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math.AT2026
Counting Barcodes with the same Betti Curve
Henry Ashley, HÃ¥vard Bakke Bjerkevik, Justin Curry +2
This paper considers an important inverse problem in topological data analysis (TDA): How many different barcodes produce the same Betti curve? Equivalently, given a function $β\c…
math.AT2025
Kan Approximations of the Persistent Homology Transform
Shreya Arya, Justin Curry
The persistent homology transform (PHT) of a subset is a map from the unit sphere to the space of persist…
math.AT2025
Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform
Justin Curry, Brennan Lagasse, Ngoc B. Lam +3
In this work, we explore the structure of the embedding space of a transformer model trained for playing a particular reinforcement learning (RL) game. Specifically, we investigate…