3 papers
cs.LG2025
Metric Space Magnitude for Evaluating the Diversity of Latent Representations
Katharina Limbeck, Rayna Andreeva, Rik Sarkar +1
The magnitude of a metric space is a novel invariant that provides a measure of the 'effective size' of a space across multiple scales, while also capturing numerous geometrical pr…
cs.LG2024
Topological Generalization Bounds for Discrete-Time Stochastic Optimization Algorithms
Rayna Andreeva, Benjamin Dupuis, Rik Sarkar +2
We present a novel set of rigorous and computationally efficient topology-based complexity notions that exhibit a strong correlation with the generalization gap in modern deep neur…
cs.LG2024
Approximating Metric Magnitude of Point Sets
Rayna Andreeva, James Ward, Primoz Skraba +2
Metric magnitude is a measure of the "size" of point clouds with many desirable geometric properties. It has been adapted to various mathematical contexts and recent work suggests…