SEIAR-D: Quantifying Error Propagation in LLM Multi-Agent Systems

Complex collaborative tasks have driven the rapid development of LLM-based multi-agent systems (LLM${}^2$AS). However, intensive interaction also introduces systemic risks. A local error can propagate, be reconstructed, and be amplified across agents, eventually leading to system-level failure. Existing studies have begun to examine error cascades and collective error retention, while the internal propagation process remains less understood. To address this gap, we develop a theoretical framework from four perspectives: relay propagation, semantic amplification, population-level criticality, and error consolidation risk. It models error evolution at both the agent and system levels. We study how normal agents become new propagation sources, how semantic amplification strengthens propagation, and when errors shift from decay to sustained expansion. We further define consolidation risk from propagation states and transitions for early warning. Experiments show that errors among LLM agents are not isolated or static events, but dynamic processes involving propagation, amplification, recovery, and critical transitions. Our framework provides a unified view for understanding and predicting error risks in LLM${}^2$AS.