Predictive Diagnostic for Multi-Agent LLM Communication Topologies

A new arXiv paper introduces a structural diagnostic for multi-agent large language model (LLM) communication graphs, enabling pre-inference evaluation of topology performance. The diagnostic uses the successor representation M = (I - γP)^{-1} of the row-stochastic communication operator, connecting three spectral quantities—spectral radius ρ(M), spectral gap Δ(M), and condition number κ(M)—to distinct failure modes: drift, failure to converge, and lack of robustness. The authors derive closed-form spectra for chain, star, and mesh topologies under row-stochastic normalization and validate predictions on a 12-step structured state-tracking task using Qwen2.5. This work addresses the current need for post-hoc evaluation by providing a pre-inference diagnostic for practitioners deploying multi-agent LLM systems.