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.
arXiv:2608.24549v1 Announce Type: new Abstract: Persistent entropy is the Shannon entropy of a persistence-based probability measure defined on a persistence diagram. However, its cross-entropy versi...
arXiv:2605. 21514v2 Announce Type: replace-cross Abstract: Diffusion-based information-theoretic approaches provide new theoretical and practical tools to study complex networks.
arXiv:2606. 11911v1 Announce Type: cross Abstract: Persistence diagrams are common representations in topological data analysis, but they do not naturally live in a vector space, and the statistical tools developed for comparing them have largely evolved separately from those used for downstream prediction.
arXiv:2507. 03065v2 Announce Type: replace Abstract: Why do some macroscopic structures remain identifiable even though their microscopic constituents continually change?
arXiv:2605. 00366v4 Announce Type: replace-cross Abstract: High-capacity associative memories based on Kernel Logistic Regression (KLR) exhibit strong storage capabilities, but the dynamical and geometric mechanisms underlying their stability remain poorly understood.
arXiv:2608. 06276v1 Announce Type: cross Abstract: Persistence diagrams (PDs) provide stable and interpretable summaries of multiscale topological structure.
arXiv:2606. 10384v1 Announce Type: cross Abstract: Criticality has been proposed as a key organizing principle in biological neural systems, yet its origin and relevance in artificial neural networks remain unclear.
arXiv:2609.23387v1 Announce Type: new Abstract: Before a machine learning model can learn a thermodynamic equation of state, it must discover what its measurements represent: which channels scale wit...
arXiv:2509. 10650v4 Announce Type: replace-cross Abstract: Effective analysis in neuroscience benefits significantly from robust conceptual frameworks.
arXiv:2512. 11415v3 Announce Type: replace-cross Abstract: We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles.
The paper introduces a unified pipeline that classifies univariate time series by first converting them into graphs using one of five constructions from three families (visibility, transition, proximity). The resulting graph is turned into a dissimilarity matrix, from which a Vietoris–Rips filtration produces persistence diagrams that are vectorized via persistence landscapes and topological summary statistics. Experiments on twelve UCR benchmarks reveal that no single graph construction dominates, diffusion distance consistently outperforms shortest-path metrics, and persistence-based features remain robust to noise.
arXiv:2606. 24000v1 Announce Type: new Abstract: We introduce cyclic denoising -- repeated forward and reverse diffusion at controlled noise amplitudes -- as an extraction attack for image diffusion models.