58 citations · 111 across the 7 of their papers we have counts for
7 papers
Morse Theoretic Signal Compression and Reconstruction on Chain Complexes
Stefania Ebli, Celia Hacker, Kelly Maggs
At the intersection of Topological Data Analysis (TDA) and machine learning, the field of cellular signal processing has advanced rapidly in recent years. In this context, each sig…
Combinatorial Conditions for Directed Collapsing
Robin Belton, Robyn Brooks, Stefania Ebli +4
The purpose of this article is to study directed collapsibility of directed Euclidean cubical complexes. One application of this is in the nontrivial task of verifying the executio…
Nerve theorems for fixed points of neural networks
Daniela Egas Santander, Stefania Ebli, Alice Patania +4
Nonlinear network dynamics are notoriously difficult to understand. Here we study a class of recurrent neural networks called combinatorial threshold-linear networks (CTLNs) whose…
Simplicial Neural Networks
Stefania Ebli, Michaël Defferrard, Gard Spreemann
We present simplicial neural networks (SNNs), a generalization of graph neural networks to data that live on a class of topological spaces called simplicial complexes. These are na…
A Notion of Harmonic Clustering in Simplicial Complexes
Stefania Ebli, Gard Spreemann
We outline a novel clustering scheme for simplicial complexes that produces clusters of simplices in a way that is sensitive to the homology of the complex. The method is inspired…
Topology of Learning in Artificial Neural Networks
Maxime Gabella
Understanding how neural networks learn remains one of the central challenges in machine learning research. From random at the start of training, the weights of a neural network ev…
Towards Directed Collapsibility
Robin Belton, Robyn Brooks, Stefania Ebli +5
In the directed setting, the spaces of directed paths between fixed initial and terminal points are the defining feature for distinguishing different directed spaces. The simplest…