Predictive Maps of Multi-Agent Reasoning: A Successor-Representation Spectrum for LLM Communication Topologies

The integration of iterative LLMs within multi-agent diagnostic frameworks requires a rigorous quantitative reevaluation of underlying communication topologies. Frequently used architectural paradigms depend on scale-free or small-world networks, assuming optimal communication efficiency. Our study mathematically dismantles that assumption for semantic data. By mapping multi-agent communication uncertainty trajectories onto a 768-dimensional Bio_ClinicalBERT embedding space via an analytical isotropic variance proxy using Barab'asi--Albert (BA) and Watts--Strogatz (WS) networks, we prove that structural bottlenecks compromise diagnostic safety. Our phase transition matrices illustrate that localized dense cliques confine hallucinated data, preventing global consensus and forcing the system toward a permanent entropy saturation threshold of $H_{\infty} \approx 5.947$. As a result, we measure a severe terminal cosine similarity degradation of 53.29%, completely overwriting the original ground-truth. Moreover, the terminal semantic drift reveals a catastrophic variance amplification of 51.81% ($ρ= 1.5181$) in highly clustered architectures, proving total system unpredictability when compared to Erdős--R'enyi configurations ($ρ= 1.0766$). Instead of reducing errors, hub-centric systems autonomously compound localized hallucinations. By introducing dynamic spectral monitoring operating at an $\mathcal{O}(N^3)$ time complexity and imposing a strict lower bound on algebraic connectivity ($λ_{2_{min}}$) via the continuous eigen-decomposition of the graph Laplacian, we present a mathematically rigorous technique to ensure global state diffusion. Securing the reliability of autonomous medical diagnostics necessitates treating topological stability as a non-negotiable quantitative imperative.

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 $λ_2$ 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 $|λ_2|$ 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.

Large language model-driven multi-agent systems enhance the reliability of complex reasoning tasks through multi-round deliberation, role specialization, and cross-validation. However, existing multi-agent debate and collaboration frameworks typically adopt fully connected communication, causing the number of messages, token costs, and end-to-end latency to grow approximately quadratically with the number of agents; although fixed sparse topologies reduce overhead, they cannot adapt communication relationships to different task instances or intermediate reasoning states, making them prone either to preserving low-value interactions or to losing critical error-correction information. To address this problem, this paper proposes DySCo (Dynamic Sparse Consensus), a dynamic trust-aware sparse consensus mechanism. In each round of reasoning, DySCo estimates the value of communication edges based on agent reliability, answer divergence, and task relevance, and selects a small number of high-value edges for message exchange under budget constraints; it then aggregates the answers of different agents through dynamic trust weights and terminates the discussion early once consensus stabilizes. This mechanism replaces universal broadcasting with on-demand communication, thereby reducing communication overhead while preserving essential cross-validation information. We further present analyses of communication complexity and consensus stability, and evaluate the performance of DySCo on mathematical reasoning, logical reasoning, and factual question-answering tasks.