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.
By Marcos Gutierrez-del-Pozo, Eduardo Paluzo-Hidalgo, Matteo Rucco
arXiv:2608. 06276v1 Announce Type: cross Abstract: Persistence diagrams (PDs) provide stable and interpretable summaries of multiscale topological structure.
By Farzana Nasrin
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.
By Juliette Murris, Bernadette Stolz, Karsten Borgwardt
arXiv:2605. 21514v2 Announce Type: replace-cross Abstract: Diffusion-based information-theoretic approaches provide new theoretical and practical tools to study complex networks.
By Samuel Koovely, Alexandre Bovet
The paper investigates how entropy over chain‑of‑thought tokens influences policy decisions such as gradient application, pruning, and collapse detection. By separating scaffold tokens from substantive content, the authors analyze entropy, Kullback–Leibler divergence, and entropy velocity for each channel, proving differences between raw and content conventions and bounding answer diversity. Empirical results across 23 configurations show that scaffold tokens can account for up to 41% of high‑entropy positions, with entropy share growing through distillation, while content conventions outperform raw surprisal on compression tasks and reveal significant answer leakage in re‑fed chains.
By Marios Papamichalis, Regina Ruane
arXiv:2608.29846v1 Announce Type: cross
Abstract: Sampled-token on-policy distillation (OPD) efficiently transfers capabilities from teacher to student using student-generated tokens, requiring teach...
By Run Yang, Runpeng Dai, Jie Sun, Jielei Zhang, Fan Zhou, Hongtu Zhu, Peiyi Li, Longwen Gao
arXiv:2603. 14169v2 Announce Type: replace-cross Abstract: Average treatment effects (ATE) and conditional average treatment effects (CATE) are foundational causal estimands, but they target changes in expected outcomes and can miss treatment-induced changes in the shape of outcome distributions.
By Amir Saki, Usef Faghihi
arXiv:2608. 15798v1 Announce Type: new Abstract: Language models are compared by their held-out per-token cross-entropy risk---the quantity scaling laws are fitted to.
By Hanti Lin
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...
By Linzhe Zhang, Changming Xu
arXiv:2609. 31469v1 Announce Type: cross Abstract: Shapley values, a solution concept from cooperative game theory, have recently become a standard tool for feature credit allocation in machine learning.
By Nikola Mili\'cevi\'c
arXiv:2607. 22758v1 Announce Type: cross Abstract: The integration of iterative LLMs within multi-agent diagnostic frameworks requires a rigorous quantitative reevaluation of underlying communication topologies.
By Amritesh Banerjee
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.
By \.Ismail G\"uzel