AgentCue: Statistical Summaries for Guiding Decentralized Multi-Agent Self-Organization

Guojun Zhu; Xinyou Chen; Kejian Zhang; Sanguo Zhang; Doudou Zhou

cs.MAOct 12, 2026

AgentCue: Statistical Summaries for Guiding Decentralized Multi-Agent Self-Organization

Authors: Guojun Zhu, Xinyou Chen, Kejian Zhang, Sanguo Zhang, Doudou Zhou

Organizations: School of Mathematical Sciences, University of Chinese Academy of Sciences · Department of Statistics and Data Science, National University of Singapore · Department of Statistics and Data Science, Tsinghua University

Abstract

Multi-agent systems (MAS) combine multiple agents to solve complex tasks, and recent MAS scale to more than a thousand agents. At this scale, decentralized MAS remove the central orchestrator that assigns sub-tasks, and the agents, which we call workers, self-organize through their own choices of sub-tasks and collaborators on a shared board. As workers keep adding participation and collaboration records, however, the information explodes: workers spend more and more effort on reading the records of other workers, and self-organization loses efficiency. In the statistical view, we represent the execution history of an MAS by two continually updated networks, a collaboration network among workers and a participation network between workers and task types. We then propose AgentCue, a method built on a new latent space model that places workers and task types in a shared latent space. Each time the networks are updated, the estimated parameters of the latent space model form a compact and interpretable statistical summary, and workers use the statistical summary to choose sub-tasks and collaborators without repeated searches of the shared board. We establish the identifiability of the latent space model and non-asymptotic error bounds for the estimates under network increments, and we show that a fixed number of gradient updates after each network update suffices for the same error rate. Experiments on LongBench v2 Multi-Doc QA show that AgentCue achieves competitive effectiveness, efficiency, and interpretability.

Figures & tables

Figure 1: Self-organization in a decentralized MAS. Workers read from and publish to the shared board (dashed lines) and collaborate with one another (solid lines), and groups of collaborators form and change over time through local choices. With few workers (upper panel), the shared board holds few records. With many workers (middle panel), records accumulate quickly, and each local choice (lower panel), which sub-task to claim and whom to collaborate with, requires a search through many records.

Figure 2: Overview of AgentCue. Upper and middle bands: once per checkpoint, the MAS publishes the statistical summary, and worker

i

reads the statistical summary once. Lower band: the local comparison, enlarged. Bars are log fitted means split as in ( 4 ); the struck-through term cancels, and hatched segments are negative affinity terms. The latent-space map shows the projections onto the line of sight of worker

i

. Small squares scale with the fitted participation mean of each candidate in the task type of the inputs that the sub-task needs; the dashed box and the rings mark the shortlist; the magnifier marks a work-record search. Superscripts

(t)

are omitted.

Figure 3: Simulation of ( 8 ) in the setting of Section 3.4 ; each line is one run. Dotted lines: fixed point without the statistical summary (

\omega=0

). Dashed lines: interior fixed point, stable for

\omega=0.5

and unstable for

\omega=2

; for

\omega=1

, no interior fixed point exists.

Measure	AgentCue	History only
Correct answers	$76.0\pm 1.0$	$72.0\pm 1.0$
Accuracy (%)	$60.8\pm 0.8$	$57.6\pm 0.8$

Table 1: Final results over three paired replicates (mean

\pm

sample standard deviation), with 256 effective sessions per trajectory and 125 questions.

Figure 4: Effectiveness, efficiency, and interpretability of AgentCue. (a) Final accuracy by domain; parentheses give question counts. (b) Accuracy over the common effective-session budget, using all 125 questions. Points and lines show means across three paired replicates; error bars and shading show one sample standard deviation. (c) One recorded choice in R1 links the fitted participation means of W15, the choice of inference , the use of version 1 of the published result of W26, and the correct designated answer, where W

i

denotes worker

i

Figure 5: Worker sessions and statistical summaries for the AgentCue trajectory in R1. Upper panels show eight statistical summaries jointly aligned to the statistical summary at the final checkpoint by orthogonal Procrustes, with consecutive checkpoints paired by column. Linear axes show worker latent positions; insets enlarge the four task-type latent positions. The color scale links panels and arrows to the checkpoints

t_{1},\dots,t_{8}

. Lower bars show all 256 sessions of 32 workers, mapped from timestamps to the number of completed effective sessions. Equal-height stripes indicate task types of work published in a session; gray denotes no publication.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Task type	Required independently reusable result
Extract	Source-located facts, values, conditions, or a documented search result.
Compare	Named objects, shared dimensions, and evidence-supported similarities, differences, or conflicts.
Inference	Inputs or premises, reasoning, conclusion, and applicable conditions. Answer synthesis also gives an option and explains its use of published results of other workers.
Review	The exact version of another worker’s published result, checks, findings, evidence, and a PASS or FAIL verdict.

Appendix

Table \thechapter .B.1: Task types defined by independently reusable results.

Replicate	AgentCue		History only		Difference	PASS	Correct + PASS
	Correct	Accuracy (%)	Correct	Accuracy (%)
R1	76	60.8	71	56.8	4.0	36/36	22/20
R2	77	61.6	72	57.6	4.0	33/41	18/23
R3	75	60.0	73	58.4	1.6	92/47	55/24

Appendix

Table \thechapter .B.2: Final results by replicate. Difference is in percentage points; PASS columns count designated answers with a PASS verdict (AgentCue/History only).

Measure	AgentCue	History only
Published works	$359.7\pm 26.8$	$348.0\pm 2.6$
Extract	$160.7\pm 3.2$	$162.3\pm 11.2$
Compare	$140.0\pm 18.4$	$153.3\pm 6.4$
Inference	$246.0\pm 56.0$	$250.7\pm 51.4$
Review	$71.3\pm 31.0$	$57.0\pm 5.3$
Collaboration count	$284.7\pm 46.9$	$248.7\pm 3.2$

Appendix

Table \thechapter .B.3: Participation and collaboration (mean

\pm

sample standard deviation). Task-type counts are column sums of

\bm{B}^{(T)}

; collaboration is

\sum_{i<\ell}A_{i\ell}^{(T)}

Replicate	Method	Works	E	C	I	R	Workers E/C/I/R	Collaboration
R1	AgentCue	350	163	119	290	56	32/32/32/28	274
R1	History only	349	175	156	288	51	32/32/32/25	250
R2	AgentCue	339	162	153	183	51	32/32/32/27	244
R2	History only	345	154	146	192	59	32/32/32/29	251
R3	AgentCue	390	157	148	265	107	32/31/32/31	336
R3	History only	350	158	158	272	61	32/32/32/30	245

Appendix

Table \thechapter .B.4: Participation by replicate. E/C/I/R denote extract/compare/inference/review; the worker column counts contributors to each task type.

Method	Estimates	Iterations	Gradient norm	$\bm{Z}$	$\bm{W}$	$\bm{\beta}$
AgentCue	24	111–469	$2.33\times 10^{-6}$ – $9.95\times 10^{-6}$	$1.33\times 10^{-15}$	$1.11\times 10^{-16}$	$6.22\times 10^{-15}$

Appendix

Table \thechapter .B.5 : Estimation diagnostics over eight checkpoints. Centering columns give maximum absolute sums of latent-position columns or node effects.

Measure	AgentCue	History only
Input tokens (millions)	$415.97\pm 2.04$	$390.06\pm 2.93$
Cached input (millions)	$392.85\pm 1.91$	$367.76\pm 2.92$
Output tokens (millions)	$2.05\pm 0.04$	$1.94\pm 0.04$
Reasoning output (millions)	$0.60\pm 0.01$	$0.56\pm 0.02$
Post-warm-up worker span (minutes)	$29.81\pm 0.70$	$24.33\pm 3.35$
Additional estimation time (seconds)	$0.314\pm 0.021$	–

Appendix

Table \thechapter .B.6: Computational resources (mean

\pm

sample standard deviation). Tokens include warm-up; worker spans exclude it. Additional estimation time covers checkpoints 64–256; History only involves no estimation.

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