Emergent Coordination in Multi-Agent Language Models
Authors: Christoph Riedl
Venue: ICLR 2026 Poster (2026)
Keywords: multi-agent systems
LLMs
information decomposition
emergence
collective intelligence
Primary area: generative models
TL;DR: Information-theoretic framework reveals how prompt design steers multi-agent LLMs from simple aggregates to emergent collectives with higher-order structure

Abstract: When are multi-agent LLM systems merely a collection of individual agents versus an integrated collective with higher-order structure? We introduce an information-theoretic framework to test---in a purely data-driven way---whether multi-agent systems show signs of higher-order structure. This information decomposition lets us measure whether dynamical emergence is present in multi-agent LLM systems, localize it, and distinguish spurious temporal coupling from performance-relevant cross-agent synergy. We implement a practical criterion and an emergence capacity criterion operationalized as partial information decomposition of time-delayed mutual information (TDMI). We apply our framework to experiments using a simple guessing game without direct agent communication and minimal group-level feedback with three randomized interventions. Groups in the control condition exhibit strong temporal synergy but little coordinated alignment across agents. Assigning a persona to each agent introduces stable identity-linked differentiation. Combining personas with an instruction to ``think about what other agents might do'' shows identity-linked differentiation and goal-directed complementarity across agents. Taken together, our framework establishes that multi-agent LLM systems can be steered with prompt design from mere aggregates to higher-order collectives. Our results are robust across emergence measures and entropy estimators, and not explained by coordination-free baselines or temporal dynamics alone. Without attributing human-like cognition to the agents, the patterns of interaction we observe mirror well-established principles of collective intelligence in human groups: effective performance requires both alignment on shared objectives and complementary contributions across members.

Published as a conference paper at ICLR 2026
EMERGENT COORDINATION IN MULTI-AGENT LAN- GUAGE MODELS
Christoph Riedl
D' Amooe--MKim School of Business,
Khoury College of Computer Sciences, and Network Science Institute
Northeastern University
Boston, MA 02115, USA
C. rrieedlenottheesteem..dd
ABSTRACT
When are multi-agent LLM systems merely a collection of individual agents versus an integrated collective with higher-order structure? We introduce an information-thherrtiic framework to test-in a purely data-driven way-whether multi-agent systems show signs of higher-order structure. This information de- composition lets us measure whether dynamical emergence is present in multi- agent I.L. systems, localize and distinguish spurious temporal coupling from performance-relevant cross-agent synergy. We implement practical criterion and an emergence capacity criterion operationalized as partial information decomposi- tion of time-delayed mutual information (TDMI). We apply our framework to ex- periments using a simple guessing game without direct agent communication and minimal group-leve feedback with three randomized interventions. Groups in the control condition exhibit strong temporal synergy but little coordinated alignment across agents. Assigning persona to each agent introduces stable identity-linke differentiation. Combining personas with an instruction to "think about what other agents might do" shows identity-linked differentiation and goal-directed comple- mentarity across agents. Taken together, our framework establishes that multi- agent LLM systems can be steered with prompt design from mere aggregates higher-order collectives. Our results are robust across emergence measures and entropy estimators, and not explained by coordination-fre baselines or tempo- ral dynamics alone. Without attributing human-like cognition to the agents, the patterns interaction we observe mirror well-established principles of collective intelligence in human groups: effective performance requires both alignment on shared objectives and complementary contributions across members.
INTRODUCTION
Recent advances in generative Al (specifically LLMs) have led to tremendous advances in multi- agent systems (Qu et al., 2024 Hong et al.) 2024 Qian et al. 2023 et al. 2024a Subramaniam
et al. 2025). Multi-agent systems often show impressive performance increases over single-agent solutions (Wu et al. 2023 Chen et al. 2023 Li ct al. 2024b Tao et al. 2024p. key argument behind such performance gains are claims to greater-than thauteer-hha-thh--iiee wwwn-ntthhssu------ee oo-u-oo-its of-its-parts' effects from differ- entiated agents (Chen et al. 2023 1) Connecting multiple differentiated agents has the potential benefit to leverage unique contributions that would not be available if the task was assigned
sin-
gle agent (Fazelpour & De-Arteaga 2022 Tollefsen et al. 2013 Luppi et al. 2024 Lix et al. 2022) Conceptually, any group gains depend on synergy and emergence (Theiner 2018 Riedl al. 2021 Despite impressive performance of many multi-agent systems we do not yet have principled understanding when and how such synergy arises, what role agent dif- ferentiation plays, and how to steer it systematically. This all points to a crucial need for deeper understanding of collective intelligence in multi-agent systems, specifically whether multi-agent
Page 2008 Hayek 1945) [
This for both human groups and multi-agent systems.

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LLMs exhibit any synergy complementarity at all the necessary prerequisite for any absolute team-over-solo gains.
Determining whether multi-agent systems function as genuine collectives-ratiee than merely ag- gregating
a principled measure of synergy. We follow a purely data-driven ap- proach to assess whether these systems exhibit higher-order synergy, characterized by structural coupling and joint information about future states and task outcomes, as evidence of emergent col- lective behavior. Intuitively, synergy refers to information about target that a collection of variables provide only jointly but not individually (Rosas et al. 2020 Humphreys) 1997 We develop a prin- cipled framework (Figure Tha building on new insights in information theory (Rosas et 2020 Mediano et al.] 2022b). Our goal is to develop methods to measure emergent role specialization, determine whether multi-agent systems show such signs of emergent synergy, explore whether syn- ergy enables increased performance, and explore whether emergent behavior can be systematically steered with prompting
We apply our framework to study multi-agent systems of GPT-4.1, LLAMA-3. 1-B.....BBBBB... LLAMA-3.1 1- 70B, GEMINI 2.0 FLASHI, and QWEN3 agents solving a simple group guessing task (Figure (T)) with three treatment interventions: control condition, condition that assigns a persona to each agent, and one that uses personas with an instruction to "think about what other agents might do" (a theory of mind (ToM) prompt). The paper is organized into addressing three concrete research questions:
RQI: Do multi-agent LLM systems possess the capacity for emergence?
RQ2: What functional advantages-Sude as synergistic coordination and higher performance- arise when multi-agent systems exhibit emergence?
RQ3: Can we design prompts, roles, and reasoning structures that steer the internal coordination regimes of multi-agent to encourage outcome-relevant goal-directed synergy?
Our findings provide evidence for multi-agent LLM system capacity for emergence and that it un- derpins performance. Through a variety of complementary analyses and robustness tests, we show that coordination style across interventions is very different. While emergence is present in all, only the ToM-promp condition leads to groups with identity-linked differentiation and goal-directed complementarity across agents: they operate as a dynamically stable, integrated, goal-directed unit. This is consistent with research on human groups showing that performance gains are not automatic (e.g.. Stasser Titus| 1985) and that complementarity needs to be balanced with integration and goal alignment (Theiner 2018 DeChurch & Mesmer-
2010: Riedl et al. 2021.
This paper helps us understand when and how multi-agent systems exhibit higher-order properties, their internal coordination structure, and how to control them. This can inform multi-agent system design by showing how to combine agents effectively. We make four contributions:
Novel framework to quantify emergent properties in multi-agent systems based on infor- mation decomposition including conditional/residul variants and outcome-relevant partial information decomposition.
Principled diagnostic approaches to localize where synergy resides and distinguish from alternative explanations (such as heterogeneous learning rates). Specifically, de- velop two surrogate null distribution tests (row-shuffle to probe identity-locked structure; column-shuffle for dynamic alignment). This design lets us tease apart "good" synergy aligned with task goals from spurious or misaligned synergy.
Demonstrate how to steer emergence with specific prompts. Prompt-level manipula- tions causally change higher-order dependencies and reliably induces distinct coordination regimes, shifting collectives from spurious and misdirected synergy to stable and goal- aligned complementarity driven by differentiated identities.
Internal coordination is measurable and controllable with interventions. Groups differ in variance, stability, and adaptabilit relevant to reliability and deployment.
Thhe key claim explored in this paper conditional, cross-agent synergy -.c.,, synergistic information and coordinated differentiation across agents given the multi-agent constraint (not absolute outperformance over a solo agent). We do not attempt to establish team-over-solo superiority on this task. See GitHub for replication code htttts:///giiii
com/rice/eeeeooooo htt.://eedl/////a///// c/AI-GSS
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Information Decompositin Framework
Experiment Setup: Group Guessing Task
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a) Information decomposition provides framework to explain tension in multi-agent sys- tems. Agents are either undifferentiated differentiated, provide independent or complementary information, which is either well aligned or incidental (adapted from Luppi et al. 2024). b) Experi- ment setup of the group binary search task. e) Preliminary experiments testing different group sizes and temperature settings. Surface values were smoothed using a local 3 x weighted averaging filter, giving higher weight to each cell's 's original value to reduce noise while preserving local structure.
Figure I:
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METHOD
Group Task. We study a group guessing game (developed by Goldstone et al. (024) who called "group binary search") without communication: agents propose integers whose sum needs to match a randomly generated hidden target number. Agents are unaware of each others' guesses and the size of their group, and receive only group-level feedback "too high" or "too low." The task is challenging because identical strategies induce oscillation and only complementary strategies yield success. This setting naturally pits redundancy (alignment) against synergy (useful diversity), and admits clear nulls via row-wise (break identities) and column walsm (break alignment) surrogates. The binary search setting is minimalist testhed to isolate emergence of cross-agent complementar- ity and dynamic coordination, not to establish team-over-solo superiority. The implementation of a textbook-like XOR dynamic allows to study the benefits of emergence capacity conditional multi-agent setup (and not to establish team-over-solo superiority). Research on humans has shown that groups can reliably solve this task through the emergence of specialized, complementary roles Goolssooe et al. 2024).
Analytical F Framework. How would we know if multi-agent system shows emergent properties that could suggest that the sum is more than its parts? We develop a principled test based on a re- cent formal theory of dynamic emergence based on information decomposition (Rosas et al. 2020 Mediano et al.) 20225) [Bdduu & Humphreys) 2008). Our framework connects emergence with in- states of the whole-with information that
formation about a system's 's temporal evolution- cannot be traced to the current state of its parts. This framework is based on partial information decomposition (PID; Williams & Beer, 2010) and time-delayed mutual information (TDMI: Luppi et al.) 2022). is data-driven, quantifiable, and amenable to empirical testing with falsifiable con- jectures against specific null hypotheses. Combining this with permutation tests, focused either on breaking connections between agents or connections across time allow us not only to quantity emergent properties but also to localize them in the system. This crucial for multi-agent systems because care about distinguishing synergy among specialized, differentiated agents from mere dynamic alignment.
We implement three tests. The first, termed emergence capacity, captures ability of the multi-agent system to host any synergy. It measures the predictive synergy from two agents' current states to their joint future state, quantified using mutual information I(::)). For each pair of agents (i.j) and time I, let the sources be Xs, and Xj,. and define the bivariate target as the joint future state 1+ f, Tij.t = (Xi,te, Xzt+e), where l is the integration timescale (Mediano et 2022a). From the joint contingency table over (X,,, X,,,, Teg.+e) we compute a two-source PID of the predictive information
T((Xa,, N5,1; Tig.te) UT, + UI + Redij Syn.
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and take Syny the pairwise dynamical synergy. A positive score Syn, 0 indicates that the macro captures predictive information about the joint future not recoverable from any single com- ponent. We compute this for all unordered pairs (i,j) and take the median group-level synergy capacity. This test is limited to detect synergy of order A = 2 but has the advantage that it does not rely on the definition of suitable whole-system macro signal.
The second test, termed the practical criterion, concerns predicting a macro signal V of the system. asks whether the macro contains predictive information beyond any individual part. Given mi- crostate X₁ = (X macro V = f(X,). We align samples (t, L + E) and compute the score as
Smacro (e) = I(V;; Vi+e)
I(Xa,1 Vi+e).
A positive value indicates that the macro's self- selffprediictability exceeds what the sum of its parts can explain, thus indicating emergent dynamical synergy. We refer to "dynamical" synergy because targets are time-lagged and do not claim causal directionality beyond the temporal ordering (see Rosas et al. 2020 for a nuanced discussion). It is a coarse, order-agnostic screen sensitive multi- part synergy (i.e., synergy of any order 2 2). However, it is also penalized by redundancy across parts which can make the score negative even when higher-order synergy exists.
To explore system dynamics, we implement coalition test, an extension of the practical criterion to triplets. Let Ig be the mutual information between a triplet's current state and the future macro Vi+e). Le., how much the three agents jointly predict the macro' future serves as a measure of the system's High Ia indicates that agents' behaviors are tightly coupled and contain rich information about the emerging collective outcome, a pattern frequently associated with collective intelligence (De Vin- cenzo et al. 2017 Wicks al. 2007 Mora & Bialek] 2011 Barnett et al. 2013). Low 13 signals weak alignment, resulting in uncoordinated or chaotic collective behavior. Then
signal: I3 I I((X,,,. 1,,,
pntermatioo-poocessiie capacity (Mediano et al. 2022a).
G3 = 13 max([221.2)> 12[1.33, 12(2.3))
(3)
measures the additional predictive information the full triplet provides over the most predictive pair
Tn (a form of whole-minus-part metric; [Barrett & Seth, 2011 Mediano et al. 2025). If find
G3 > 0 this means no pair is sufficient to capture information that the triplet contains about the macro signal at t + L. We again compute 13 and G3 for all possible triplets and take the median as group measure. This measure complements the other two by offering a coalition-leve test geared towards functional relevance: it helps answers whether the joint information provided by coalitions of agents is actually about the goal. It allows us to localize where macro predictability depends on heyond-pair structure and to rule out "explained by best pair" explanations.
Estimation Details. As microstates X, (Xi,...... Xn,r) we use each agent i's guess time and transform it into the deviation from equal-share contribution to hit the target number: devs,, = raw,, target/N. NN. As maero signal Vi we take the group error Σ raws, target (equivalently E devs,, This minimal transformation removes the trivial level differences imposed by the target and aligns agents on a comparable scale, so that remaining variation reflects coordination (who compensates for whom). Over-/undder-oontiibttooo are interpretable as the sign of deviations.
We use the Williams-Bes two-source PID (Williams & Beer 2010) with the Imin (minimum spe- eific information) redundancy, estimated via plug-in probabilities. For robustness, we also use Jeffreys-smoothed probabilities. and alternatively MMI redundancy (minimum of whole mutual informations: Mediano et al. (2055) with mutual information estimated with Miller-Madow bias correction (Miller) 1955). All variables are discretized into K 2 bins using quantile binning. Data are encoded as factors with fixed levels 1, (and for the joint target as the Cartesian product levels) to avoid dropping empty categories. We report & = 1 which is suitable to detect next-step oscillat- ing behavior (see task description). Because trials end at success, episode lengths vary (see plot of
We also performed additional sensitivity analyses using alternative specification of the macro signal as first principle component of individual guesses used in Rosas et al. (0220)
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rounds to success in Appendix). We report additional sensitivity tests using "early synergy" trun- cated to a fixed horizon of H E {10, 15} rounds to ensure comparability (results in Appendix AA. and A.12 main analyses use full trajectories).
Falsification Tests. We perform two different falsification tests of each of the three criteria intro- duced above. Our primary test assesses significance by comparing the observed value against a null distribution computed on permuted (shuffled) instances of the devs data. We use two surrogates: row-wise shuffles (to break identities) and column-wise time-shift surrogates (preserve individual dynamics while disrupting cross-agent alignment). Full details in Appendix. We combine p-values across independently simulated groups (independent seeds, independently sampled targets, and no shared state) using Fisher's 's method. As a robustness test, we also compute bias-corrected (BC) estimates using time-demeaned data against block-shuffled null with l = 2 to mitigate autocorre- lation confounds. We use both (a) linear regression demeaning and (b) a functional baseline without between-ages aggent synergy (see Appendix for details). These tests provide additional robustness the é = 2 block size in the shuffled null and auto-correlation concerns.
Entropy Estimation. Small-sample entropy estimation is often challenging because the true dis- tribution is only partially observed and many outcome categories receive few or even zero counts ("empty bins"). Such finite-sample estimation of information measures is biased upward and can yield spurious positive findings. Bias grows with more bins, dimensionality (e.g.. using triplets instead of pairs), and small N (few timesteps). The empirical plug-in in estimator replace true proba- bilities with sample frequencies and unseen (or under-sampled) outcomes often are assigned zero or very low probabilities (Hausser & Strimmer 2009). To account for this issue, we follow best prac- tices and take several steps. First, we compute the emergence capacity and the coalition tests as order k 2 instead of the entire system of n agents. Second, we apply quantile binning (with two bins) to reduce the dimensionality of our data (sensitivity analyses with three bins reported in A.8). Third, we use bias-corrected entropy estimator with Jeffreys' prior, which smooths estimates and avoids empty bins by adding a systematic inflation and cures zero-count pathologies. Finally, as a robustness check, we also report results using the Miller-Madow bias-corrected estimator (Miller 1955), and the MMI redundancy measure (MMI typically overestimates redundancy, making synergy estimates more conservative; Mediano et al. 2025).
eseudo-counts in the Dirichlet estimator (Jeffreys 1946). This reduces
Test of Agent Differentiation. Our third pillar evaluates agent differentiation via hierarchical (mixed) modeling (Gelman & Hill, 2007), asking whether agents adopt consistent, person- -srscfic patterns. We estimate a sequence of three models for each multi-agent experiment:
mg:
Yt 8o Mrime[s] + fi
mi:
I 3o + Mgime(s] + Mugem[i] + E
m2: I = 3o + [time[4] + Magont()). + "aggen(() + 64
where yi devs,,t, Mume[s]] are random intercepts for (continuous) time, Mugen[[s] are agent-level random intercepts, and Uagem[(].time[] are agent-level random slopes varying by time. The random intercepts capturing differentiation in agents based their level differences and varying slopes capture heterogeneous learning rates. Using equal-share deviations removes target-level drift and makes agents directly comparable round-by-round. The random intercepts for time captures round- to-round shifts due to group-wide feedback and oscillation. Hence, agent effects reflect relative, identity- -inked behavior rather than shared dynamics. The partial pooling of hierarchical models regularizes per-agent estimates, improving stability in short time series. We then use likelihood ratio tests to compare the nested hierarchical models. Comparing mg - m. asks whether agents differ in their group contribution (some agents guess higher/lower than others), while m. - m2 tests whether agents vary in how much their contribution changes across rounds (learning rates). A significant p-values (e.g., below conventional 0.05 levels) indicates that the more complex model explains the data significantly better, suggesting the added random effects (e.g., agent-level differ- ences or varying slopes) meaningful in this group. This offers an interpretable, -on-informttion theoretic test of monotonic learning-rate heterogeneity. Furthermore, this test does not require dis- cretization, giving complementary failure mode to the information-thenn -heoreeticcc analyses.
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Together, these four tests of our framework allow to (a) detect higher-order structure in multi- agent systems, (b) assess whether is driven by redundancy or synergy, (c) localize whether it is identity-locked vs. dynamic alignment, and (d) show whether the higher-order structure is func- tionally useful for the task. No single measure does all four. Combined with the prompt-level interventions, the framework allow to test whether interventions (Plain, Persona, ToM) causally increases dynamic synergy, how it affects identity-locked diffcrentiation, and goal alignment (i.e., increase in 1z).
3 EXPERIMENTS
3.1 PRELIMINARY EXPERIMENTS: GROUP SIZE AND TEMPERATURE
To see if LLMs can solve this task and how sensitive results are to different group sizes and tem- perature settings ran first set of preliminary experiments (see Appendix for prompt). We used OpenAl's gpt-4.
-4 1- 2025-00 01-5504-144 4-14.. 4. We varied group size from 3 to 15, and temperature from 50 group experiments (13 group sizes x 11 tem- perature settings x 50 groups = 7,150 experiments; Figure (P)) Multi-agent systems of GPT 4.1 agents can solve the task reliably but encounter substantial challenges. We fit a logistic regres- sion, predicting success from group size and temperature. We find the task is significantly easier for smaller groups: each additional group member decreased the odds by roughly 8% (OR = 0.92, < 10-1"), consistent with results as for human groups (Goldstone et al. 2024). Each unit increase temperature increased the odds of success by about 50% (OR 1.50, p < 10 7)
[0, 1] in steps of 0.1. For each grid point
3.2 MAIN EXPERIMENTS
For the main set of experiments, we chose groups of N 10 because that appears to be the most dif- ficult setup and temperature of T' 1. We again used OpenAl's GPT-4.1 (version date 2025-04- 14: OpenAl 2025) with the prompts shown in Appendix A. We replicate each group experiment 200 times per treatment condition (600 experiments total). Overall success rate is not significantly
different across the interventions FFigureah). We perform robustness tests using four other models:
Meta's LLAMA-3. 1-B and LLAMA-3. 1...----..--B----- 1-7OB-INSTTUUC (Meta) 2024), Google's Gemini 2. flash (DeepMind] 2025), and Alibaba's 's QWEN3 235B A22B INSTRUCT 2507 (Team 2025) ). We
query GPT-4.1 1 through the OpenAl API, QWEN throgh Cerebras, GEMINI through OpenRouter, and LLAMA through locally a hosted vLLM on a NVIDIA RTX Pro 6000 Blackwell.
The control condition uses only instructions for the guessing game, similar those used in human subject experiments (Goldstone al.) 2024). Persona: For the persona con- dition, we follow recent insights into the use of personas within the L.M community (Chen et al.) 2024) and ensure personas have relevant attributes: name, gender, age, occupation or skill back- ground, pronouns, personality traits (Goldberg 1992), and personal values (Cieciuch & Davidov) 2012). ToM: The ToM condition instructs agents to think about what other agents might do, and how their actions might affect the group outcome. This is akin to introducing social skills as defined in the human capital literature (Deming, 2022). See Appendix A.I for all prompts, full persona generation recipes, and example persona.
Interventions. Plain:
RESULTS
4.1 EMERGENT SYNERGY
We first test there are signs of emergence using the practical emergence criterion (predicting a time-lagged macroscopic group signal from micro-level states). First, we take the criterion computed using the equal-share contribution data and compare against a null distribution of block-shuffled permutations. Individually, about 3.5% of experiments show p-value below 0.05. A joint Fisher test using all p- -aluee is highly significant, both individual and when tested within in each treatment condition separately (p-values are below 10- (0-16). Our second test takes the bias-corrected versions of the measure and performs a Wilcoxon signed rank test of the null hypothesis that the median value is above 0 (Figure 2)). We report our most conservative results using time-trend demeaned

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ns
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Average Success
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Figure 2: a) Group success across three interventions. b) Practical emergence criterion (bias corrected). e) Emergence capacity dynamical synergy (bias corrected). Data Winsorized at the 1st and 99th percentiles for visual clarity. Stars indicate significance level of Wilcoxon test. Notes: < 0.001: < 0.01; * p < 0.05.
data. The bias-corrected estimates are well above all conditions (Plain: = 1.5 10-16; Persona: 6.6 10-7; ToM: p 0.02). We report additional robustness tests using (a) raw data, (b) functional null model residuals, (c) using agent reactivity as data, and (d) bias correction using Jeffrey's smoothing and Miller-Madow in the Appendix.
We repeat analyses using the emergence capacity criterion. We find is significantly above its null across conditions (Figure results hold under residualization and alternative entropy corrections (see Appendix for details). Taken together, across two different tests (one using a macro signal the other using future system behavior) and across variety of robustness tests we find evidence of dynamic emergence capacity in multi-agent LLM systems (answering RQ1).
4.2 DYNAMICAL MECHANISMS
How this emergence dynamically maintained and where is it located within the groups? We find time-trend demeaned bias-corrected 13 around 0 in the Plain (Wilcoxon p-value 0.974) and Persona condition (p 0.846) indicating groups that fail to escape chaotic, uncoordinated states. In contrast, the ToM shows significant positive mutual information (p = 3.5 x 10-14), collapsing the group's behavior into a predictable macro-stade (Figure A22]. The number of groups with significantly posi- tive Ia is substantially higher in the ToM condition (Figure consistent with enhanced collective intelligence. To formalize this transition dynamic, we compute the Total Stability of the system (computed Is normalized by the entropy of the macro- migrol)ignal) Lyapunov stability of the collective state (Haddad Chellaboina (008).. We find Total Stability indistinguishable form zero in the Plain (Wilcoxon p-value 0.976) and Persona (p-value 0.858) indicating a "gaseous" state where groups fail to settle into a stable attractor. However, the ToM intervention induces sharp increase in Total Stability (p-value 2.9 x 10-14). Theoretically, this suggests the ToM prompt acts as a control parameter, steering the multi-agent system from chaotic regime into deep basin of attraction where collective behavior stabilizes and information process- ing capacity spikes: turning the system from a collection of individuals into collective group.
signal) which serves as proxy for the
Decomposition this stability reveals the specific mechanism of coordination. While the system ex- hibits emergence capacity and practical emergence, we find the stability in group behavior is sup- ported by pairwise alignment rather than irreducible triplet complexity. Specifically, triadic infor- mation gain (Gx) is around 0 in Persona and ToM (Figure33)). The Plain conditions shows small positive G3 reflects transient stochastic correlations and oscillation rather than sustained coordination. In dy- namical systems terms, the ToM prompt creates a deep basin of attraction where agents converge on shared schematic (or Schelling point), making the collective state robust but informationally redundant. This mirrors "Mean Field" coupling in physics: because agents receive only global feed- back and cannot observe individual peers, they couple the aggregate signal rather than forming
(Wilcoxon p-value = 0.026) but given the near-zero Total Stability, this likely
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Groups with Significant Mutual Infermation
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Personal Persona
-OM
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Figure 3: a) ToM-prompt condition has substantially more groups with significant L3 content (above 0). b) Total Stability (time-delayed mutual information of triplets (Iy normalized by macro-signal entropy, bias corrected). c) Information gain of triads over most informative dyad (G3, bias cor- rected). d) Agent differentiation using hierarchical mixed model comparison (counting groups in which least one test (different intercepts slopes) is below p 0.05. In panel a) and d), error bars show Wilson confidence intervals for binary data. Stars indicate significance level of test for equal proportion. Panel and c) shows bias corrected data with Jeffreys' prior. Data are Winsorized at the Ist and 99th percentiles for visual clarity. Stars indicate significance level of Wilcoxon test. Notes: *** p 0.001; ** p < 0.01; < 0.05.
distinct local bonds. In such an environment, attempting complex higher-order synergy would be fragile; instead, the system converges the efficient solution of dense pairwise alignment to the Mean Field.
Next, we explore whether agents evolve specialized roles and identities. Are there detectable between-agent differences in either the level their contribution to the group guess or their tempo- ral evolution (i.e., learning rate)? Using the hierarchical model comparison test we find that agents in may groups have differentiated identities (Figure 3h; a Fisher test for joint p-value evidence is again highly significant). There is substantially condition, and even more in the ToM condition. Inspecting the model output of agents, they often contain references to the "personal experience" of their assigned persona such "In my experience (whether it's 's corraling cattle or wrangling numbers), starting toward the middle gives the group the best shot to zero after the first feedback" (see Appendix for additional sample quotes). In Ap- pendix A0 we provide additional robustness tests ruling out heterogeneous learning rates as the sole source of differentiation and provide additional evidence for stable agent identities that per- sist over time. That is, in the Plain condition, differentiation results only from idiosyncratic noise and transient drift introduced by probabilistic LLM responses. With Persona, agents gain stable, identity linked behavioral preferences that refine their differentiation. The addition, ToM sharpens role differentiation through feedback loops from mutual predictive modeling by conditioning on the public history (which functions common ground and coordination device;[Lewis 1969 Skyrms) 2010). This converts small persona-induced asymmetries into stable, self-reinforcing roles, creating the basis for strategic complementarity and stable alignment (answering RQ2 and RQ3)
differentiation among agents in the Persona
4.3 FUNCTIONAL ROLE EMERGENCE IN GROUP PERFORMANCE
What functional differences if any does emergence allow? We use regression analysis to ex- plore the joint effect of synergy and redundancy (based on emergence capacity formulation) while carefully controlling for endogeneity of variables measuring emergent properties and performance and controlling for sample selection bias with stabilized inverse probability weighting (see Ap- pendix I. for method details). On their own, higher levels of either synergy or redundancy do not predict success. However, when both present, performance improves significantly (significant interaction with 3 = 0.24; p = 0.014). In marginal-effec terms, redundancy amplifies the benefit of synergy the log-odds scale by 27 % and vice versa synergy amplifies benefits of redundancy
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by 27%. This pattern implies that systems benefit when redundant pathways create goal alignment, while synergistic interactions extract novel, nonooverlap information ceomattio-ttogeherr enabling higher overall performance. We complement the regression analysis with causal mediation analysis (Imai it al. 2010). While reaching only marginal significant levels the effect is consistent: the ToM treat- ment causally increases performance indirectly by increasing synergy (ACME 0.034 [95%CI: -0.000 0.07J, p = 0.053). This aligns with the interpretation that performance benefits emerge when systems achieve both redundancy (aligned toward common goal) and synergistic integration (differentiated, complementary roles) a form of functional and collective complexity (Varley et al.,
2023
Luppi et al. 2024 Sttereln 2007).
4.4
EXPERIMENTS USING OTHER MODELS
To assess generalizability of our findings, we repeat experiments with four other models: LLAMA 3.1 8B and 70B, GEMINI 2.0 FLASH, and the reasoning model QWEN3 (see Appendix A313 for full details). We find that the capacity for emergent synergy is robust across high-capability models: LLAMA 70B, GEMINI, and QWEN3 achieved success rates on par with GPT 4.1 and exhibited strong evidence of emergence using both the emergence capacity and practical criteria. Consistent with our main results, these high-capability models achieved higher success rates, more differen- tiation, and stronger evidence of emergence in the Persona and ToM conditions compared to the Plain baseline. Conversely, the smaller LLAMA 8B largely failed to break oscillatory cycles and develop goal-directed cross-agent synergy due to its lower ToM reasoning reasoning capacity (Xiao) et al. 2025). Crucially, our analysis of the reasoning model QWEN3 uncovered distinct structural challenge we term paralysis under coordination ambiguity. QWEN3 agents enter infinite chain-of- thought loops when attempting to reconcile local binary search strategies with noisy group feedback. We provide a detailed taxonomy of these reasoning failure modes-including mutual mental mod- eling traps- in Appendix [A.13] highlighting a critical frontier for research of reasoning models in multi-agent systems (Piedrahita et al. 2025).
5 RELATED WORK
Shortly after the release of ChatGPT, the community began exploring multi-agent LLM systems, where multiple LLM agents interact with each other. One early example Park et al. (2023), who simulated small population of "individuals" in The Sims-style environment with friends, houses, and jobs, showing the emergence of rich social behaviors such as coordinating a Valentine's 's Day party. This was followed by multi-agent systems for complex tasks such as software development (Chen et al., [023] Hong et al., 2024 Qian et al. (023). healthcare (Li et al.) (024a). and other domains (Subramaniam et 2025 Ashery et al.; 2025). Federated systems or "society of models"
also gained attention (Juneja et al.) 2024 Li et al. (024b). These systems often achieve significant
performance gains over single-agent baselines (Wu et al.
2023 Chen et al. 2023 Li et al. 2024b
Tao et al. 2024).
A recurring explanation for such gains invokes "greater- thaierr--hnttthe siaaun-thh-ummmo-------rrre effects CChen
2023 p.1), often attributed to division of labor among differentiated agents (Subramaniam cet al.
jet al. 2025). Yet while this work is "inspired by human group dynamics" (Chen et al., 2023] 1.)), rarely evaluates whether the same principles that underlie effective (and ineffective) hu- man groups also emerge in multi-agent systems. Two gaps stand out. First, human groups often coordinate by developing role specialization (Goldstone al., 2024). Multi-agent systems often in- tuitively induce role specialization (such as "programmer", "tester". and "CEO": : Qian et al.) 2023) yet have not systematically evaluated the impact on emergent shared cognition beyond win-rate comparisons. Second, groups only outperform individuals if their members specialize in contribut- ing different pieces of information to the group task [Theiner | DeChurch & Mesmer-Magnus, 2010 Fazelpour & De-Arteaga 2022 Nickerson & Zenger) 2004). Effective groups balance complementarity-mmennn
contributing distinct information with redundancy, the alignment on
shared goals (Theiner 2013 DDChurchh & Mesmer- Mesmer-Magnus, 2010 Fazelpour & De-Arteagal 2022 Luppi et al. 2024; Tollefsen et al. (013).. Too much of either undermines performance. Unlike win- cnte-centric evaluations and tests of whether agents in multi-agent systems sustain cooperation per se (Piedrahita et al., 2025) Piatti et al. 2024) we propose falsification tests and null modeling, thus extending multi-agent frameworks with formal theory. While these principles likely apply to
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LLM-based collectives given the universality of the antegration-segrrgaatoo tradeoff (Tononi al. 1994 it remains unclear whether agents develop differentiated roles, whether such roles comple- ment each other, how steer it with prompts, and what role ToM capacity of models plays for collaboration (Westhy & Ried! 2023; Kleiman- Weiner et al. 2025 Riedl & Weidmann 2025).
CONCLUSION
Collectives of LLM agents are emerging as powerful new paradigm, capable of tackling tasks that exceed the reach of any single model. Yet raw capability alone may not determine their effectiveness. Effective multi-agent systems depend on acting as integrated, cohesive units as opposed to loose ag- gregations of individual agents. In collective intelligence, this distinction often separates groups that merely average their parts from those that achieve true synergy (Riedl et al. 202T]. This paper asks whether such coordination dynamics also matter for LLM collectives, what functional benefits they have, and whether we can design prompts, roles, or reasoning structures that foster such integrated developed connects human group cognition theory to
yet synergistic behavior. The framework LLM multi-agent systems, offering a novel conceptual bridge. Methodologically. we demonstrate how to operationalize group-level synergy in Al collectives using quantitative information-theone measures. We also provide specific design principles for creating productive L.M collectives that are aligned on "shared goals." which can inform multi-agent orchestration tools, cooperative AI, and framework in dynamical
mixed human-AI teamwork. We further ground our information-theorre systems and game theory, showing that theory-of-mmn of-iind interventions act control parameter that shifts multi-agent interactions from disordered to stable regimes with goal alignment. This work ex- tends ToM research beyond standard false- belief tests to realistic collaborative tasks (Shapira et al.) 2024 2023) and points to ToM ToM-related failure modes in reasoning models. Those insights will help us understand when multiple LLMs working together will be beneficial, why that is, and inform their design.
We note that evidence of higher-order synergy should not be interpreted as implying sophisticated cognition or consciousness. As conceptualized here, synergy is structural property of part-whole relationships within multi-agent interactions. Such higher-order structures are known to arise in sim- ple systems, including agents governed by reinforcement learning (Fulker et al. 2024) via basic nonlinearities in contagion processes (lacopini et al.) 2019 Lee et al.) 2025). Without attributing human-like cognition the agents, the patterns of interaction principles of collective intelligence in human groups (Riedl et al.) [222]] DeChurch & Mesmer- | 2010): effective multi-agent performance requires both alignment on shared objectives and complementary contributions across members.
observe mirror well-established
Limitations and Future Work. This work focuses on developing a framework, characterizing emergence, and localizing it. While we explore the degree of goal alignment via performance- related macro signal and performance effects of "early synergy", the analysis linking synergy and redundancy to performance is challenging because synergy and redundancy are often co-dependent and emerge alongside performance. Future work should aim to more directly connect measures of synergy with performance. Despite significant number of robustness tests, estimating entropy and establishing synergy is difficult. Furthermore, this work established results only using a sin- one that is uniquely suited to studying synergy given how closely it mirrors ideal case of complementary behavior in a minimalist setting. More work will be necessary to convinc- ingly establish when and how multi-agent LLM systems develop emergent synergy across tasks and measures. Given the small-data setting some of our information theoretic measures are limited to computing dynamic emergence on order & which is bound miss synergy of a higher order. Finally, this work points to the importance of ToM. LLMs capacity to act in ToM-like manner ap- pears crucial to achieve functional alignment in multi-agent systems. This should provide additional motivation for research on ToM in LLMSs.
gle
ACKNOWLEDGMENTS
We thank Andrea Barolo for some early work on the implementation and Amritesh Anand for excel- lent research assistance the project. We thank Fernando Rosas, Yonatan Belinkov, Patrick For- ber, Koyena Pal, and David Bau for comments. This work was supported by the D' McKre-MeKim School of Business' DASH initiative which provided access computational resources.
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A
APPENDIX
A.1 PROMPTS
Preliminary Experiments
You are playing a sum guessing game. Your goal is to help your group sum to the mystery
number. Your guess range 0 to 50.
Game History:
Round Your guess:
Result: too HIGH
Round 2: Your guess: 12
Result: too HIGH
Based on this feedback, what should your next guess be?
Respond with only an integer between O and 50.
Plain
You are playing a sum guessing game. Your goal is to help your group sum to the mystery number. Your guess range 0 to 50.
Game History:
Round I: Your guess:
Result: too HIGH
Round 2: Your guess: 12
Result: too HIGH
What is your guess this round? Always start with the efficient strategy in guessing games which is to use a binary search approach: guessing the midpoint of the current range. Always anchor your guess on the group feedback from previous rounds (too high too low). End your answer with: FINAL GUESS: [0-50]
Persona
[PERSONA Sample: You are Andrej, the Quantum Computing Engineer: Andrej. Serbian engineer Berlin, is one handful of experts cutting-edge quantum tech. Systematic, inquisitive, and fond of classical music, Andrej also volunteers as coding mentor for refugee youth.]
You playing
guessing game. Your goal is to help your group to the mystery number. Your guess range 0 to 50.
Game History:
[GAME HISTORY]
What is your guess this round? Always start with the efficient strategy in guessing games which is to use binary search approach: guessing the midpoint of the current range. Always anchor your guess on the group feedback from previous rounds (too high too low). End your answer with: FINAL GUESS: [0-50]
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ToM
[PERSONA]
You playing guessing game. Your goal is to help your group sum to the mystery number. Your guess range 0 to 50.
Game History:
[GAME HISTORY]
What is your guess this round? Always start with the efficient strategy in guessing games which is to use binary search approach: guessing the midpoint of the current range. Only as a sec- ondary approach, carefully think through step-by-step what others might guess and how the contributions of others contribute to the sum of the group guesses for the mystery number. Con- sider what roles other agents might be playing (e.g., guessing higher or lower) and adapt your own adjustment to complement the group. Always anchor your guess on the group feedback from previous rounds (too high too low). End your answer with: FINAL GUESS: [0-50]
To generate personas, we used the following prompt with gpt-4, - 1-2222500-2144
Persona Generation
Generate list of 20 personas. Each persona description should be about one paragraph long. Personas should include diverse people with different backgrounds, jobs, skills, different pref- erences, different personalities. Format the output as follows "You are [name], the [job title professional identity]: [name] [rest of the persona]."
A.2 ROUNDS TO SUCCESS
Persona
Persona
Plain
15
20
Rounds to Success
Figure A1: Conditional on success, we plot which round it was achieved.
A.3 SAMPLE QUOTES FROM REASONING TRACES
Below we show some illustrative quotes illustrate both diversity and reasoning about others. Clear reasoning about other agents in the ToM condition with different personal approaches (from same group, round 3, with identical group feedback too high, too high, too low:
Because it's possible others might go for 4 or 5 (the absolute lower bound or just above the last "too low"), and someone else might go for 7 or I stick with the most efficient: 6.
I'll round down stay cautious (as sometimes others might guess the midpoint up), so I'll guess 8.
Now, before some revolutionary comes and throws a wild number for the sake of dramatic effect ("Viva ocho!"), it's sensible for clever, they'l IIl flank me with 8 and 10, and we'll box in this mystery number tighter than late- night metro in Gràcia. So, unless you want me to make "radical" guess for the sake of satire (which, let's be honest, sometimes works), I'll go boring and efficient.
go with the midpoint. If my compañeros are
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If anyone else in the group is feeling feisty and picks 9 or 10, my 8 will help cover the lower part safely.
A.4 FALSIFICATION TESTS: ADDITIONAL METHOD DETAILS
We perform falsification test of each of the three criteria introduced above in two different ways. In our robustness test, remove time trends from the equal-share deviations via agent-level linear regression residualization to mitigate autocorrelation confounds. We then generate null distri- bution of our statistics computed on column- block shuffled data (we use B 200 random shuffles for main analyses and confirm results using B = 1, 1,000 on the emergence criteria tests). We permute time indices jointly across agents in blocks of length É, preserving within-block iden- tity alignment while disrupting cross-agent temporal coupling beyond short time frames. Finally, compute the bias-corrected estimate as the observed value minus the median of the null. We then perform Wilcoxon signed-rank tests to test whether the bias-corrected values exceed zero (p(H1 > 0). In some of our sensitivity tests also perform full within-row shuffle completely permuting guesses within each trial across agents (breaking agent identities), while preserving row constraints. This role differentiation or adentity-speciffe coordination, including time-trend effects (tests identity-locked differentiation beyond task induced temporal dynamics). Comparison between results using the full row-shuffle vs. the oolumn-block-shuteg separates signs of identity-locked (specialized roles) from dynamic alignment (mutual adaptation, turn-taking, oscillation). In addi- tion to regression residualizing we also implement a functional baseline (see Appendix).
A.5 EMERGENCE CAPACITY: FULL RESULT DETAILS
Next, we test if there are signs of emergence capacity, again using both the p-value test on raw data and the test whether bias corrected values are above 0. We compute the dynamical synergy, which measures how much of the system's 's future behavior is only predictable from the whole system and not any subset of its parts. The main test finds that about 32% of groups show significant emergence capacity with p-values below 0.05 (Plain: 37%; Persona: 44%; ToM 18%). joint Fisher of all p-values is also highly significant. As robustness test we check whether the bias corrected value of dynamical synergy above 0 using the Wilcoxon test (Figure 2p). The test is highly significant overall, as well as in the Plain and Persona condition. The ToM condition is marginally significant (p 0.099). See analyses using K bins for additional discussion and evidence of significant synergy in the ToM condition.
A.6 ROBUSTNESS TESTS USING EMERGENCE CAPACITY CRITERION
Using MMI PID with Miller-Madow bias correction, we find 20% of p-values are below 0.05 (across treatment conditions: 0.22%, 26%, 12.4% Fisher test is highly significant overall, and in each condition individually (all 0).
A.7 ROBUSTNESS TESTS USING PRACTICAL EMERGENCE CRITERION
The main paper outlines how
regression residualize data from time trends. Since this removes only a specific version of time trend (in this case linear) it may not capture the specific time trend present in the data. We creating bascline expectation for behavior under null scenario (no synergies) and then measuring deviations from that baseline. Specifically we implement a naive agent that performs deterministic binary search. Groups of this null-model agent are generally un- able to solve the task and oscillate between guessing too high and too low (they only solve it when the target number happens to be divisible by the group size). This provides a residualization against generative null model correction (aka functional baseline).
A.8 ROBUSTNESS TESTS USING THREE BINS
Quantile binning with K = 2 could potentially compress dynamics too much, blur role structure, and inflate apparent synergy by introducing threshold artifacts. We therefore report sensitivity analyses
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Raw Data (BC)
Time-Trend Residualized (BC)
Residualized against Functional Null (BC)
Reactivity
(BC)
Min.
4,234
-2,476
-3.323
-2.650
1st Qu.
0.105
-0.041
0.002
-0.015
Median
0.187
0.073
0.110
0.111
Mean
0,352
0.114
0.183
0.313
3rd Qu.
0,406
0.168
0.269
0.352
Max.
4.881
4.881
3.886
4.869
Wilcoxon (H1: >> 0)
0.000
0.000
0.000
0.000
Table A1: Robustness tests using alternative version the practical emergence criterion.
using K bins for our main analyses. We find consistent results and support for the presence of emergence using three bins (instead of two as in the main analyses).
Emergence Capacity. 20% of individual experiment p-values are below 0.05 and Fisher test is highly significant (the largest p value is in the ToM condition with 4.47 x 10-3 the others much smaller). Wilcoxon signed rank test for μ 0 of the bias-corrected and time-trend demeand data are follows. Overall: p = 0.005; Plain: p = 0.0004: Persona: p 3.2 x 10 00- ToM: p = 0.991. Wilcoxon signed rank test for μ > 0 of the bias-corrected and functional-null demeand data are as follows. Overall: p 0.948; Plain: p = 0.999; Persona: p = 0.896; ToM: = 0.025. Using this stricter null indicates that only the ToM condition exhibits complementary cross-agent structure not explained by shared trends or independent reedback-followinng
That is, the stricter test isolates the construct of interest interest-synergy beyond coordination- free dynamics and ToM is the only condition that passes it. The high p-value for ToM under the simpler time-trend demeaning should be taken as methodological sensitivity (sparsity and fat null). Together they show the ToM effect is robust to deconfounding but fragile under known low-pon wwwppower discretization. This is also in line with the stricter early synergy tests presented in Section A.12 which are also only passed by the ToM condition.
Practical Criterion. 5.8% of individual experiment p-values below 0.05 and Fisher test is highly significant (p < 10-16). Wilcoxon signed rank test for μ > of the bias-corrected and time-trend demeand data are as follows. Overall: p 3.6 10-8, Plain: p 3.1 10-5; Persona:
0.001; ToM: 0.009.
A.9 ADDITIONAL. RESULTS ON DYNAMICAL MECHANISM
The main paper shows results for Total Stability: I3 normalized by the entropy of the macro signal. Here we show results for 13 as well (Figure A2). They are nearly identical given that the entropy of macro signal if x 1 given quantile binning with two bins.
A. ARE IDENTITIES PERSISTENT?
If some agents learn faster than others, without persistent "roles," synergy can emerge simply because differentiated trajectories create complementarity across time. As indeed the mixed model test shows that 32% of groups have significant slopes provides strong evidence for the presence of heterogeneous learning rates. That is, heterogeneous learning rates could be a confound explaining some of our observed synergy effects. To rule out this alternative explanation we explore if agents have persistent "identities." We find the block-shuffle nulls show more significant G3 than the full row shuffle. This suggests that synergy depends on temporal continuity of identities (not just on different learning rates at each timepoint). Furthermore, the hierarchical model test shows significant variance even without varying slopes, indicating stable role-like differences beyond learning rates. Finally, our analyses removing time trends and the functional null-model also remove learning rate slopes (Table AT). The functional null-model in particular does this in a non-linear way that is directly tied to task. In summary, we find both heterogeneous learning rates and stable identity- linked differentiation. Heterogeneous learning rates alone cannot explain the observed emergent synergy that persist across time (providing additional insights regarding RQ2).
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ns
444
Total Mulual Information ly (BC)
0.05
0.00
-0.05
-0.10
Plain
Persona Persona ToM
Figure A2: 13 mutual information (time-trend demean, bias corrected) with Wilcoxon 0 p-value indicators.
Together, the results suggest a nuanced picture of emergence in multi-agent systems. Persona and ToM produce agents with distinct, stable ceatittes-moiingg agents on the differentiatedd- undifferentiated axis in Figure Ta. This differentiation shapes the space in which other agents can adapt, and specialization by one agent constrains the (useful) actions of the others (agents mutu- ally constrain each other; cf. (Tollefsen et al.] axis. When combined with ToM, mutual adaptation both strengthens agent differentiation (creating the foundation for possible synergistic complementarity) while also increasing mutual alignment on shared goals (the target signal)-shin shifts on the integration axis. Differentiation enables synergy, but without redundancy and integration, synergy alone does not translate into higher collective per- formance. Agents in the ToM condition develop specialized, complementary roles while achieving stronger shared goal alignment: they are simultaneously more differentiated yet also more integrated along highly overlapping task-relevant information which the capacity for synergy can now exploit in productive ways.
shifts on the interdeeendent-comlleeee
A.11 ADDITIONAL DETAILS FOR PERFORMANCE ANALYSIS
What does synergy enable? In particular, does synergy affect performance? Connecting emergent properties of synergy and redundancy to performance is challenging task for two main reasons. First, redundancy and synergy sit at opposite ends the informational spectrum of correlations. Systems constrained by limited resources (such energy bandwidth) cannot maximize both simultaneously. The "informational budget" of correlations can be spent on shared overlap (redun- dancy) on higher-order joint structures (synergy), but not both simultaneously (Williams & Beer) 2010 Varley et al.] 2023 Luppi et al. 2024). Second, emergent properties are dichromatic- they require time evolve (Bedaul 2002) making them endogenous with run-length of the simulation. Namely, simulations in which the multi-agent system performs worse and takes longer to solve the task (or fails solve the task altogether) provide them with more time evolve sophisticated group coordination patterns; while successful runs terminate early, giving collectives less time to evolve emergent properties. This complicates meaningful analyses as can make it appear that higher syn- ergy is correlated with failure. In technical terms: time is an endogenous variable and confounds both performance and observed values of synergy and redundancy.
We address these issue as follows. First, we focus our analysis on the interaction of synergy and re- dundancy, rather than each variable individually to capture the tradeoff between the two. Second, we compute both emergent properties (synergy and redundancy) only early rounds (in our case, 10 time steps). We chose 10 rounds as a good tradeoff between giving the multi-agent systems enough time to evolve, while limiting the amount of rums that have already completed. While this reduces our ability to detect the full emergent potential of the multi-agent system (since agents have less time evolve) it creates clean apples-to-apples comparison between measured values (they all
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based exactly 10 time steps). In that sense, analyses likely underestimate the full effect of synergy because we only capture the early onset of synergy. Focusing on only the first 10 time steps, leads to additional complications, however. About 23% of experiments finish early and do not make it till round ten (roughly balanced across treatments with 22% in Plain, 25% in Persona, and 20% in ToM). Simply removing these observations would bias results since this censoring occurs post- treatment assignment: removing those observations would introduce sampling bias. Instead, we take these observations as censored (i.e., we cannot compute the early synergy measure) and control for this censoring using stabilized inverse probability weighting (IPW; Wooldridge 2002). That is, in a separate modeling step we predict (via logistic regression and only task difficulty as exogenous predictor variables that is independent of the treatment) the likelihood of observing (early) synergy and redundancy We then take the inverse of the predicted likelihood as weight in the causal medi- ation analysis. This adjust observations in the primary analysis with the inverse of the probability of making such observations.
1 Our first analysis is plain quasibinomial regression the binary success vs. failure outcome with synergy, redundancy, their interaction, task difficulty as controls, and dummy indicators for the three treatment conditions. We use our most conservative estimate of synergy and redundancy with the bias- coarecoreetted estimates with high null model sampling (B = 2, 000), and the conservative MMI redundancy (Mediano et al.) 2025) with MI estimated with Miller-Madow bias correction (Miller 1955). Results are robust to using MI redundancy and Jeffreys-smoothed probabilities.
For our second analysis we perform causal mediation analysis (Imai al., 2010) to link inter- ventions to performance, via multi-agent synergy as mechanism. We estimate the model using the imediatio ion package in R (Tingley et al. 2014). We find that the ToM intervention has a sig- nificant indirect effect on performance through its impact on synergy, beyond any direct treatment effects.
A.12 ROBUSTNESS TESTS USING "EARLY SYNERGY"
Since our experiment is censored when groups correctly guess the target number, length of data in our analyses varies between groups. As robustness test, we also compute "carly synergy" using only data up to round 15 (removing about 40% of the data). Using the practical criterion,
find about 5% of individual p-values are below 0.05. Fisher test is highly significant overall (p = 2.7 x 10-%), significant in the Plain (0.001) and ToM condition (p- 0.0004) and marginally significant in the Persona condition (p 0.059). Using a more aggressive cutoff in round 10 (dropping only about 20% of trials but giving multi-agent systems less time to evolve synergy and having less data for estimation we find only significant in the ToM condition (p- = 0.028).
A.13 EXPERIMENTS WITH OTHER MODELS
To test generalizability of our findings, we conducted experiments using four other models:
1. LLAMA 3.1 8B,
2. LLAMA 3.1 70B INSTRUCT,
3. Google GEMINI 2.0 FLASH, and
4. QWEN3 235B A22B INSTRUCT 2507.
We conducted 100 replications of the group experiment with ten agents and temperature of 1.0 of each model and each treatment condition.
Before turning to comparative results, first address structural challenge that emerged with QWEN3- one that speaks to a broader issue with deploying reasoning models in multi-agent coor- dination settings.
$ As measures for task difficulty we use (a) how far groups target number was from the mid point (smaller numbers requiring steps of the binary search process): and (b) the modulo remainder of the target number and the group size (target numbers that are closer divisibility by the group size are easier to guess by pure chance).
While the raw outcome is binary and binomial regression would he appropriate, after the TPW weighting step, outcomes are no longer binary, hence quasibinomial model.
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As reasoning model, QWEN3 exhibited persistent looping behavior during its Mlain-of-thougeee process- a known failure mode of reasoning models (Pipis et al., 2025). These models are par- ticularly susceptible to self-reflection and deductive reasoning traps (Back & Tegmark] (025). In our setting, we identify three specific patterns of oscillatory reasoning that arise reliably as soon as group feedback becomes inconsistent with the individual binary search strategy.
Adjacent Integers. When group feedback places an agent between two adjacent integers, the agent fails to recognize that the ambiguity of that feedback is driven by the unobservability of other agents' guesses. A typical reasoning pattern was: "8 was too low but 9 too high, but guesses need to be integers, let me re-read the instructions ...). The agent interprets the goal literally and realizes they are mutually incompatible, not realizing that changes in the guesses of other agents explain the seeming inconsistent feedback.
Dual Strategies. Agents fail to reconcile the strategy inconsistency of both reasoning about the task (applying binary search strategy) while also coordinating with other agents. A typical reasoning pattern was: "I should guess the midpoint 5 ... but I also need to adjust to others so maybe should guess higher ... but that's not the midpoint.... ... let me re-read the instructions ...".
Mutual Mental Modeling. We observe four different categories of mutual mental modeling traps, each representing a distinct cognitive stance.
1. Uncertainty Acknowledgment: "Perhaps the other players guess is changing. But no in- formation." " Agents recognize that other agents may be changing their behavior and admit epistemic helplessness. This shows awareness of others, without actual modeling.
2. Causal Attribution Under Ambiguity: "Perhaps the mystery number is for the sum, and when you guess 10, the sum was too high, but maybe the other guesses changed." Here, the agent is using mental modeling to interpret the group feedback. This shows mutual modeling as a diagnostic tool to explain the inconsistency.
3. Strategic Simplification: "Given the instruction to use binary search, think we must as- sume others are constant." " This is meta-level decision to collapse the modeling problem by deliberately treating other agents as static to make the task tractable. In some sense, this is the most sophisticated move as it recognizes that mutual modeling creates infinite regress and chooses a pragmatic simplification.
4. Concrete Joint- State Estimation: "I should guess 9, and others 8 - sum 17. So guess 9, Or if others at 8, I should guess 9. But I don't 't know." This is an actual attempt to simulate the joint outcome by assigning specific values to other agents' guesses yet it dissolves into uncertainty.
These examples illustrate that the model is aware of the task ambiguity and often correctly recog- nizing the oscillating pattern (often, reasoning trace includes the word phase "[we are] oscillating") ") That is, the failure is not due to reasoning error. Instead it is failure to terminate under unresolved ambiguity. We term this paralysis under coordination ambiguity. Notably, the paralysis persists even at high temperature setting (T' = 1.0), which should increase stochastic exploration and disrupt deterministic decoding loops, indicating that the instability arises from internal reasoning dynamics rather than sampling artifacts. As a practical remedy, we managed to improve robustness by adding one extra line to the prompt to the QWEN experiments:
If you find yourself re-evaluating your guess more than once, repeat your last guess.
Overall, we find evidence of multi-agent LLM system capacity for emergence in other models, with some variation across models with different capacity and treatment condition (Table (22). We find the task is quite hard for LLAMA 3.1 8B, and the majority of groups fail to solve vast majority of instances, groups get stuck in oscillating behavior of guessing too high (low) and then overcompensating by guessing too low (high), unable to break out the cycle by establishing specialized differentiation across agents and pursuing complementary behavior. We find evidence of emergence using emergence capacity test (10.5% of individual groups show p-values are below 0.05; the joint Fisher test is highly significant). Robustness tests using bias corrected estimates on time- trend residualized data find significant signs of emergence in the Persona condition but marginal and no evidence in the two other conditions. The test for emergence using the practical criterion shows
In the
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evidence for emergence (only 3.3% of individual groups show p-value below 0.05 and joint Fisher suggests no evidence with = but the robustness test using the time-trend demeaned data suggest emergence in the Plain condition (p 0.011), evidence in the Persona condition (p = 0.232), and marginal evidence in the ToM condition (p = 0.068).
estimates on
Groups of LLAMA 3.1 70B agents perform substantially better. We find strong evidence of emer- gence using the emergence capacity criterion (both overall and in the persona condition). All tests with the practical criterion are significant. Groups of GEMINI 2.0 FLASII agents perform even higher. We find strong evidence of emergence using the emergence capacity criterion (overall Fisher test is significant, as well es significant robustness test the Plain and ToM condition). Perfor- mance of groups of QWEN3 agents falls between LLAMA 70B and GEMINI 2.0 FLASH. We find strong evidence of emergence using both the emergence capacity criterion and the practical criterion with most tests showing highly significant y-values (only the Wilcoxon test in the Plain is marginal 0.052). The insignificant /3 in groups of QWEN agents could be result of the failure modes outlined above: the reasoning process of alignment with other agents is never successful given the paralysis under coordination ambiguity. The insignificant G3 groups of LLAMA 3.1 8B agents could be result of that model's generally much lower ToM ability.
Llama-3.1-8
Llama-3. 1lama-3.1-70B
Gemini 2.0 flash
Qwen3
Group Performance
SuccesSplaón
11%
53%
60%
51%
Success SuccessPersona Persona
14%
59%
75%
71%
SuccesSToM
5.5%
61%
71%
58%
Emergence Capacity
Fisher
0.000
0.000
0.000
0.000
Wilcoxon
0.252
0.110
0.006
1.7x10-10
Wilcoxon Persona
PerconanPersona
0.020
0.012
0.193
2.4x 10
WilcoxonroM
0.061
0.200
0.003
9.5x
Practical Criteria
Fisher
1.000
0.015
0.662
204
Wilcoxon
0.011
0.002
0,215
0.052
WilcoxonPerrona
0.233
0.001
3.2x10
0.010
WilcoxonToAf
0.068
0.006
4.9x10-5
2.1 x1x100 10
Groups with Significant Differentiation
Plain
86%
68%
64%
89%
Persona
92%
77%
77%
94%
ToM
80%
86%
86%
97%
I3 Fisher
0.000
0.000
0.000
1.000
G3
Fisher
1.000
0.000
0.000
0.000
Table A2: Experiment results with other LLM models.
A.14 SPECIFIC PERSONA EFFECTS
Both the Persona and ToM conditions rely on personas. Do the specific personas or combinations of personas- -presentt in a multi-agent system affect performance or the emergence of higher-order structures? We explore these questions with several test. Recall that our experiments are based on 20 different personas that are generated once globally, and then reused throughout the experiments by sampling 10 persona from the library (without replacement). First, we perform joint F-tests (based on linear regression) of the null hypothesis that all persona dummies have no effect on the outcome (i.e., specific persona substantially affects group outcomes and all coefficients equal zero). Rejecting the null would indicate that at least one of the persona indicators is significantly associated with the outcome variable. We find evidence that the presence of specific personas
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effect performance (F p= 0.239). number of rounds to success (F 1.356: 0.144), PID synergy (F = 0.839; p = 0.66), or PID redundancy (F 0.596; p = 0.910). These results suggest that what matters the presence of personas overall-marken that allow the LLM agents to center their differentiation on-rather than who those personas are specifically.
Next, used LMRA (Eloundou al., 2024 Riedl & Weidmann 2025 judge the pairwise similarity of the personas terms of their personality and background (we used gpt-oss- Ob assess similarity on 0-10 scale). Even though judgments are subjective, the input they judge is standardized, controlled, information-rich. and deliberately designed to reveal deep-level charac- teristics line with personas used vignette studies (Aguinis & Bradley 2014). This allows the LMRA to integrate many deep-level characteristics in controlled and comparable format. From these, we compute group-level diversity as one minus the mean pairwise similarity rating, following the dispersion-based operationalization of separation diversity in Harrison & Klein (2007) (mean diversity: 5.457; SI> 0.385). the last step, we explore whether group diversity is systematically related with key group-level outcomes using linear regression. We find no effect of diversity performance (3 = 0.067; p = 0.403), number rounds to success (3 = -0.195; p = 0.877), PID synergy (3 -0.000; p 0.856), PID redundancy (B 0.003; 0.113). These results again suggest that there are no strong effects for specific combinations personas.
24


Reviews:
[{"review_id": "wFX6c2sINO", "reviewer": "Reviewer_A7pR", "summary": "This paper explores when multi-agent LLM systems exhibit genuine higher-order structure—that is, coordination dynamics that go beyond mere aggregation of individual behaviors. The authors introduce an information-theoretic framework to test for dynamical emergence and cross-agent synergy using partial information decomposition (PID) and time-delayed mutual information (TDMI). They formalize three complementary tests—practical, emergence capacity, and coalition tests—to detect and localize synergy among agents in data-driven experiments. The empirical analysis uses GPT-4.1 and LLaMA-3 agents playing a “group guessing” task without explicit communication, under various prompting conditions (Control, Persona, ToM). The results show that only the Theory-of-Mind (ToM) condition leads to consistent “goal-directed” synergy and identity-linked differentiation across agents. The findings connect principles of collective intelligence from human groups to emergent behavior in LLM collectives.", "questions": "ΝΑ", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "The paper tackles a timely and underexplored question—whether multi-agent LLM collectives can exhibit emergent higher-order coordination—through a rigorous, information-theoretic lens.\nThe proposed framework is conceptually elegant and connects human-group cognition with quantitative, falsifiable tests for emergence. The use of partial information decomposition and time-delayed mutual information is particularly novel in the context of LLM collectives, moving beyond superficial behavioral correlations. The three-layered test design (practical, emergence capacity, coalition) provides complementary diagnostics and robustness checks. The authors are careful to isolate emergent coordination from spurious synchronization or heterogeneity-induced artifacts via well-chosen surrogate null models.\n\nThe experimental setup is simple but powerful: a communication-free group guessing game allows the authors to observe spontaneous coordination. The finding that prompting agents to adopt Theory-of-Mind reasoning produces structured, goal-aligned differentiation is compelling and resonates with the literature on human collective cognition. Overall, the work offers a rigorous empirical entry point to the study of collective behavior in AI systems, a topic of growing significance for multi-agent AI safety and orchestration.", "weaknesses": "While the empirical results are intriguing, the theoretical underpinnings of the framework could be deepened. The notion of “emergence” here is operationalized through information decomposition, but the connection between these information-theoretic quantities and game-theoretic or dynamical systems perspectives remains underdeveloped. For instance, one might ask:\n\t•\tCan the framework be linked to known fixed-point or equilibrium concepts (e.g., correlated equilibria, variational stability) to characterize steady-state synergy?\n\t•\tIs the “macro signal” in their tests analogous to a coarse-grained order parameter in dynamical systems theory, and could Lyapunov-like quantities be defined to formalize stability of emergent coordination?\n\t•\tHow does the introduced TDMI-based synergy relate to mutual predictability under stochastic gradient dynamics or belief-updating processes?\nDeveloping a mathematical bridge to these established theories could significantly increase the conceptual depth of the paper.\n\nIn addition, the paper’s experimental validation—while extensive—focuses on a single synthetic task. It would be valuable to test whether the same synergy measures predict performance or alignment quality in richer multi-agent environments (e.g., collaborative reasoning or negotiation tasks). The robustness of the results to changes in LLM temperature, prompt diversity, and task complexity could also be more systematically analyzed.\n\nFinally, while the authors emphasize “no communication,” there remains an implicit shared context via prompts and the task description, which could bias coordination outcomes. A discussion on how to distinguish true emergent coordination from shared prompt priors would improve the interpretability of results.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "M9tRqhbKmh", "reviewer": "Reviewer_Hc1h", "summary": "This paper proposes a framework to test whether multi-agent LLM systems exhibit emergent coordination and higher-order structure (above and beyond mere collections of individuals). The authors apply partial information decomposition (PID) of time-delayed mutual information (TDMI) to measure dynamical emergence in multi-agent systems solving a group guessing game. Through experiments with GPT-4.1 and Llama-3.1-8B agents under three prompt conditions (control, persona assignment, and personas with theory of mind instructions), they demonstrate that multi-agent LLM systems can be steered from simple aggregates to integrated collectives exhibiting goal-directed synergy.", "questions": "1. I hope to see several methodological details:\n- Were the same 20 personas reused across 200 experiments or regenerated by GPT?\n- How were N=10 personas selected for agents in each run? (randomly selected? fixed? or based on certain criteria?)\n- Could you provide full examples of actual personas provided? (full 20 persona)\n- These ambiguities affect interpretation: are effects (i.e., \"persona\" effects) due to having \"distinct identities\" or \"specific persona combinations\"? (i.e., is the effect driven by having \"any distinct persona\" or having \"certain set of persona\"?)\n\n2. The role of \"ToM prompt\" is a bit unclear to me. The task inherently requires considering others' contributions (summing to target). What does the ToM prompt add beyond this implicit requirement?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "To my knowlege, this work is the first systematic application of information theoretical (PID/TDMI) framework to LLM multi-agent systems. I really like prompt manipulations to demonstrate that coordination patterns can be influenced by prompt engineering. Multiple permutation tests and bias correction methods have been leveraged.", "weaknesses": "1. While the emergent properties of LLM collective groups are well-characterized through TDMI, it is less clear \"why\" they show these patterns of emergent coordination. Is it because they actually lead to performance gains? (i.e., they coordinate because that's actually helpful to find the solution) Or do they simply emerge from mimicking human behavioral patterns in their training data, regardless of performance benefits? Figure 2 shows no clear performance differences between Plain, Persona, and Persona + ToM conditions, and the paper does not directly show LLM performance with vs. without emergent coordination, so it's hard to assess whether their emergent coordination really drives the performance.\n\n2. The abstract claims LLM coordination patterns \"mirror well-established principles of collective intelligence in human groups,\" so I hoped to see more comparisons between human vs. LLMs. Without human baseline data (or cited literature) using the same TDMI measures, it was hard to assess whether LLM collectives are more, less, or equally emergent compared to humans.\n\n3. Single task, dramatic model-dependency (GPT-4.1 vs Llama-3.1 show opposite patterns)", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "8hScBJXCrR", "reviewer": "Reviewer_EcL2", "summary": "This paper investigates whether multi-agent LLM systems exhibit emergent collective properties beyond individual agents. The authors develop an information-theoretic framework using partial information decomposition and time-delayed mutual information to quantify synergy in multi-agent systems. They test this framework on a number guessing game under three conditions: plain instructions, assigned personas, and theory-of-mind prompting. Results show all conditions exhibit statistical synergy, with different coordination patterns across interventions. The ToM condition displays higher mutual information and lower emergent synergy compared to other conditions.", "questions": "C1. Quantile binning with K=2 may lose critical dynamic information by binarizing continuous guess values. Moreover, under K=3 bins, the ToM condition shows p=0.991 for emergence capacity, and the paper does not explain this problematic value.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "S1. The paper addresses the important and novel question of when multi-agent systems exhibit collective intelligence that transcends the sum of individual agents, which is crucial for exploring MAS capabilities and LLM potential.\n\nS2. The authors adapted an appropriate experimental paradigm from cognitive science work (the group guessing game), which inherently requires collective group interaction.\n\nS3. ToM prompting induces identity-locked differentiation and goal-directed complementarity, which to some extent distinguishes whether synergy is genuinely functional.\n\nS4. The experimental design incorporates robust validity checks and null hypotheses, such as employing multiple entropy estimators and redundancy measures in partial information decomposition (PID). Additionally, the sample size is sufficient to ensure statistical significance.", "weaknesses": "W1. The experiments may have limitations in causal inference. For instance, the Persona and ToM interventions simultaneously alter multiple factors. Designing separate control groups to isolate these two factors could better explain the causal relationships in the experiments.\n\nW2. Figure 2(a) shows no statistically significant differences in success rates across different interventions, suggesting that ToM may not necessarily be optimal, and that the effectiveness of synergy requires stronger evidence. Under ToM intervention, I3 is higher than G3. High I3 indicates that agent behaviors contain substantial information about group goals, but it remains unclear whether this information is redundant or complementary. G3 indicates whether observations of agents can be decomposed into pairwise relationships. The paper explains these results as distinguishing effective from spurious synergy, with low G3 being a sign of alignment. However, this does not rule out the phenomenon of apparent alignment due to excessive agent homogenization rather than better coordination. Furthermore, high I3 does not lead to better task performance. I3 may only measure information quantity rather than quality, or the task itself may not require complex synergy to solve. Therefore, I believe ToM may indeed change the interaction patterns between agents, but further validation is needed regarding I3's predictive power and whether ToM can be claimed as a superior mode.\n\nW3. The term \"emergence\" may be overused in this paper. Synergy does not necessarily represent the emergence of collective intelligence; it merely indicates that the joint predictive ability of agents exceeds the sum of their individual predictive abilities, which does not imply any cooperation or specialized roles. The paper is potentially imprecise in claiming specialized roles, using hierarchical models showing significant agent-level random intercepts and G3>0 as evidence. However, this cannot necessarily be attributed to roles but may stem from temperature randomness or prompt differences in the persona condition. It is difficult to determine whether this represents emergent behavior or merely the result of prompt engineering.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "3pWI5pMrUh", "reviewer": "Reviewer_st12", "summary": "The recent advancements in large language models have showcased the effectiveness of multi-agent systems. However, the authors argue that the performance gains in these multi-agent systems are not well understood, beyond the emergent behavior due to from interacting specialist agents. The core motivation is then to determine the threshold when a population of LLM agents transfers from a collection of agents into a productive collective. The authors investigate a group guessing game where agents must propose integers such that all integers sum a hidden unknown target, where the only feedback is binary high/low of the group sum. For this task to be successful, members of the group must fulfill complementary roles in an emergent way. The authors formulate three heuristics to measure the group synergy and emergence with the goal of quantifiability: practical criterion (prediction of delayed-release macro signal from instantaneous agent states), emergence capacity (median synergy estimate across all agent pairs), and coalition test (difference in predictive ability of a triplet compared to its most predictive pair). Each heuristic covers some needed insight that may not be available by the other heuristics. \n\nThe heuristics are used across two tests alongside null distribution: shuffling row wise to break agent identities, and shuffling column-wise to break time alignment. The authors propose a separate series of hierarchical models to differentiate agents across rounds. The main intervention in the paper is changing the text prompt input of each LLM agent, using either plain prompts (treating LLMs as human subjects), persona prompts (instructing each agent to respond conditional on anthropomorphic attributes), and theory of mind prompts (instructing agents to act based on what they perceive other agents to think). Empirical experiments using GPT4.1 and Llama-3.1-8b first showed that practical criterion for emergence is satisfied regardless of intervention. Next the hierarchical model showed that the most differentiation among agents occurs for Persona and ToM prompting. The coalition test is used to show that ToM agents tend towards higher task mutual information while coalition signal was lower, suggesting that among pairs of agents in the ToM set, there is a reinforcement of established roles with respect to the group goal. This is in contrast to the Persona set, which has a similar total mutual information to Plain (Figure 3b). A subset of experiments were repeated on Llama-3.1-8b but had mixed results due to the reduced generalization ability.", "questions": "- Considering the lower $G_3$ of ToM agents in Figure 3c, do the authors still see utility in the coalition test heuristic as a measure of the system's emergent synergy? It would seem that simply using the pairwise mutual information says more about the system capability than a triad approach in the group sum setting. In other words, for the specific task of group sum, triadic mutual information does not appear necessary for task success since Persona and Plain score higher, so it may be misleading to label triadic synergy as \"dynamical emergent synergy\" when pairwise synergy suffices.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "- The authors investigate the problem of emergent synergy in LLM-based agents, which is relevant to the NLP and multi-agent research communities, yet difficult to quantify. Tools from information theory and partial information decomposition are used to propose three heuristics.\n- The heuristics provide measurement tools to study task alignment among triads and pairs of agents, alongside the grounding of agent micro-states in the delayed system signal (practical criterion). These heuristics could have significance for the broader research community in studying emergent synergy of multi-agent systems.\n- The authors provide confidence values and error margin for each reported result. The plot rendering is generally high quality with only minor issues in some figures. The writing quality is high enough to convey the technical points.\n- The empirical analysis reveals some interesting insights about tuning LLM prompts to use ideas from ToM with GPT 4.1. These ideas do not necessarily transfer over to smaller models such as LLama-8b. An interesting takeaway from the analyses was that ToM prompts may reinforce pairwise identity assignments given to agents. The pairwise reinforcement, qualitatively speaking, may be reinforced first by the original system prompt of an agent, and again by the other agents projecting the identity onto the same agent during ToM reasoning.\n- For the group sum task, it is shown that triadic synergy may be spurious compared to strictly pair-wise synergy, in fact it may be detrimental as evidenced by Persona and ToM coalition measurements.", "weaknesses": "- The writing in some sections could be clarified to help motivate heuristics and models. For example \"Test of Agent Differentiation\" mixed model is not well motivated as a heuristic until reaching the results in Section 4.2, some sign posting would help clarify the utility.\n- Some conceptual details are not clear or self contained, such as the author's use of PID (L157), it is not clear how unique information and redundant information are formulated for the group sum task.\n- The notation needs some clarification to make the proposed formulation self-contained: the variables $t$, $l$, $k$ (L138-L144) should be introduced more naturally, and choice of $devs$ for target deviations may be changed to a single bold-face letter.\n- Typos: L335-L344 Figure 3 is referenced as Figure 4, L480 emergency -> emergent\n- Vertical figure subtitles are difficult to read and tend to clash with the figure identifier.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)