9 papers
Density-Robust Spherical Coordinates from Persistent Cohomology
Nick Nordwald, Inés GarcÃa-Redondo, Anthea Monod
Persistent cohomology provides a principled framework for constructing nonlinear coordinates that reflect the topology of data. However, these topological coordinates can be severe…
Topological Signatures of Grokking
Yifan Tang, Qiquan Wang, Inés GarcÃa-Redondo +1
We study the grokking phenomenon through the lens of topology. Using persistent homology on point clouds derived from the embedding matrices of a range of models trained on modular…
The Shape of Adversarial Influence: Characterizing LLM Latent Spaces with Persistent Homology
Aideen Fay, Inés GarcÃa-Redondo, Qiquan Wang +2
Existing interpretability methods for Large Language Models (LLMs) predominantly capture linear directions or isolated features. This overlooks the high-dimensional, relational, an…
Effective Resistance in Simplicial Complexes as Bilinear Forms: Generalizations and Properties
Inés GarcÃa-Redondo, Claudia Landi, Sarah Percival +3
The concept of effective resistance, originally introduced in electrical circuit theory, has been extended to the setting of graphs by interpreting each edge as a resistor. In this…
Finding the Cores of Higher Graphs Using Geometric and Topological Means: A Survey
Inés GarcÃa-Redondo, Claudia Landi, Sarah Percival +3
In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, al…
Confidence Bands for Multiparameter Persistence Landscapes
Inés GarcÃa-Redondo, Anthea Monod, Qiquan Wang
Multiparameter persistent homology is a generalization of classical persistent homology, a central and widely-used methodology from topological data analysis, which takes into acco…