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Degrees of Freedom in Multi-Agent Coordination: Between Centralized and Decentralized Regimes

Yiqing Peng, Hehai Lin, Zixuan Wang, Dongyi Zhang, Zhengjie Zhu, Yi Han, Yangyang Zheng, Hao Wang, Qian Li, Chengwei Qin

arXiv:2610.17751v1cs.MAcs.AIcs.LG

TL;DR

Centralized and decentralized LLM-based multi-agent systems have complementary trade-offs, but intermediate configurations remain underexplored under matched conditions. The paper introduces DoF, a controlled configuration space between those regimes. Its organizational and performance patterns vary by task, with intermediate settings attaining the highest observed mean accuracy in several settings.

  • Problem

    Existing systems typically instantiate one complete architecture or optimize selected coordination mechanisms, leaving the space between centralized and decentralized coordination underexplored under matched conditions.

    Source: §1 · p. 2

  • Method

    DoF configures coordination between centralized and decentralized endpoints by jointly controlling delegated granularity and per-unit branch-routing probability.

    Source: §1 · pp. 2–3

  • Results

    Performance is task-dependent: intermediate configurations attain the highest observed mean accuracy in several settings, while endpoint or near-endpoint configurations remain preferable in others.

    Source: §1 · p. 3, §5.3 · p. 9

  • Takeaways & Limitations

    The findings characterize coordination as a task- and state-conditioned design choice rather than a fixed preference for either endpoint.

    Source: §1 · p. 3, §6 · p. 10

    Cross-branch comparisons concern branch-specific profile composition, not equality of work volume or specialization quality.

    Source: §3.3 · p. 6

Abstract

from arXiv · show

Large language model (LLM)-based multi-agent systems (MAS) are commonly organized around two coordination regimes. Centralized coordination provides explicit control but can create a bottleneck at a single coordination locus, whereas decentralized coordination offers local autonomy but must achieve effective collaboration through distributed decisions and experience. These trade-offs motivate a systematic study of the space between the two regimes. We introduce Degrees of Freedom (DoF), a continuous configuration framework that quantifies the size of the decision space delegated to downstream agents. DoF controls the granularity of delegated work and the target probability that each task unit is assigned to the branches. Its endpoints recover the two coordination regimes. Across multiple task domains, DoF reveals a hierarchy of organizational effects. Delegated granularity and within-regime routing produce structured but bounded profile reallocations, whereas task domain and retained experience are associated with stronger differences between the centralized- and decentralized-branch profiles. The resulting performance landscape is task-dependent: different domains favor different DoF configurations, while atomic-target conditions are more consistent across runs. In-domain retained experience brings the two branch profiles closer together. The same controlled sweep reveals a task-dependent coordination landscape: some domains exhibit higher-performing configurations, whereas others show flatter responses and no single configuration dominates across domains. In five of the six evaluated state, an intermediate DoF configuration achieves higher mean accuracy than both endpoints, demonstrating the value of exploring the coordination space between them. Together, these findings provide empirical guidance for studying and designing intermediate coordination regimes in LLM-based MAS.

1 INTRODUCTION

Centralized and decentralized coordination offer complementary advantages and costs, while leaving intermediate configurations underexplored under matched conditions. The introduction presents DoF as a controlled space between these endpoints and previews task-dependent organizational and performance findings.

1 INTRODUCTION

  • Centralized coordination offers global oversight but can bottleneck at one locus, whereas decentralized coordination offers local autonomy but depends on distributed decisions and experience.The two regimes have complementary advantages and structural costs rather than one universally preferable organization.Source: §1 · pp. 1–2
  • DoF uses delegated granularity and per-unit branch-routing probability to configure intermediate coordination between centralized and decentralized endpoints.At d = 0, coordination is centralized; at d = 1, it is decentralized. Within each granularity regime, increasing d raises the target probability of decentralized assignment.Source: §1 · pp. 2–3, Figure 1 · p. 2
  • The evaluation holds the model, five-agent roster, and branch implementations fixed while repeatedly sweeping 15 DoF configurations across five reasoning domains.The centralized and decentralized branches use MetaAgent and AgentNet, respectively, with Qwen3-Next-80B.Source: §1 · pp. 2–3
  • DoF treats centralized and decentralized coordination as endpoints of a common configuration space, jointly controlling delegated decision scope and processing locus.Its common index compares configurations between the endpoints without collapsing their distinct mechanisms into a third regime.Source: §1 · pp. 2–3
  • Task domain and retained experience are associated with stronger branch-profile differences than delegated granularity and within-regime routing, and performance preferences vary by task.In-domain retained experience brings the two branch profiles closer together; atomic-target conditions are generally more consistent across runs.Source: §1 · p. 3
  • Delegated granularity and routing produce bounded branch-profile changes, while task domain, execution branch, and retained experience are associated with stronger profile differences.The introduction also previews task-dependent accuracy peaks and greater run-to-run consistency for atomic-target conditions.Source: §1 · p. 3

2 RELATED WORK

Prior work studies centralized and decentralized architectures and analyzes organizational mechanisms through diagnostic and intervention-based approaches. This section positions DoF as a matched configuration-space study connecting the regimes and their intermediate settings.

2.1 AUTOMATIC MULTI-AGENT SYSTEMS

  • Centralized systems retain coordination authority in a controller, hierarchy, or generated workflow, while decentralized systems distribute execution and interaction decisions among agents.The former enable explicit control; the latter depend on local decisions, peer context, and retained agent state.Source: §2.1 · p. 3
  • Centralized and decentralized systems expose different organizational costs, and DoF represents them as endpoints of a common space with intermediate configurations modeled through granularity and routing.Intermediate configurations attain the highest observed accuracy in several settings, while endpoint or near-endpoint configurations remain preferable in others.Source: §2.1 · pp. 3–4

2.2 EMPIRICAL ANALYSIS OF AUTOMATIC MULTI-AGENT SYSTEMS

  • Prior empirical work examines organizational dimensions such as delegation, routing, roles, interaction paths, and retained experience through diagnostic and intervention-based views.These studies measure outcomes including performance, cost, robustness, and consistency.Source: §2.2 · p. 4
  • Existing studies typically vary mechanisms within particular architectures, whereas DoF holds the model, roster, and branch implementations fixed across 15 endpoint and intermediate configurations.It uses allocation profiles, cooperation paths, repeated-run accuracy, and retained-state comparisons to characterize organizational behavior and outcomes.Source: §2.2 · p. 4

3 DEGREES OF FREEDOM FRAMEWORK

DoF configures intermediate coordination by controlling delegated-unit granularity and branch assignment between centralized and decentralized endpoints. The Coordinator executes and aggregates routed units, while trace-derived distributions and Jensen–Shannon divergence characterize organizational profiles.

3.1 PROBLEM FORMULATION AND OVERVIEW

  • Intermediate DoF switches between atomic- and subtask-granularity regimes while varying the target probability of assigning units to the decentralized branch.At d = 0, the original request goes directly to centralized coordination; at d = 1, it goes directly to decentralized coordination.Source: §3.1 · p. 4

3.2 DOF-CONTROLLED EXECUTION

  • For intermediate configurations, the Coordinator decomposes the input into dependency-linked units, routes each ready unit, and aggregates completed outputs.It provides predecessor outputs as context and sends the original request directly to the corresponding branch at the endpoints.Source: §3.2 · pp. 5–6, §3.1 · p. 5
  • MetaAgent uses a plan–select–execute–review loop, whereas AgentNet agents execute, split, or forward assigned units using available context and retained experience.Coordinator decomposition sets a unit’s initial scope; AgentNet’s internal split operation can divide that unit further.Source: §3.2 · p. 6

3.3 TRACE-DERIVED ORGANIZATIONAL MEASUREMENTS

  • Branch-specific profile distributions normalize worker selections for centralized execution and node activations for decentralized execution; cross-branch comparisons concern profile composition, not work volume or specialization quality.The paper uses base-2 Jensen–Shannon divergence for aligned profile distributions, with values in [0, 1].Source: §3.3 · p. 6

4 EXPERIMENTAL SETUP

The experiments hold the model, agent roster, and branch implementations fixed while varying DoF across benchmarks and retained states. Repeated sweeps compare endpoints and intermediate configurations, including matched-routing comparisons of delegation granularity.

4 EXPERIMENTAL SETUP

  • All conditions use Qwen3-Next-80B, the same five-agent roster, and MetaAgent and AgentNet as the centralized and decentralized branches.DoF changes decomposition granularity, task-unit schedules, and per-unit branch assignments while the listed model and branch settings remain fixed.Source: §4 · p. 6
  • The primary BBH-trained state is evaluated on five domains, with a separate MMLU-Pro-trained state evaluated on MMLU-Pro; training and evaluation items are disjoint.Each retained state remains fixed throughout its evaluation sweep.Source: §4 · p. 7
  • Fifteen DoF values span the centralized and decentralized endpoints and atomic-target and subtask-target regimes; datasets receive three sweeps, except MMLU-Pro-trained, which receives two.The evaluated values range from 0 to 1 and include intermediate configurations.Source: §4 · p. 7
  • Granularity comparisons use six pairs matched for target probability of assignment to the decentralized branch.Figure 3 compares profile changes from atomic-target to subtask-target delegation and contrasts granularity, routing, and repeated-run effects; colors encode effect type and opacity encodes branch.Source: §4 · p. 7, Figure 3 · p. 7

5 RESULTS

Across the results, local DoF adjustments produce bounded profile changes, while task domain, execution branch, and retained experience are associated with stronger organizational differences. Accuracy peaks and run-to-run consistency vary by task and configuration.

5.1 DELEGATED GRANULARITY AND ROUTING AFFECT BRANCH-SPECIFIC PROFILES

  • Granularity changes produce localized profile reallocations, while within-regime routing changes are also bounded, with all plotted JSD values below 0.2.Matched-q granularity differences and within-regime routing differences are of similar order for several dataset–branch pairs; Figure 3 compares these effects with repeated-run variation.Source: §5.1 · pp. 7–8

5.2 BRANCH-SPECIFIC PROFILES VARY ACROSS TASK DOMAINS AND RETAINED STATES

  • Task domain and execution branch are associated with distinct profiles, and the MMLU-Pro-trained retained state reduces cross-branch JSD from approximately 0.583 to 0.015.Figure 4 compares branch-normalized profile composition across domains and retained states, not absolute workload volume.Source: §5.2 · pp. 8–9, Figure 4 · p. 8

5.3 COORDINATION CONFIGURATIONS AFFECT ACCURACY CONSISTENCY AND TASK PERFORMANCE

  • BBH peaks at the decentralized endpoint, but the other five settings reach their highest observed mean accuracy between endpoints; no DoF configuration dominates across tasks.The MMLU-Pro-trained setting has two tied intermediate peaks; the results support task-conditioned configuration, not a universally best DoF.Source: Table 1 · p. 9, §5.3 · p. 9
  • Atomic-target conditions are generally more consistent across repeated runs than subtask-target conditions.For datasets with valid complete-run variance estimates, every reported subtask-to-atomic variance ratio exceeds one; mean accuracy and reproducibility are distinct.Source: §5.3 · p. 9

6 CONCLUSION

The conclusion presents DoF as a controlled framework connecting centralized and decentralized coordination through delegated decision space. It summarizes configuration, organizational, performance, and stability findings, and the supplementary roadmap identifies the additional implementation and evaluation materials.

6 CONCLUSION

  • DoF connects centralized and decentralized LLM-based multi-agent systems through the size of decision space delegated to downstream agents.The conclusion describes configuration changes as modest profile influences, with task domain, execution branch, and retained state providing stronger organizational conditions; organization is associated with performance and stability.Source: §6 · p. 10

A SUPPLEMENTARY ROADMAP

  • The supplementary material covers implementation settings, datasets and retained states, DoF sweeps, MMLU-Pro sampling, routing fidelity, and trace-archive limits.It also documents prompt contracts and the error-handling protocol.Source: A SUPPLEMENTARY ROADMAP · p. 14

B IMPLEMENTATION DETAILS AND PROMPT CONTRACTS

The implementation uses a shared model and agent roster across two coordination branches, with distinct capability profiles and branch-specific prompts, controls, and execution limits. The appendix describes reusable prompt contracts and dataset-specific evaluation settings.

B.1 MODEL AND AGENT ROSTER

  • All five agent profiles use Qwen3-Next-80B and share interfaces and memory procedures, differing only in their initialized capability vectors.The vectors encode seven dimensions, including reasoning, mathematics, language, knowledge, sequence, spatial, and inference.Source: §B.1 · p. 14

B.2 AGENT GRAPH AND RETAINED STATE

  • AgentNet starts with a complete directed five-agent graph; retained state can include capability values, success statistics, edge weights, router experience, and executor experience.Edge weights update from forwarding outcomes and execution time, and edges below the active threshold are removed; the loaded state remains fixed during each primary sweep.Source: §B.2 · p. 14

B.3 EXECUTION AND MODEL-CALL SETTINGS

  • AgentNet is limited to three forward hops and five executions per task, while MetaAgent allows twelve planning rounds and one redo per step.The AgentNet router and executor retrieve three experiences by default, and executor memory is limited to 40.Source: §B.3 · p. 14

B.4 PROMPT CONTRACTS

  • The Coordinator receives task, granularity, and dependency-mode instructions and returns unit descriptions without solving the task; parsing failures trigger one retry and then a single-unit fallback.Runtime prompts also insert dynamic task text, retrieved experiences, agent states, and prior results.Source: §B.4 · p. 15
  • Coordinator aggregation assembles or extracts answers from completed unit outputs without new computation, while MetaAgent plans steps, selects workers, and reviews execution.MetaAgent review can complete, continue, or redo a step.Source: §B.4 · p. 15
  • AgentNet’s router chooses among execute, split, and forward, and its executor runs the current request or an internally split unit before a separate completion check.The appendix gives reusable contracts rather than task-populated prompt dumps; runtime values and configuration details are excluded pending license, privacy, and credential review.Source: §B.4 · p. 15
  • The repeated sweeps target fifteen DoF conditions, with summary-run cohort sizes of 3/3/3/2/3/3 and failed or missing conditions retained explicitly.The table presents the training-state and evaluation allocation in canonical analysis order.Source: Table 2 · p. 16

B.5 DATASET PROFILES

  • BBH and MMLU-Pro use parallel task-unit dependencies, whereas AIME, RBench-T, and SMFR use sequential dependencies; dataset profiles also specify answer format, extraction, and aggregation.Correctness is evaluated after the final output is produced.Source: §B.5 · p. 16

C.1 EVALUATION COLLECTIONS AND SWEEP ALLOCATION

The evaluation uses disjoint training and evaluation items across retained-state settings and records explicit run failures rather than imputing missing accuracy. Available summaries and cooperation paths support repeated-run and branch-profile analyses, but the raw per-task traces are not retained.

C.1 EVALUATION COLLECTIONS AND SWEEP ALLOCATION

  • The BBH-trained state uses 634 disjoint training items and is evaluated across five domains, while the MMLU-Pro-trained state uses 600 training items and a separate MMLU-Pro evaluation sample.Training and evaluation items are disjoint within each retained-state setting.Source: §C.1 · p. 16

C.2 RUN AND ERROR HANDLING

  • Incomplete planned cohorts remain in condition records but are excluded from variance summaries; failed or null conditions retain errors, and missing accuracy is never imputed.Accuracy means use all valid observed runs, whereas variance comparisons require a complete planned cohort.Source: §C.2 · p. 16

C.3 TRACE INSTRUMENTATION AND AVAILABLE RECORDS

  • The analysis checkout lacks raw per-task traces, so quantitative analyses cannot reconstruct question text, answers, dependency graphs, or branch communications.The execution runner supports a fuller trace schema, but current records preserve summaries and derived task-level paths instead.Source: §C.3 · p. 16
  • Preserved records include correctness, DoF, cooperation paths, path length, condition accuracy, routed-unit counts, and realized assignment fractions for alignment and profile analyses.These fields also support repeated-run, matched-routing, routing-fidelity, and retained-state comparisons.Source: §C.3 · p. 16
  • Figure 5 compares target and realized decentralized assignment fractions across collections and retained-state settings, showing individual runs, condition means, and agreement with the target.Marker shape distinguishes atomic-target from subtask-target conditions; endpoint conditions are excluded.Source: Figure 5 · p. 17

D MMLU-PRO SAMPLING QUOTAS

  • The MMLU-Pro training and evaluation samples preserve the original fourteen-category proportions through largest-remainder allocation and are disjoint.The samples contain 600 training items and 168 evaluation items.Source: D MMLU-PRO SAMPLING QUOTAS · p. 17, Table 3 · p. 17

E SUPPLEMENTAL ROUTING-CONTROL VALIDATION

The routing-control validation compares each intermediate condition’s target assignment probability with its realized decentralized assignment fraction. Deviations are small on average but expected when finite task-unit counts limit assignment draws.

E SUPPLEMENTAL ROUTING-CONTROL VALIDATION

  • Finite numbers of routable units can produce deviations from target probabilities, especially with coarser subtask decompositions that yield fewer assignment draws.Assignments are sampled independently, so realized fractions need not equal the target within a run.Source: E SUPPLEMENTAL ROUTING-CONTROL… · p. 17
  • Across 216 valid intermediate run–condition points, mean absolute deviation from the routing target is 0.0098.This comparison measures routing-control fidelity, not task accuracy.Source: E SUPPLEMENTAL ROUTING-CONTROL… · p. 17
  • The validation sidecar records the complete point set and all 39 exclusions from the 255-condition planned matrix: 34 endpoints, four failed intermediate conditions, and one missing intermediate condition.Source: E SUPPLEMENTAL ROUTING-CONTROL… · p. 18

F ANALYSIS ARTIFACTS AND AVAILABILITY

The analysis artifacts derive from condition summaries and task-level cooperation-path records, with errors and missing states kept explicit. Because raw per-task traces are absent, the manuscript restricts its claims to the available summaries and paths.

F ANALYSIS ARTIFACTS AND AVAILABILITY

  • The canonical collection contains 33,030 unique task-path records, alongside 1,785 same-run DoF pairs and 328 matched-routing granularity pairs.The surviving records are condition summaries and task-level cooperation paths.Source: F ANALYSIS ARTIFACTS AND AVAILABILITY · p. 18
  • Validation joins 32,348 path records to valid condition summaries and accounts separately for 144 null or error records, 442 empty paths, and 96 unmatched records.The analysis runner produces accuracy, profile, routing, repeated-run, validation, and provenance outputs without imputing missing accuracy.Source: F ANALYSIS ARTIFACTS AND AVAILABILITY · p. 18
  • Without raw per-task trace JSON, the checkout cannot recover task text, decomposition responses, dependency graphs, model answers, review decisions, or communication content.Manuscript claims are restricted to condition summaries and derived cooperation-path records.Source: F ANALYSIS ARTIFACTS AND AVAILABILITY · p. 18

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