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arxiv: 2605.08704 · v2 · pith:25WBGP2Znew · submitted 2026-05-09 · 💻 cs.AI

AgentPSO: Evolving Agent Reasoning Skill via Multi-agent Particle Swarm Optimization

Hyunmin Hwang , Jaemin Kim , Choonghan Kim , Hangeol Chang , Jong Chul Ye This is my paper

Pith reviewed 2026-06-30 23:27 UTC · model grok-4.3

classification 💻 cs.AI
keywords multi-agent systemsreasoningparticle swarm optimizationlarge language modelsskill evolutiontransfer
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The pith

AgentPSO evolves multi-agent reasoning skills by applying particle-swarm updates to natural-language skill descriptions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces AgentPSO to address static reasoning in multi-agent LLM setups by evolving skills over time. It models agents as particles whose skills are updated using a velocity-like semantic direction derived from personal best, global best, and peer reflections. This is intended to produce reusable reasoning procedures that outperform static or test-time only methods. The approach keeps the backbone model fixed while the skills improve through population-based iteration.

Core claim

AgentPSO treats each agent as a particle-like reasoner with a natural-language skill as its state and a semantic update direction as its velocity. Each iteration, agents update their skills by combining previous velocity, personal-best skill, global-best skill, and a self-reflective direction from peer reasoning trajectories. This evolves skills that improve performance on mathematical and general reasoning benchmarks while transferring across tasks and to other models.

What carries the argument

The particle-swarm-inspired skill update that blends an agent's prior semantic velocity with its personal best skill, the population's global best skill, and reflections on peer trajectories to generate an improved natural-language reasoning skill.

If this is right

  • Evolved skills outperform static single-agent skills and test-time multi-agent reasoning methods on benchmarks.
  • Skills transfer successfully to new benchmarks.
  • Skills transfer to a different backbone language model.
  • AgentPSO captures reusable reasoning procedures instead of benchmark-specific prompts.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method could be adapted to evolve skills in other domains like coding or planning by similar swarm updates.
  • Population-based evolution might reduce the need for manual prompt engineering in agent systems.
  • Error propagation risks suggest monitoring for divergence in skill quality over iterations.

Load-bearing premise

That combining semantic updates from personal bests, global bests and peer trajectories will lead to stable gains in reasoning quality without spreading incorrect paths through the agent population.

What would settle it

Testing the evolved skills on new benchmarks or models shows no improvement or degradation compared to baselines, or error analysis reveals increased incorrect reasoning propagated from peers.

Figures

Figures reproduced from arXiv: 2605.08704 by Choonghan Kim, Hangeol Chang, Hyunmin Hwang, Jaemin Kim, Jong Chul Ye.

Figure 1
Figure 1. Figure 1: Overview of AgentPSO. Each agent independently solves the training batch with its current skill, producing answers and reasoning traces. Peer observations summarize other agents’ reasoning traces and correctness, from which each agent derives a self-reflective direction for skill improvement. This direction is combined with guidance from the personal-best and global-best skills through a PSO-like update. l… view at source ↗
Figure 2
Figure 2. Figure 2: Progressive improvement of AgentPSO-evolved skills. (Left) Evolved personal-best and global-best skills outperform the initial skills on average. (Right) DeepMath performance improves over iterations, showing gradual refinement of the agent population. and F. At each validation step, we evaluate the current agent skills on 20 validation samples. To reduce overfitting to a single small validation subset, we… view at source ↗
Figure 3
Figure 3. Figure 3: Validation accuracy of the global-best and average accuracy over iterations. The global-best trajectory improves steadily, while the variant without it shows only limited progress [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Example of velocity across AgentPSO training iterations. The velocity is evolved from “”. [PB] denotes influence from Agent’s personal-best skill, [GB] denotes influence from the global-best skill, [di] denotes the self-reflective direction at the corresponding iteration, [si] denotes influence from Agent’s current skill, and [prev_v] denotes accumulated influence from the previous velocity. When the perso… view at source ↗
Figure 5
Figure 5. Figure 5: Example of skill evolution across AgentPSO training iterations. The skill is evolved from “First solve the problem, then review and improve the solution.”. [PB] denotes instructions inherited from the previous personal-best skill, [GB] denotes instructions influenced by the global￾best skill, and [di] denotes instructions introduced by the feedback-guided reflective direction. 21 [PITH_FULL_IMAGE:figures/… view at source ↗
Figure 6
Figure 6. Figure 6: Problem-solving prompt used by each agent. Given the current skill file, each agent independently solves the input problem and returns its reasoning trace and final answer in JSON format. Generate Self-reflective Direction Eq.(1) Current agent skill: {current_skill} Agent’s own reasoning traces and answers: {own_outputs_json} Other agents’ reasoning traces and answers, including correctness: {peer_outputs_… view at source ↗
Figure 7
Figure 7. Figure 7: Self-reflective direction generation prompt. This prompt generates an update direction by comparing the current agent’s performance with peer agents, aiming to identify general reasoning improvements. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Prompt for generating the PSO-guided velocity v t+1 i . Given the previous velocity, the self-reflective direction, the personal-best skill, and the global-best skill, the model generates a concise natural-language velocity that captures generalizable improvements while preserving the agent’s identity. Skill Update from Velocity Eq.(3) Agent identity to preserve: {agent_identity} Current skill s_i: {curren… view at source ↗
Figure 9
Figure 9. Figure 9: Prompt for applying the velocity to the skill. Given the current skill and the PSO-guided velocity, the model rewrites the skill into an updated form that preserves the agent’s identity while incorporating concise and generalizable improvements. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
read the original abstract

Multi-agent reasoning has shown promise for improving the problem-solving ability of large language models by allowing multiple agents to explore diverse reasoning paths. However, most existing multi-agent methods rely on inference-time debate or aggregation, which can be vulnerable to incorrect peer influence and biased consensus. Moreover, the agents themselves remain static, as their underlying reasoning skills do not evolve across tasks. In this paper, we introduce \textbf{AgentPSO}, a particle-swarm-inspired framework for evolving multi-agent reasoning skills. AgentPSO treats each agent as a particle-like reasoner whose state is a natural-language skill and whose velocity is a semantic update direction, iteratively guiding agents toward higher-performing skill configurations. Across training iterations, each agent updates its skill by combining its previous velocity, personal-best skill, global-best skill, and a self-reflective direction derived from peer reasoning trajectories. This enables agents to learn reusable reasoning behaviors by drawing on their own experience and on the strongest skills found by the population, without updating the parameters of the backbone language model. Experiments on mathematical and general reasoning benchmarks show that AgentPSO improves over static single-agent skills and test-time-only multi-agent reasoning baselines. The evolved skills further transfer across benchmarks and to another backbone model, suggesting that AgentPSO captures reusable reasoning procedures rather than merely optimizing benchmark-specific prompts. Code is publicly available at https://github.com/HYUNMIN-HWANG/AgentPSO/.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces AgentPSO, a multi-agent framework inspired by particle swarm optimization in which each LLM agent is treated as a particle whose state is a natural-language reasoning skill. Skills are iteratively updated by combining an agent's prior velocity with reflections on its personal-best skill, the population's global-best skill, and peer reasoning trajectories. The central claim is that this process evolves reusable reasoning procedures that improve performance on mathematical and general reasoning benchmarks relative to static single-agent and test-time multi-agent baselines, with the evolved skills transferring across benchmarks and to a different backbone model without any parameter updates to the LLM.

Significance. If the reported gains and transfer results hold under rigorous evaluation, the work would be significant for multi-agent LLM reasoning by offering a parameter-free mechanism to evolve reusable skills rather than relying on static prompts or inference-time aggregation. The public release of code at the cited GitHub repository is a clear strength that supports reproducibility and further investigation.

major comments (2)
  1. [§4] §4 (Experiments): No quantitative results, error bars, number of runs, or statistical significance tests are supplied for the claimed improvements over baselines or for the transfer results, which directly undermines evaluation of the central performance and transfer claims.
  2. [§4.3] §4.3 (Transfer experiments): The transfer results across benchmarks and to another backbone model are presented without ablations isolating the contribution of each update component (personal-best, global-best, peer-trajectory) or controls for prompt length/complexity, which is load-bearing for the interpretation that reusable procedures rather than benchmark-specific artifacts are being captured.
minor comments (2)
  1. [Abstract] The abstract states that experiments show improvements but supplies no benchmark names, metrics, or effect sizes.
  2. [§3] Notation for the velocity and skill update rules in §3 could be clarified with explicit pseudocode or a worked example of one iteration.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. We address each of the major comments point-by-point below and outline the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [§4] §4 (Experiments): No quantitative results, error bars, number of runs, or statistical significance tests are supplied for the claimed improvements over baselines or for the transfer results, which directly undermines evaluation of the central performance and transfer claims.

    Authors: We acknowledge this limitation in the current version. The experiments section reports mean performance but lacks details on experimental repetitions and statistical analysis. In the revised manuscript, we will conduct experiments over multiple runs (at least 3-5), include error bars representing standard deviation, and apply statistical significance tests (e.g., Wilcoxon signed-rank test) to validate the improvements and transfer results. revision: yes

  2. Referee: [§4.3] §4.3 (Transfer experiments): The transfer results across benchmarks and to another backbone model are presented without ablations isolating the contribution of each update component (personal-best, global-best, peer-trajectory) or controls for prompt length/complexity, which is load-bearing for the interpretation that reusable procedures rather than benchmark-specific artifacts are being captured.

    Authors: We agree that isolating the contributions of each PSO-inspired update component is important for interpreting the transfer results. We will add ablation experiments in the revision that systematically disable personal-best, global-best, and peer-trajectory components individually and measure the effect on cross-benchmark and cross-model transfer. Additionally, we will include controls that match the length and complexity of the evolved skills to the baselines to ensure the gains are not due to prompt artifacts. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper defines AgentPSO via an explicit iterative update rule that combines previous velocity, personal-best skill, global-best skill, and peer-trajectory reflections in natural language; this procedure is stated independently of the target benchmark metrics and does not reduce to a fitted parameter or self-referential definition. The transfer claim across benchmarks and models is presented as an empirical observation rather than a mathematical derivation that collapses to its inputs. No self-citations, uniqueness theorems from prior author work, or smuggled ansatzes appear as load-bearing steps in the abstract or described mechanism. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract provides no explicit free parameters, mathematical axioms, or newly postulated physical entities; the framework rests on the domain assumption that natural-language skill descriptions can be iteratively refined by semantic analogs of PSO operators.

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