8 citations · 13 across the 9 of their papers we have counts for
10 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…
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…
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…
Accelerated Shapley Value Approximation for Data Evaluation
Lauren Watson, Zeno Kujawa, Rayna Andreeva +3
Data valuation has found various applications in machine learning, such as data filtering, efficient learning and incentives for data sharing. The most popular current approach to…
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…
Machine learning and Topological data analysis identify unique features of human papillae in 3D scans
Rayna Andreeva, Anwesha Sarkar, Rik Sarkar
The tongue surface houses a range of papillae that are integral to the mechanics and chemistry of taste and textural sensation. Although gustatory function of papillae is well inve…
Metric Space Magnitude and Generalisation in Neural Networks
Rayna Andreeva, Katharina Limbeck, Bastian Rieck +1
Deep learning models have seen significant successes in numerous applications, but their inner workings remain elusive. The purpose of this work is to quantify the learning process…
Differentially Private Shapley Values for Data Evaluation
Lauren Watson, Rayna Andreeva, Hao-Tsung Yang +1
The Shapley value has been proposed as a solution to many applications in machine learning, including for equitable valuation of data. Shapley values are computationally expensive…
Euler Characteristic Surfaces
Gabriele Beltramo, Rayna Andreeva, Ylenia Giarratano +3
We study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appea…