuring the dynamical…

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,…

In magnetism, skyrmions correspond to classical three-dimensional spin textures characterized by a topological invariant that keeps track of the winding of the magnetization in real space, a property that cannot be easily generalized to the…

Model-based paradigms for decision-making and control are becoming ubiquitous in robotics. They rely on the ability to efficiently learn a model of the system from data. Structured Mechanical Models (SMMs) are a data-efficient black-box…

In this study, we present a novel approach along with the needed computational strategies for efficient and scalable feature engineering of the crystal structure in compounds of different chemical compositions. This approach utilizes a…

Skyrmions, as quasiparticles with topological spin textures, has recently garnered great attention for both condensed matter and structured wave communities, promising next-generation large-density robust information technologies. However,…

This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…

We train artificial neural networks to distinguish the geometric phases of a set of bands in 1D photonic crystals. We find that the trained network yields remarkably accurate predictions of the topological phases for 1D photonic crystals,…

This paper explores the automated analysis of palmar features using machine learning techniques. We present a computer vision pipeline that extracts key characteristics from palm images, such as principal line structures, texture, and shape…

Chiral magnets give rise to the anti-symmetric Dzyaloshinskii-Moriya (DM) interaction, which induces topological nontrivial textures such as magnetic skyrmions. The topology is characterized by integer values of the topological charge. In…

Magnetic skyrmions are topologically non-trivial spin textures of potential interest for future information storage applications, and for such purposes, the control and understanding of single skyrmion creation is required. A scheme is…

One of the major difficulties in medical image segmentation is the high variability of these images, which is caused by their origin (multi-centre), the acquisition protocols (multi-parametric), as well as the variability of human anatomy,…

Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging…

The Euler Characteristic Transform (ECT) is a robust method for shape classification. It takes an embedded shape and, for each direction, computes a piecewise constant function representing the Euler Characteristic of the shape's sublevel…

Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…