arXiv:2608. 06276v1 Announce Type: cross Abstract: Persistence diagrams (PDs) provide stable and interpretable summaries of multiscale topological structure.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.
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. 07156v2 Announce Type: replace-cross Abstract: Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram.
The paper demonstrates that a stochastic hybrid system (SHS), which combines continuous dynamics governed by a stochastic differential equation (SDE) with discrete resets triggered by a Markov kernel, can be approximated by a single SDE in a higher‑dimensional latent space. By encoding the reset branches with auxiliary variables, the resets become deterministic, allowing the system’s manifold to be glued and embedded into Euclidean space. This embedding eliminates the need for explicit reset terms in the hybrid Fokker‑Planck equation, and the authors propose a loss function that matches evolving state distributions, enabling the latent SDE to recover the SHS’s probability evolution without mode labeling, trajectory segmentation, or event‑based simulations.
arXiv:2606. 00427v1 Announce Type: new Abstract: State abstraction in reinforcement learning is usually formulated as a partition of states based on reward and transition similarity.
arXiv:2606. 29763v1 Announce Type: cross Abstract: Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.
arXiv:2608. 04334v1 Announce Type: cross Abstract: Contemporary model-free reinforcement learning algorithms can achieve very high performance, but have low sample efficiency and are not robust to changes in the environment.