Persistent Entropy as a Detector of Phase Transitions
Read the original on arXiv AI →The paper presents a model‑agnostic theorem that provides conditions under which a structural change in a persistence barcode leads to a detectable change in persistent entropy. By treating persistence diagrams as random objects indexed by a control parameter, the authors identify a dispersion‑condensation mechanism in the normalized persistence weights and derive an explicit lower bound on the entropy difference between two regimes, valid with high probability at finite sample size and independent of the absolute scale of bar lifetimes. The criterion is applied to convolutional networks, revealing a sharp topological phase transition in the circular organization of learned filters, and it also detects the Kuramoto synchronization and Vicsek order‑disorder transitions.
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