A novel framework based on Koopman operator theory is developed and validates its theoretical guarantees on multi-agent consensus dynamics, making spectral certification a practical layer for trustworthy collective reasoning.
Abstract
Orchestrated collectives of large language model (LLM) agents that debate and vote are an emerging form of computational intelligence: the intelligent behaviour resides in the \emph{interaction}, not in any single agent. They improve task accuracy, yet remain black boxes at the system level: there is no principled test of convergence, no bound on the rounds needed, and no faithful account of what drove a decision. This paper develops a novel framework based on Koopman operator theory and validates its theoretical guarantees on multi-agent consensus dynamics. Treating the collective as one nonlinear dynamical system on a communication graph, we read its essential behaviour off the spectrum of its Koopman transfer operator, an exact linear representation of the nonlinear dynamics estimated from interaction traces. The spectrum yields three machine-checkable certificates: the sub-dominant eigenvalue $\lambda_2$ fixes the intrinsic timescale of reasoning and yields a convergence deadline computable \emph{before} the debate runs; its eigenvector names the coherent factions the collective reasons in, and $|\lambda_2|$ certifies when that explanation is valid; and the leading spectral coordinates form a compressed, auditable message basis. On an attention-consensus model, the deadline tracks observed convergence with log--log correlation $0.93$ and bounds it in 96\% of 24 configurations; attribution is exact whenever the spectrum certifies metastability; eight of 32 coordinates preserve the decision at 99.7\% fidelity; and a certificate learned from 15 debates held on 60/60 held-out debates. The study runs in minutes on a CPU, making spectral certification a practical layer for trustworthy collective reasoning.
Multi-agent LLM systems commonly use an orchestrator to decompose a task for a team of workers and then improve through textual reflection. Despite strong empirical results, these systems lack a unified account of coordination, memory improvement, and the role of external verification. We model orchestrator-worker interaction as a bilevel coordination game: under bounded coupling, the workers'local-update game is an approximate potential game whose equilibrium slack is controlled by decomposition quality. We then analyse reflection as stochastic movement over semantic memory states. For free-form reflection, we derive a finite-time upper bound, prove worst-case tightness, and give a positive lower bound under a falsifiable persistent-harm condition. We further prove an information-theoretic impossibility result: no gate that observes only the generated transcript can improve uniformly over text-indistinguishable environments, whereas an environment-grounded gate can. Motivated by this separation, we introduce Stochastic Reflective Memory Ascent (SRMA), which accepts a candidate memory only after a grounded evaluation risk strictly decreases. Under calibration and non-degenerate corrective mass, SRMA converges exactly, geometrically or polynomially; matching constructions show that both rate regimes are order-tight. We also provide confidence gating for stochastic evaluation and re-anchoring guarantees for piecewise-stationary environments. Experiments instantiate these objects with environment-grounded metrics and test the predicted coordination and drift laws. On 500 SWE-bench instances, the complete Kimi-based system resolves 72.2% versus a 70.8% public mini-SWE-agent reference. Code: https://github.com/YihangChen9/Bilevel-Coordinated-Reflection
Yihang Chen, Yu-Xiang Chen, Yuxuan Huang et al.· 0 citations
Multi-agent systems powered by large language models (LLMs) have demonstrated potential for collaborative problem-solving, yet increasing the number of agents often introduces redundant reasoning and communication overhead, sometimes degrading performance. We propose AgentDropout, a dynamic strategy inspired by dropout regularization in neural networks, which selectively deactivates low-contribution agents during multi-agent collaboration. At each round of discussion, AgentDropout computes a semantic novelty score for every agent by measuring the divergence of its output relative to the current group consensus. Agents whose novelty score falls below an adaptive threshold are temporarily deactivated, reducing token consumption without sacrificing viewpoint diversity. We evaluate AgentDropout on mathematical reasoning (GSM8K), commonsense reasoning (StrategyQA), and collaborative code generation (HumanEval) tasks. Across three independent runs, AgentDropout achieves accuracy comparable to or modestly above fixed 5-agent debate while reducing total token consumption by 38.0–43.5% and debate rounds by 20.5% on average. Pareto analysis reveals a promising efficiency–quality trade-off, suggesting that dynamic agent deactivation may be useful for deploying multi-agent LLM systems under computational budget constraints.
Zhengxi Xiao, Qi Guo, Yuyue Wang et al.· 2026 8th International Confe...· 1 citation
A recurring question in the design of scalable multi-agent systems -- from robot swarms to collectives of large-language-model (LLM) agents -- is whether adding more agents can, on its own, overcome performance limits, or whether a qualitatively \emph{deeper} organization is required. A recent preprint argues that flat, homogeneous multi-agent systems face an irreducible, population-independent ``causal floor''on achievable error, removable only by hierarchical (nested-loop) organization. Using a controlled disturbance-rejection testbed with an exactly computable optimum, we show this conclusion is too strong and replace it with a quantitative resource model built on three resources: population \emph{width} $N$, per-agent internal-model \emph{memory} $d$, and prediction across the observation \emph{delay} $\tau$. We establish three claims. (i) The achievable floor is governed not by architectural hierarchy but by per-agent internal-model content: a flat, homogeneous swarm whose agents carry a matched internal model of the disturbance matches or beats a designed two-loop hierarchy at equal per-agent memory -- so temporal depth can be dynamical (recurrent memory), not architectural (nesting). (ii) The three resources are \emph{not mutually interchangeable}; we chart the exchange rates and the hard non-exchange boundaries on an explicit width$\times$memory map, including a strict equal-total-state-budget comparison. (iii) A residual floor is set by the observation delay and the environment's unpredictability over that horizon, which we verify against the optimal controller. We quantify the price of replacing oracle knowledge of the disturbance spectrum with online learning, provide a preliminary robustness check against a mild bounded nonlinearity and a spatially-extended plant, and distill four design rules for practitioners.
The collaboration tax is formulated as the team-decentralisation loss of a two-player cooperative game with private information, with two propositions characterising its sign and its equivalence to a max-superadditivity violation.
Wei-Xiang Sun, Zehong Wang, Hong Huang et al.· 0 citations
Shared autonomy requires principled mechanisms for allocating and transferring control between a human and an autonomous agent. Existing approaches often rely on blending control inputs or heuristic switching rules, which lack theoretical guarantees and fail to account for the dynamics of authority transfer. This paper develops a cooperative game-theoretic framework for authority switching in shared autonomy. We formulate the control switching problem as an identical-interest dynamic game in which authority transitions are embedded into the system dynamics, yielding optimal switching policies rather than ad hoc rules. We establish the existence and characterization of team-optimal policies in pure strategies under stochastic human override, accounting for asymmetric authority where humans retain override capability. For linear-quadratic systems, we derive closed-form recursions for the optimal switching policies and value functions, enabling efficient computation independent of the continuous state. We validate the framework on scalar and multi-dimensional linear systems, demonstrating how optimal switching adapts to varying system dynamics, cost structures, and override probabilities. The results reveal fundamental trade-offs between human adaptability and autonomous efficiency, illustrating the practical benefits of grounding shared autonomy in cooperative game theory.
Decentralized populations of Large Language Model (LLM) agents can spontaneously reach consensus on shared conventions, yet the microscopic mechanisms by which their internal stochasticity shapes macroscopic ordering remain unexplored. We study a minimal LLM Naming Game in which the listener's decision is a single-token LLM call at decoding temperature $T$, replacing the inventory check of the deterministic Naming Game. Each interaction decomposes into an in-inventory and an out-inventory channel with conditional rates $\pi(T)\!\equiv\!P(\text{YES}\mid w\in P_j)$ and $\phi(T)\!\equiv\!P(\text{YES}\mid w\notin P_j)$, whose balance controls an ordering-disordering drift. A mean-field theory of the two-rate dynamics yields an analytical ordering condition that generalizes the consensus threshold of the stochastic Naming Game to a critical line in the $(\pi,\phi)$ plane. Across three open-weight architectures, consensus is always reached, but through three distinct listener regimes: permissive (repaint-noise dominated), near-deterministic, and conservative (missed-collapse dominated). The effective finite-size exponent $\beta(T)$ in $t_{\rm conv}\!\sim\!N^{\beta}$ shifts with temperature, and the temperature-sensitivity $\alpha$ in $t_c\!\sim\!e^{\alpha T}$ ranges from ${\approx}\,0.67$ to ${\approx}\,0$ across architectures. Decoding temperature thus emerges as an architecture-dependent control parameter for decentralized LLM populations, quantitatively characterized by the statistical-physics toolkit.
C. Nobili, Vijayasri Iyer, A. Codello et al.· 0 citations
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