topology

This paper introduces topology as a distinct generalization axis for neural operators in PDE solving, using Hodge heat flow and the TopoBox-3D framework to show its influence across the Hodge spectrum beyond geometric compatibility.

This article describes a rendering technique for creating hand-hatched, non-photorealistic images of topological surfaces, inspired by Francis' book and various academic methods in computer graphics.

This paper investigates the existence or properties of a complex structure on the six-dimensional sphere S^6.

Microsoft Research introduces MindTopo, a benchmark that tests whether multimodal AI models understand topological relationships like connectivity, enclosure, and knots. Current models perform well on static recognition but struggle with interactive planning tasks, revealing a key gap for robotics and interactive environments.

Presents ArchEGraph, a large-scale graph dataset for building energy modeling with aligned geometry, topology, weather, and thermal loads, along with benchmark tasks for graph reconstruction and load prediction.

This paper proves that the Burau representation of the braid group B_4 is faithful, settling the final unknown case in a long-standing problem in low-dimensional topology.

Introduces TopoTuner, a topology-guided fine-tuning framework that selectively freezes attention projection matrices by measuring topological drift via Wasserstein distances between persistence diagrams. It achieves competitive performance to full fine-tuning while training only 1-2% of parameters and outperforms LoRA in most settings.

Cotal is an open standard for AI agent coordination that allows configurable topologies (peer-to-peer, supervised, hierarchical, or hybrid) using NATS messaging, complementing existing protocols like MCP and A2A.

An open-source 2.5D diagram engine in Go that separates topology from geometry to enable LLMs to generate clean architecture diagrams without spatial hallucinations.

This thread argues that standard transformers have a topological flaw: once a state representation reaches the top layer, they cannot update beliefs over time, causing collapse as depth increases.

This paper introduces TopVAE, a topology-optimized VAE that reduces 'dark areas' in molecular latent diffusion by making the decoder internalize structural and chemical constraints, achieving significant improvements in molecular generation quality.

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.

A comprehensive guide to building multi-agent workflows using Claude Code's orchestration primitives, covering six orchestration topologies and how to implement them with subagents, agent teams, and dynamic workflows.