When Does Communication Help? Beyond Spectral Descriptions of Collective Intelligence

Xuening Wu

cs.MASep 20, 2026

When Does Communication Help? Beyond Spectral Descriptions of Collective Intelligence

Authors: Xuening Wu

Organizations: AI Engineering, Pfizer, Shanghai, 200041

Abstract

Communication can bring agents into agreement while making their decisions worse. We identify two limits of aggregate descriptions of communication gain in distributed inference. First, stable linear systems with fixed evidence, network and readout can have interaction and finite-time state operators with identical eigenvalue and singular-value spectra, yet produce gains of opposite sign. Changing only message orientation raises accuracy from 72.6% to 91.2% or lowers it to 65.9%. A standard task-projected local-response approximation retains the directional information missing from spectral summaries. Using labeled calibration data separate from the test set, it predicts multi-round gains in small trained nonlinear agents with a root-mean-square error of 0.45 percentage points on two synthetic tasks; tests with natural edge changes and handwritten digits extend the evaluation. Second, under community-shared bias, higher mean individual accuracy can coexist with harm to unaffected communities or lower global-vote accuracy. At fixed communication rounds, calibration constraints reduce observed community harm while retaining much of the mean benefit, but do not guarantee protection. Full direct calibration performs similarly. The results connect spectral insufficiency, task-aware prediction and the distribution of communication benefits, while leaving broad transfer and practical superiority open.

Figures & tables

Figure 1: Scalar insufficiency and preliminary task transfer. Left: primary linear gains across all predeclared orientations; points are Monte Carlo estimates and the line is the exact Gaussian calculation. The dashed line is zero gain. Graph, evidence, readout and full operator spectra are fixed. Right: preliminary three-coordinate prediction across two task-transfer directions. Grouped-condition prediction is shown separately because it is a different generalization test.

Predictor	$R^{2}$	RMSE (pp)	Sign BA (%)
Task-aware response	0.9988	0.454	99.95
Zero-message approximation	0.9981	0.568	99.95
One-step gain	0.8817	4.499	99.61
Orthogonal readout	-0.6486	16.798	66.31
Full direct calibration	0.9989	0.426	99.95
$\Lambda,\mu_{T},\mathcal{I}_{\mathrm{vote}}$	-0.1044	13.749	58.74

Table 1: Primary response study. RMSE is in percentage points; BA is sign balanced accuracy in percent. Fitted controls use simultaneous task/activation holdout. Unfitted predictors use the target-condition calibration set without fitting a response-to-gain surface. The predictors have different information access.

Figure 2: Calibration response predictions versus independent-test gains, separately by task and activation. Each panel contains 1,080 primary conditions. Color denotes coupling and the diagonal denotes perfect prediction. Dense, related parameter sweeps should not be interpreted as independent task replications.

Figure 3: Community and readout effects in all 576 biased comparisons with

T>1

. Each point compares a nonzero inter-community weight with within-only communication at the same

T

. Left: positive mean individual effects can coexist with negative effects on unaffected communities. Right: positive mean individual effects need not improve global-majority accuracy. Related conditions share models and evidence; points are not independent replications.

Task	Selector	Benefit (pp)	Strict (%)	Material (%)
Digits	Fixed 0.5	1.963	46.39	28.06
Digits	Response, unconstrained	2.218	33.33	20.56
Digits	Response, point constraint	1.929	17.78	5.28
Digits	Direct, point constraint	1.925	17.22	4.44
Digits	Response, guarded	0.128	0.00	0.00
XOR	Fixed 0.5	7.317	46.11	37.78

Table 2: Fixed-round community selection at

\varepsilon=1

percentage point, averaged over 360 dependent blocks per task. Benefit is mean individual accuracy change relative to within-only communication, in percentage points (pp). Strict and material violation rates are percentages of blocks with any community losing more than 1 or 2 points, respectively. Direct calibration uses the same labels and candidate set. The guarded response’s zero observed violations accompany frequent within-only fallback, not certified protection.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Selector	Gain (pp)	Regret (pp)	Harm (%)	Rounds
No communication	0.000	14.670	0.0	0.00
Fixed setting	4.779	9.891	50.0	3.00
One-step selection	10.646	4.023	0.0	0.94
Response selection	14.631	0.039	0.0	5.47
Direct calibration	14.636	0.033	0.0	5.49
Test oracle	14.670	0.000	0.0	5.62

Appendix

Table 3: Communication selection over 144 condition blocks. Gain and regret are in percentage points (pp); regret is the difference between the test-oracle gain and the selected gain in the same block. Harm is the percentage of blocks with test gain below

-1

percentage point. The test oracle selects the best candidate using test labels and serves only as a diagnostic upper reference. Different mean round counts preclude claims of equal-compute superiority.

Task	Policy	Normal (%)	Fault (%)	Recovery (%)	Lag
XOR	Fixed 0.5	93.85	82.74	94.30	3.00
XOR	Fixed 0.125	92.69	79.26	92.98	3.71
XOR	Intermittent	92.55	79.27	92.92	3.54
XOR	Random gate	92.51	78.98	92.91	3.12
XOR	Local response	93.43	84.46	94.31	3.21
XOR	Local exact	93.43	84.46	94.31	3.25

Appendix

Table 4: Streaming coherent-fault results, averaged over 24 dependent blocks per task. Stage accuracies are percentages; lag is measured in steps relative to each policy’s paired clean stream. Fixed 0.5 denotes the hierarchical graph with that inter-community weight, not an all-to-all graph. All blocks reach the stated mean-accuracy criterion within the recovery window.

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Multi-agent LLM systems can improve reasoning by pooling diverse perspectives, but their effectiveness depends on coordinating communication, particularly in hidden-profile settings where each agent holds only part of the evidence required for a correct decision. Existing protocols, including fixed schedules, round-robin exchange, and unstructured debate, provide no guarantee that a conversational action is appropriate. We propose Consilience, an inference-time orchestration framework that both steers and certifies multi-agent communication under distributed private information. At each turn, Consilience summarizes the discussion using a compact state capturing uncertainty, disagreement, evidence gain, redundancy, and premature consensus, then selects both a communication intervention (challenge, clarify, seek evidence, or route) and an appropriate speaker. Its central contribution is a round-wise conformal calibration procedure that provides a distribution-free, finite-sample guarantee: at each discussion round, conditional on reaching that round, the one-step regret of a controller's proposed action is bounded by a calibrated threshold with marginal probability at least 1 - alpha; an acceptance mechanism enforces the same guarantee for the executed action by replacing inadmissible proposals. On HiddenBench-style hidden-profile tasks spanning 12 open and closed weight language models, Consilience improves decision accuracy and communication efficiency over fixed and unstructured discussion protocols, sometimes surpassing a full-information baseline where every agent observes all evidence. These results demonstrate that certified adaptive communication control can be more valuable than increasing information availability, providing a practical mechanism for reliable multi-agent LLM coordination.

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