Unclaimed Errors: When Every Agent Is Right but the Team Is Wrong
This post is a detailed Chinese-forum commentary (translated and summarized) on the paper *Global Coherence: When Every Agent Is Right and the Team Is Still Wrong — A Local-to-Global Semantic Foundation for Multi-Agent Collaboration* by Xin Heng (sole author, Tote AI), arXiv:2610.02036 [cs.AI]. It is the third installment in the forum's "Rebuilding Trust" series, following pieces on cryptographic verification and external observation.
Key points
- The opening anecdote: A three-agent team (Planner / Executor / Verifier) with a shared budget of twenty command runs exhausts it mid-task. Every individual spending decision was locally justified—extra tests because the environment looked suspect, extra verification because output formats mismatched, extra planning because requirements changed—yet collectively they spent nearly triple the budget. The paper names this the global coherence problem: local validity does not imply global coherence.
- Two failure modes, mirror images of each other:
- Observational aliasing: two worlds are indistinguishable to all participants but require different actions. An impossibility theorem (Thm 2.1) states that with k indistinguishable worlds and pairwise-disjoint valid actions, worst-case optimal success is exactly 1/k. No reasoning, chain-of-thought, role decomposition, voting, or stronger model can recover the missing distinction; a b-bit hint raises success to at most 1/⌈k/2^b⌉.
- Incoherent fragments: all information is present and local checks pass, but pieces fail to compose. A beam example: three segments state 1 meter, 1000 mm, and 39.37 inches; every pairwise conversion checks out, but going around the loop reveals a rounding-convention mismatch. The mathematics of groupoids of invertible transformations and gluing conditions shows pairwise consistency ≠ global consistency.
- The probe experiment: when a decisive event is visible, frontier models answer 40/40; hidden, they score 12–17 out of 40 (random baseline ≈ 13.3), with planners, verifiers, majority voting, and tool use all indistinguishable from chance. Restoring the one missing fact returns performance to 40/40. The model's intelligence was never the bottleneck—its visibility was.
- Five walls to full information sharing: computing the minimal sufficient information set is NP-hard (Thm 2.5); cycles let inconsistency hide beyond pairwise views; detection is easy but repair is max-cut-hard; shared constraints need coordinated enforcement; change and time introduce staleness and atomicity issues.
- The prescription: *models propose; the harness owns shared state and governs commits.* The harness is a runtime layer—like a notary or customs office—between models and the shared world. A "manager agent" cannot substitute, because it is itself a participant subject to the same impossibility theorem.
- Budget experiment (three acts): baseline—5/5 runs over budget; adding real-time visible counters—still 4/5 over budget (transparency is not ownership); commit-time budget gates—0/5 overruns with no loss in task progress. Per-role escrowed quotas also achieve zero overruns without any central gate. Moral: *information display is not the answer; ownership is.*
- Silent revocation experiment: in a telecom customer-service scenario where committed changes are secretly reverted, ordinary strategies score 0.07—essentially blind. The coherence harness, keeping a ledger of budget balance plus each agent's last-read version numbers, scores 1.00, redoing the reverted change in all 15 rounds. Where conventional tools already own state (dependency engines, coupled solvers), the harness only ties—theory matches experiment exactly.
- Ontology alignment evidence: across 45 public alignment networks (2018–2024), 23 contain ontological identity conflicts invisible to pairwise checks;拆-visibility agents reproduced 9 conflicts in 40 merges, network-level checks caught all 9, pairwise checks fired 0 times.
- The broader thesis: this is not an AI problem but an ancient coordination problem. Distributed databases solved it with atomic commits; finance with double-entry bookkeeping; contracts with notarization (drafters and sealers must differ). The paper's contribution is a unifying mathematical language (topology, categories, transformations, gluing, history) and a proof of why certain institutional patches are uniquely shaped—the impossibility theorem applies to all distributed decision-makers, silicon or human.
- Xin Heng. *Global Coherence: When Every Agent Is Right and the Team Is Still Wrong — A Local-to-Global Semantic Foundation for Multi-Agent Collaboration.* arXiv:2610.02036 [cs.AI], 2026-10-01. Code and run records for nine studies promised for release.
Original reference
Closing thought from the forum author
The overspent team's problem was simple: the twenty-run budget belonged to "the team," and "the team" is no one. Give the gate to a hand that belongs to no member, and errors gain an owner and budgets gain a ledger. Collective correctness cannot rest on individual correctness alone—it needs a claimant for the unclaimed. Let the smart do the smart things, and the bookkeeping go to the bookkeeping.