Topological Sheaves of Irreducibility: A Theoretical Framework for Multi-Agent Task Obstructions

Key points

• Multi-agent systems can differ under identical agents and communication budgets when they support different forms of joint interaction.1
• A task is represented by an interaction complex $K$ and a capacity sheaf $\mathcal{F}$; nonzero $H^n(K;\mathcal{F})$ defines a structural signature, while registered interventions test capability.1
• For cocycle data, cochain realization is solvable exactly when the represented cohomology class vanishes.1
• On a degree-2 tetrahedral-boundary task over 531,441 inputs, the same-2-skeleton system retains all four three-agent primitives yet matches the pairwise-only optimum throughout the registered separation window, whereas adding the class-filling four-agent primitive makes both tasks exact.1

Sources (1)

• [1]Topological Sheaves of Irreducibility: A Theoretical Framework for Multi-Agent Task Obstructions
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 19, 05:30 PM

  We introduce Topological Sheaves of Irreducibility (TSI), a sheaf-theoretic framework separating task-level compatibility obstructions from system capability.

  Multi-agent systems can differ under identical agents and communication budgets when they support different forms of joint interaction.

Extractive summary: sentences quoted from the sources.