New spectral diagnostic predicts multi-agent LLM failure modes

Deploying multi-agent LLM systems currently forces a blind choice between topologies like chain, star, or mesh—with no way to predict which will cause drift, converge to consensus, or resist perturbations until after running the task. In a new preprint, researchers Ethan David James Park and Dalal Alharthi propose a structural diagnostic based on the successor representation M = (I - γP)^{-1} of the row-stochastic communication operator. They connect three spectral quantities—spectral radius ρ(M), spectral gap Δ(M), and condition number κ(M)—to three distinct failure modes: cumulative error, consensus dynamics, and perturbation robustness. Closed-form spectra are derived for chain, star, and mesh topologies under row-stochastic normalization.

Validating on 100 trials of a 12-step structured state-tracking task using Qwen2.5-7B-Instruct, the results are striking: the condition number is a perfect rank-order predictor of empirical perturbation robustness (Spearman r_s = 1.0), the spectral gap partially predicts consensus dynamics (r_s = 0.5), and the spectral radius shows a perfect inverse relationship with cumulative error (r_s = -1.0). The authors trace this inversion to a regime where linear spectra miss non-contracting bias drift and propose an affine-noise extension that recovers the correct ordering. This work represents a first step toward drift-aware, pre-inference structural diagnostics for multi-agent LLM systems, bridging classical spectral and consensus theory with practical AI deployment.