Phase Transition for Budgeted Multi-Agent Synergy

Summary

A formal theory of when multi-agent organization amplifies or destroys weak signal, built from exactly the primitives this paper cares about: a per-agent compute-performance exponent, a communication fidelity curve, an effective shared-error correlation rho, and a context window that imposes fan-in limits and thereby makes hierarchy necessary. For binary tasks with majority aggregation they prove a sharp phase transition for deep b-ary trees under correlated inputs and lossy communication, and derive an organization exponent s such that outperforming the best single agent under the same budget occurs exactly when s exceeds the single-agent scaling exponent. Closed-form risks for star, chain and tree organizations make correlation- and communication-induced performance floors explicit. Effectively a Sah-Stiglitz-style organizational-design theorem restated for LLM agent stacks, and the strongest formal complement to the paper's argument.

Contribution

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Method

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Relevance to RISE

Surfaced by the 2026-08-29 literature sweep as a high-priority candidate for the Architecture as Epistemology (ISR) paper (angle: MAS topology / structure vs. aggregation rule; correlated errors / homogeneity across LLM agents; MAS failure and cost analyses). Verified against: Opened https://arxiv.org/abs/2601.17311 (arXiv abstract page, v2 12 Feb 2026)

Critique / open questions

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Key quotes

Multi-agent systems can improve reliability, yet under a fixed inference budget they often help, saturate, or even collapse. (abstract)

We develop a minimal and calibratable theory that predicts these regimes from three binding constraints of modern agent stacks: finite context windows, lossy inter-agent communication, and shared failures among similar agents. (abstract)