Self-Organizing Agent Network (SOAN)

• SOAN is a decentralized multi-agent system where local interactions produce emergent global behavior without relying on a central planner.
• It integrates diverse architectural patterns such as local task routing, shared-state coordination, and service-oriented workflows to manage dynamic agent populations.
• SOAN has practical applications in decentralized reasoning, scientific experimentation, enterprise workflow automation, and adaptive network control.

Searching arXiv for the cited SOAN-related papers to ground the article in current literature. A Self-Organizing Agent Network (SOAN) denotes a decentralized multi-agent arrangement in which agents, agent groups, or network nodes adapt their collaboration structure, task routing, or communication topology without a fixed central planner. Across recent arXiv literature, the term covers several closely related constructions: a “Self-Organizing Multi-Agent System (SO-MAS)” for local next-hop task routing (Yang et al., 30 Nov 2025), decentralized long-running scientific teams organized around a shared experimental state (Gao et al., 27 May 2026), structure-driven workflow automation in which structural units become agents (Xiong et al., 19 Aug 2025), and dynamic agent populations whose birth, specialization, and death follow equilibrium and demographic dynamics (Garnier, 23 Feb 2026). In a broader systems sense, SOAN also includes communication and control networks whose topology self-organizes through local learning or graph rewiring (Bakhshipoor et al., 10 Mar 2025, Yazicioglu et al., 2015). Taken together, these works define SOAN as a family of systems in which global behavior emerges from local policies, shared artifacts, structural decomposition, or adaptive topology control rather than from a single global scheduler.

1. Concept and formal definitions

In one explicit formulation, a self-organizing network is written as

$\mathcal{S} = \left\langle \mathcal{A}, \mathcal{C}^{\mathcal{A}, \phi_\pi \right\rangle,$

where $\mathcal{A} = \{a_i \mid i = 1, \dots, n\}$ is a set of agents, each agent $a_i$ has a description $\mathbf{Desc}(a_i)$, $$\mathcal{C}^{\mathcal{A}} = \{\mathcal{C}^{a_i} \mid a_i \in \mathcal{A}\}$$ gives each agent’s known successor candidates, and $\phi_\pi$ is the successor-selection policy (Yang et al., 30 Nov 2025). In that formulation, SOAN is a graph of agents with local neighborhood information and a local policy that determines the “next hop” for a task. The same paper distinguishes a centralized setting, in which all agents are globally visible, from a decentralized setting in which each agent knows only a small neighborhood, there is no central coordinator or global view, agents are heterogeneous, and communication and routing are local (Yang et al., 30 Nov 2025).

A second formalization treats SOAN as a variable population of autonomous micro-agents grouped into families. In the Agentic Hive framework, the population is $A_t$, family populations are $N_j(t)$, and demographic dynamics obey

$\dot{N}_j = \Phi_j(N) = V_j(N)\, N_j,$

where $V_j(N)$ is the marginal social value of one more agent in family $\mathcal{A} = \{a_i \mid i = 1, \dots, n\}$0 (Garnier, 23 Feb 2026). This makes agent creation, duplication, specialization, and death endogenous rather than fixed at design time. The paper proves existence of a Hive Equilibrium via Brouwer’s fixed-point theorem, Pareto optimality of the equilibrium allocation, multiplicity of equilibria under strategic complementarities between agent families, Stolper-Samuelson and Rybczynski analogs, Hopf bifurcation generating endogenous demographic cycles, and a sufficient condition for local asymptotic stability (Garnier, 23 Feb 2026).

A third formal perspective models self-organizing multi-agent systems as $\mathcal{A} = \{a_i \mid i = 1, \dots, n\}$1, where $\mathcal{A} = \{a_i \mid i = 1, \dots, n\}$2 is a concurrent game structure and $\mathcal{A} = \{a_i \mid i = 1, \dots, n\}$3 is a set of local rules (Luo et al., 2021). In that framework, agents act from local communication and prescribed rules, and one reasons about structural independence, semantic independence, and full contribution of coalitions to global behavior. This suggests that SOAN is not only an engineering pattern but also a formally analyzable class of systems in which local rules induce emergent global trajectories.

Across these definitions, the shared invariant is that self-organization is produced by local interactions, local observations, or local optimization rather than by a privileged planner. A plausible implication is that “SOAN” functions less as a single architecture than as a unifying systems concept spanning routing, experimentation, workflow execution, and topology formation.

2. Core architectural patterns

A recurring architectural pattern is local observation with local decision-making. In the SO-MAS/BiRouter setting, when agent $\mathcal{A} = \{a_i \mid i = 1, \dots, n\}$4 handles query $\mathcal{A} = \{a_i \mid i = 1, \dots, n\}$5, its observation is

$\mathcal{A} = \{a_i \mid i = 1, \dots, n\}$6

where $\mathcal{A} = \{a_i \mid i = 1, \dots, n\}$7 (Yang et al., 30 Nov 2025). Routing paths are then formed by repeated local successor choices,

$\mathcal{A} = \{a_i \mid i = 1, \dots, n\}$8

This yields a decentralized chain in which a globally useful route emerges from local next-hop decisions (Yang et al., 30 Nov 2025).

Another common pattern is shared-state coordination. In AutoScientists, all agents read and act on a shared experimental state $\mathcal{A} = \{a_i \mid i = 1, \dots, n\}$9 with four layers: the champion $a_i$0, experiment log $a_i$1, shared forum $a_i$2, and team-local state including queues $a_i$3 and dead-end registries $a_i$4 (Gao et al., 27 May 2026). Agents discover this state using a list–decide–read protocol, propose research directions, self-organize into teams, critique each other’s proposals, and re-open discussion when progress stalls (Gao et al., 27 May 2026). Here, the network is self-organizing not because links are absent, but because team structure, membership, and research direction assignment are generated by agent interaction with shared evidence.

Service-oriented formulations add another structural layer. In AaaS-AN, an Agent Network is a dynamic directed graph $a_i$5, with vertices representing individual agents or agent groups and edges representing routes that encode task-flow dependencies, context-flow, and collaboration patterns (Zhu et al., 13 May 2025). The framework distinguishes HARD routes for fixed collaboration patterns, SOFT routes for intra-group self-collaboration, and EXT routes for inter-group self-collaboration (Zhu et al., 13 May 2025). The associated RGPS decomposition maps Role to agent role knowledge $a_i$6, Goal to agent groups $a_i$7, Process to routes, and Service to executable service-oriented agents (Zhu et al., 13 May 2025). This suggests a SOAN variant in which self-organization happens through route reconfiguration over registered services rather than through message-passing alone.

Structure-driven workflow SOAN makes the structural unit itself the agent. There, atomic agents are defined as

$a_i$8

with goal $a_i$9, internal atomic process $\mathbf{Desc}(a_i)$0, tools $\mathbf{Desc}(a_i)$1, and context constraints $\mathbf{Desc}(a_i)$2 (Xiong et al., 19 Aug 2025). Composite workflows are formed through a structural composition operator $\mathbf{Desc}(a_i)$3, and failure-driven refinement uses linear insertion, branching, and nesting (Xiong et al., 19 Aug 2025). In this architecture, self-organization is inseparable from workflow structure.

3. Mechanisms of self-organization

A central mechanism in agentic task-routing SOAN is local scoring. BiRouter computes an Importance Branch and a Cohesion Branch,

$\mathbf{Desc}(a_i)$4

and combines them with candidate reputation as

$\mathbf{Desc}(a_i)$5

ImpScore estimates long-term importance to the global task goal, GapScore estimates contextual continuity for the current chain state, and reputation acts as a multiplicative gate that suppresses unreliable agents (Yang et al., 30 Nov 2025). The overall chain probability is

$\mathbf{Desc}(a_i)$6

This yields a decentralized Markov decision process whose decisions remain purely local (Yang et al., 30 Nov 2025).

Long-running experimentation uses self-organization through deliberation and roster formation. AutoScientists begins with no teams and a single discussion trigger in the forum $\mathbf{Desc}(a_i)$7. Agents propose axes, rank them with hypotheses, critique earlier proposals, and cast [DISCUSS-MORE] or [DISCUSS-DONE] votes; once a majority votes [DISCUSS-DONE], the alphabetically-last analyst that participated writes the roster $\mathbf{Desc}(a_i)$8 (Gao et al., 27 May 2026). When analysts detect stagnation, such as no improvement in the last 10 experiments or overly narrow proposals, they post new [DISCUSSION-TRIGGER] entries, leading to creation, merging, splitting, or retiring of teams (Gao et al., 27 May 2026). Self-organization here is a repeated cycle of team formation, critique, execution, and reorganization.

In workflow automation SOAN, self-organization is structural and evolutionary. For a new goal $\mathbf{Desc}(a_i)$9, related agents are retrieved by semantic similarity, decomposition proceeds recursively through

$$\mathcal{C}^{\mathcal{A}} = \{\mathcal{C}^{a_i} \mid a_i \in \mathcal{A}\}$$0

and candidate workflows are composed as

$$\mathcal{C}^{\mathcal{A}} = \{\mathcal{C}^{a_i} \mid a_i \in \mathcal{A}\}$$1

with the requirement

$$\mathcal{C}^{\mathcal{A}} = \{\mathcal{C}^{a_i} \mid a_i \in \mathcal{A}\}$$2

When verification fails, structure is repaired by linear insertion, branching, or nesting (Xiong et al., 19 Aug 2025). The agent pool is then controlled by life values

$$\mathcal{C}^{\mathcal{A}} = \{\mathcal{C}^{a_i} \mid a_i \in \mathcal{A}\}$$3

with positive terms from correct execution, symmetry-based reuse, and successful generalization, and negative terms from failures, semantic drift, and redundancy (Xiong et al., 19 Aug 2025).

Topology-focused SOANs rely on graph dynamics. In the random regular graph approach, agents rewire their local edges through graph-grammar rules so that the interaction graph converges in distribution to a connected random $$\mathcal{C}^{\mathcal{A}} = \{\mathcal{C}^{a_i} \mid a_i \in \mathcal{A}\}$$4-regular graph with $$\mathcal{C}^{\mathcal{A}} = \{\mathcal{C}^{a_i} \mid a_i \in \mathcal{A}\}$$5, where $$\mathcal{C}^{\mathcal{A}} = \{\mathcal{C}^{a_i} \mid a_i \in \mathcal{A}\}$$6 is the initial average degree (Yazicioglu et al., 2015). In the reinforcement-learning communication-network approach, each node adjusts its transmission radius using local observations—density, radius, and degree—to minimize a Hamiltonian

$$\mathcal{C}^{\mathcal{A}} = \{\mathcal{C}^{a_i} \mid a_i \in \mathcal{A}\}$$7

thereby producing a large communication cluster without a centralized administrator (Bakhshipoor et al., 10 Mar 2025). These variants show that self-organization may concern communication topology itself, not only task allocation.

4. Coordination substrates and information flow

SOAN implementations differ most sharply in the substrate used for coordination. One substrate is local neighborhood messaging. In BiRouter-based SO-MAS, each agent sees only the query and past chain, its own profile, and descriptions of its neighbors (Yang et al., 30 Nov 2025). The network is therefore local, decentralized, and open, with dynamic chains formed at runtime rather than precomputed (Yang et al., 30 Nov 2025).

A second substrate is a shared, evolving artifact store. AutoScientists coordinates through common artifacts rather than commands: champion $$\mathcal{C}^{\mathcal{A}} = \{\mathcal{C}^{a_i} \mid a_i \in \mathcal{A}\}$$8, experiment log $$\mathcal{C}^{\mathcal{A}} = \{\mathcal{C}^{a_i} \mid a_i \in \mathcal{A}\}$$9, shared forum $\phi_\pi$0, queues $\phi_\pi$1, dead-end registries $\phi_\pi$2, and team-local knowledge files (Gao et al., 27 May 2026). This allows long-horizon memory of both successes and failures, reduces redundant exploration, and enables reorganization without a central planner (Gao et al., 27 May 2026). A plausible implication is that shared-state SOANs are especially suited to tasks where failure memory and cumulative evidence are first-class objects.

A third substrate is formal service infrastructure. In AaaS-AN, service registration, discovery, interoperability, a Service Scheduler, and an Execution Graph provide runtime coordination, context tracking, and task-state management (Zhu et al., 13 May 2025). This arrangement supports agent groups, RPA workflows, and MCP servers within a single agent network, and the released dataset contains 10,000 long-horizon multi-agent workflows (Zhu et al., 13 May 2025). In this service-oriented variant, self-organization is mediated by discoverable services and typed routes rather than only by direct agent-to-agent reasoning.

A fourth substrate is hierarchical milestone management. TheBotCompany uses a three-phase state machine, Strategy $\phi_\pi$3 Execution $\phi_\pi$4 Verification, persistent manager agents, dynamic worker hiring and firing, a SQLite issue tracker, skill files, and asynchronous human oversight (Lyu et al., 26 Mar 2026). Workers are ephemeral, each worker belongs to exactly one manager, and verification can reject milestone completion claims and trigger corrective iterations (Lyu et al., 26 Mar 2026). This makes the network self-organizing at the level of project workforce composition.

Finally, some SOANs make information flow itself the object of formal reasoning. In the ATL-$\phi_\pi$5 framework, local rules are pairs $\phi_\pi$6 specifying who agent $\phi_\pi$7 communicates with and how received information maps to actions (Luo et al., 2021). Structural independence is defined by $\phi_\pi$8 for all $\phi_\pi$9, semantic independence is expressed as $A_t$0, and full contribution identifies minimal coalitions that both structurally and semantically determine a global property (Luo et al., 2021). This clarifies how local communications generate global patterns.

5. Empirical regimes and applications

Recent SOAN work spans at least four empirical regimes: decentralized reasoning, scientific experimentation, enterprise workflow automation, and network/control systems. In decentralized reasoning, BiRouter outperforms single-agent baselines, static multi-agent planners, and dynamic multi-agent methods; in a centralized MAS setting it reports average accuracy 91.73%, with gains of +5.86–7.06% versus single-agent baselines, +4.65–7.58% versus static MAS, and +4.52–5.23% versus dynamic MAS (Yang et al., 30 Nov 2025). In a local-information SO-MAS setting on GSM8K and HumanEval, BiRouter achieves 91.99% GSM8K accuracy at $A_t$1 tokens and 89.63% HumanEval Pass@1 at $A_t$2 tokens, compared with DyLAN and MaAS at higher cost or lower accuracy (Yang et al., 30 Nov 2025). These results are presented as evidence that local, score-based routing can preserve both performance and token efficiency under decentralization.

In long-running scientific experimentation, AutoScientists improves over prior AI agents under matched experimental budgets across biomedical machine learning, language-model training optimization, and protein fitness prediction (Gao et al., 27 May 2026). On BioML-Bench it reaches a mean leaderboard percentile of 74.4% across 24 tasks, improving over the strongest AI agent by +8.33%; on GPT training optimization it reaches a target validation bits-per-byte 1.9x faster than Autoresearch and continues discovering improvements from a starting champion where the single-agent approach finds none, with 7 accepted improvements versus 0; on ProteinGym fitness prediction it improves over the prior state of the art by +6.5% Spearman correlation across all 217 assays (Gao et al., 27 May 2026). In this regime, SOAN is tied to parallel exploration, memory of failed directions, and adaptive team restructuring.

In workflow automation, the structure-driven SOAN for enterprise workflows reports substantial gains under long and deeply nested execution paths. On gflowQA, SOAN attains 90.1 while AFlow attains 61.2; on PrOntoQA-OOD it reaches 90.8, compared with 81.3 for AFlow and lower values for CoT variants; on long linear and nested workflow scheduling, SOAN maintains pass@1 performance above 89% where AutoGen, Camel, and MetaGPT fall sharply with complexity (Xiong et al., 19 Aug 2025). The paper attributes this to explicit structural abstraction, workflow verification, structural hypothesis generation, and scale control (Xiong et al., 19 Aug 2025).

Service-oriented agent networks also report gains on reasoning and code generation. AaaS-AN reaches 63.62% on 504 MATH problems with qwen2.5-32b-instruct, compared with 57.52% for MetaGPT, 57.85% for AutoGen, and 35.13% for MACM, while maintaining token cost comparable to MetaGPT and lower than AutoGen (Zhu et al., 13 May 2025). It also describes a deployed MAS containing agent groups, RPA workflows, and MCP servers over 100 agent services (Zhu et al., 13 May 2025). This indicates a SOAN regime where interoperability and service composition are central.

Continuous software-development SOAN provides a different operational profile. TheBotCompany ran for 137 hours across four real-world software projects, completed 164 milestones and 616 cycles, and on ProjDevBench obtained average execution and overall scores of 53.2 and 70.0 respectively, compared with 43.6 and 59.3 for a Claude Code Sonnet 4.5 single-agent baseline (Lyu et al., 26 Mar 2026). Verification rejected 18.6% of verification cycles in the RustLaTeX project and 5.3% in M2Sim, demonstrating the role of independent verification as a stabilizing mechanism in long-horizon self-organization (Lyu et al., 26 Mar 2026).

Network-control applications show that the SOAN concept is not restricted to LLM systems. The RL-based communication network produces connectivity $A_t$3 in static scenarios and $A_t$4 in dynamic scenarios for the collaboration approach, while baseline large-radius connectivity is about 99.9% and 99.8% respectively, and pure NN without collaboration is about 77.0% and 78.4% (Bakhshipoor et al., 10 Mar 2025). The random-regular-graph SOAN raises algebraic connectivity in simulation from 0.02 to about 0.25 while keeping the network sparse (Yazicioglu et al., 2015). In distributed voltage regulation, subnetworks autonomously regroup through $A_t$5-decomposition and independently regulate voltages under changing conditions (Faiya et al., 2022). These systems show that SOAN includes classical distributed control and adaptive communications, not only agentic cognition.

6. Limitations, tensions, and open directions

Across the literature, three tensions recur. The first is decentralization versus global optimality. BiRouter addresses this through ImpScore, GapScore, and reputation (Yang et al., 30 Nov 2025); workflow SOAN addresses it through structural abstraction and verification (Xiong et al., 19 Aug 2025); AutoScientists addresses it through shared logs, discussion, and reorganization (Gao et al., 27 May 2026). This suggests that SOANs generally need a coordination substrate richer than unconstrained peer-to-peer exchange if they are to avoid local-myopic failure.

The second is adaptability versus stability. Agentic Hive shows formally that self-organizing populations can exhibit multiplicity of equilibria, endogenous cycles, and instability depending on externality strength and returns to scale (Garnier, 23 Feb 2026). The communication-network SOAN describes a phase transition in connectivity as density decreases, analogous to percolation in random geometric graphs (Bakhshipoor et al., 10 Mar 2025). Coordination work in communication networks models self-organizing mechanisms as coupled ODEs and shows that parallel stable loops can become unstable unless a coordination matrix $A_t$6 is chosen so that $A_t$7 (Tall et al., 2013). A plausible implication is that SOANs often require explicit stabilizers—reputation, verification, Lyapunov-style coordination, or bounded local actions—once agent interactions become dense.

The third is scalability versus observability. AutoScientists notes that communication is mostly text-based forum posts and that team size is fixed a priori, while dynamic scaling remains open (Gao et al., 27 May 2026). Workflow SOAN notes that its method assumes reusable atomic workflows and stable structural patterns, making it less suitable for highly creative or ad hoc domains (Xiong et al., 19 Aug 2025). TheBotCompany reports higher output-token cost per attempt than single-agent coding on average, even when overall scores improve (Lyu et al., 26 Mar 2026). Service-oriented SOAN lacks a fully formalized Execution Graph semantics and concrete interoperability protocol syntax (Zhu et al., 13 May 2025). These are not contradictions; they indicate that self-organization shifts cost from centralized planning to representation, memory, verification, or communication overhead.

Several open directions are explicit. AutoScientists points to structured exploration, topology maintenance, and more robust evaluation protocols (Gao et al., 27 May 2026). Agentic Hive points to empirical calibration, mechanism design for strategic agents, meta-Hives, continuous specialization manifolds, and chaos (Garnier, 23 Feb 2026). Workflow SOAN points to more adaptive optimization strategies, robustness to noisy feedback, and dynamic agent evolution beyond structured enterprise processes (Xiong et al., 19 Aug 2025). Formal logic work points to exponential worst-case complexity for full-contribution analysis and the need for graph-based decomposition (Luo et al., 2021). Together these suggest that future SOAN research is likely to focus less on the existence of decentralized behavior and more on verifiable governance of self-organizing systems under partial observability, noise, and changing objectives.