4 papers
Neural collapse in the orthoplex regime
James Alcala, Rayna Andreeva, Vladimir A. Kobzar +4
When training a neural network for classification, the feature vectors of the training set are known to collapse to the vertices of a regular simplex, provided the dimension of…
Fractal dimensions of complex networks: advocating for a topological approach
Rayna Andreeva, Haydeé Contreras-Peruyero, Sanjukta Krishnagopal +3
Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods hav…
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…
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…