arXiv:2511. 04873v2 Announce Type: replace-cross Abstract: Prototype selection methods compress a training set, but the existing taxonomy of condensation, edition, hybrid, competence-based, optimization-based, and clustering-based families does not include methods that operate on the multi-scale topological structure of the data.
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.
We introduce pVR, a topological machine learning framework for alignment-free genomic sequence classification that combines $p$-adic numbers with topological data analysis. Each DNA sequence is encoded along two complementary axes: a $p$-adic distance on $k$-mer prefixes, which captures hierarchical positional structure, and a compositional $L_1$ distance on $k$-mer frequencies, which captures local sequence content.
arXiv:2606. 06117v1 Announce Type: cross Abstract: We introduce pVR, a topological machine learning framework for alignment-free genomic sequence classification that combines $p$-adic numbers with topological data analysis.
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:2606. 09806v1 Announce Type: cross Abstract: We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains.
arXiv:2605. 00725v2 Announce Type: replace Abstract: Topological neural networks have emerged as effective tools for modeling higher-order relational structures beyond pairwise graphs, including hypergraphs, simplicial complexes, and cell complexes.
arXiv:2607. 09971v1 Announce Type: new Abstract: Archive-based exploration methods such as Go-Explore select which visited state to return to using visitation rarity, and frontier methods return to the boundary of the unknown; neither asks whether the unexplored region behind a boundary is enterable at all.
arXiv:2608. 15388v1 Announce Type: new Abstract: Topological deep learning (TDL) methods rely on lifting raw data into higher-order discrete domains such as simplicial complexes, cell complexes, and hypergraphs.
arXiv:2606. 29403v1 Announce Type: cross Abstract: Conformal prediction guarantees marginal coverage, but pooled calibration averages over heterogeneous regions and can mask regional undercoverage in safety-critical subgroups.
arXiv:2404. 03082v3 Announce Type: replace Abstract: Partially ordered sets (posets) are discrete mathematical structures that formalize the notion of comparison without forcing every pair of objects to be comparable.
arXiv:2606. 23880v1 Announce Type: new Abstract: From climate teleconnections to gene regulation, modern time-series datasets encompass tens or hundreds of interacting variables, making causal discovery increasingly challenging.
arXiv:2607. 17962v1 Announce Type: cross Abstract: TabPFN is a transformer-based foundation model for tabular prediction that performs inference without task-specific training by conditioning on a support set and query inputs.