topology

This paper introduces Topological Neural Operators, which lift neural operators from point-only domains to cell complexes, embedding geometry and topology to reduce the learning burden. It demonstrates that operator learning improves when geometry is not an afterthought, though the topology remains prescribed.

This paper introduces a categorical framework for transfer learning using Kan extensions, defining a transfer discrepancy that compares target invariants against those forced by a prescribed task transformation. It proves finite cokernel formulas for chain complexes and persistence modules and validates the approach on neural latent point clouds.

This article delves into the division of labor design in multi-agent systems, including trigger mechanisms, topology structures, and call chains, analyzing the engineering practices of systems such as Codex, Claude Code, OpenClaw, and Hermes Agent.

Introduces scShapeBench, a benchmark dataset for shape detection in high-dimensional single-cell data, and scReebTower, a baseline method that uses diffusion geometry and Reeb graphs to classify data shapes into clusters, trajectories, multi-branches, and archetypes.

This paper reports the discovery of a molecule with a half-Möbius topology, a novel molecular structure that could have implications for materials science and synthetic chemistry.

This paper introduces a topology-enhanced alignment framework for LLMs, utilizing trajectory topology loss and topological preference optimization based on persistent homology to regularize semantic trajectories in hidden space.

This paper empirically investigates whether image classifier decision regions are simply connected by verifying if loops between images with the same label can be filled by label-preserving surfaces.