Toward Green Multi-Agents: Understanding and Tackling Dynamic Residual Decay via Cross-Lifecycle Graph

As multi-agent systems adapt their collaboration across tasks, they retain information from earlier rounds that can become outdated while continuing to influence decisions. Reusing such history can propagate invalid evidence; recomputing all affected work increases inference cost. Existing work on topology, persistent memory, and dependency updates does not jointly determine which persistent historical influence is associated with declining current-task utility and which computations the current task needs. We present the first systematic study of Dynamic Residual Decay (DRD), a cross-lifecycle phenomenon where residual influence persists across multi-turn tasks while its positive utility for the current task decays. To tackle DRD while preserving reusable work, we propose the cross-lifecycle graph (CLG), which traces invalidation forward and current demand backward, stops historical tracing at valid replacements, and re-executes the selected dependencies in order. Across four models and three multi-agent task sets, historical influence persists after positive utility declines. In cross-task recovery evaluations, CLG achieves a macro-averaged normalized utility of 0.9781 across task–model cells, compared with 0.9485 under Global Rerun, while reducing model calls by 39.8%, tokens by 29.9%, and elapsed time by 33.9%. Selectively retiring invalid influence and retaining useful history offers a route toward green multi-agent execution that is computationally cleaner and more resource-efficient.