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Found 10 papers, 1 papers with code
A topological model for partial equivariance in deep learning and data analysis
In this article, we propose a topological model to encode partial equivariance in neural networks.
Low-Resource White-Box Semantic Segmentation of Supporting Towers on 3D Point Clouds via Signature Shape Identification
In this paper, we propose SCENE-Net, a low-resource white-box model for 3D point cloud semantic segmentation.
Generalized Permutants and Graph GENEOs
In this paper we establish a bridge between Topological Data Analysis and Geometric Deep Learning, adapting the topological theory of group equivariant non-expansive operators (GENEOs) to act on the space of all graphs weighted on vertices or edges.
GENEOnet: A new machine learning paradigm based on Group Equivariant Non-Expansive Operators. An application to protein pocket detection
Nowadays there is a big spotlight cast on the development of techniques of explainable machine learning.
On the geometric and Riemannian structure of the spaces of group equivariant non-expansive operators
Group equivariant non-expansive operators have been recently proposed as basic components in topological data analysis and deep learning.
On the finite representation of group equivariant operators via permutant measures
This result makes available a new method to build linear $G$-equivariant operators in the finite setting.
Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learning
The aim of this paper is to provide a general mathematical framework for group equivariance in the machine learning context.
Position paper: Towards an observer-oriented theory of shape comparison
In this position paper we suggest a possible metric approach to shape comparison that is based on a mathematical formalization of the concept of observer, seen as a collection of suitable operators acting on a metric space of functions.
Combining persistent homology and invariance groups for shape comparison
In many applications concerning the comparison of data expressed by $\mathbb{R}^m$-valued functions defined on a topological space $X$, the invariance with respect to a given group $G$ of self-homeomorphisms of $X$ is required.
G-invariant Persistent Homology
Roughly speaking, the main idea consists in defining persistent homology by means of a set of chains that is invariant under the action of G. In this paper we formalize this idea, and prove the stability of the persistent Betti number functions in G-invariant persistent homology with respect to the natural pseudo-distance d_G.
