Many methods for automated multi-agent system design optimize prompts and topologies during an initial design stage and then deploy the resulting system unchanged on subsequent samples. Experience from these samples is rarely consolidated into reusable system updates, while accuracy-oriented designs may incur high token costs. We introduce EMAS (Evolving Multi-Agent System), which uses this experience to revise MAS topology and prompts without updating LLM parameters, either to improve accuracy or to reduce cost. EMAS converts traces into structured diagnoses that specify a revision operation and target. It generates a candidate revision only when the same diagnosis recurs across samples and applies it only if paired validation against the current MAS meets the corresponding acceptance criterion. Across four benchmarks and two LLMs, EMAS attains the highest task-weighted overall accuracy for both backbones and is best or tied in six of eight model--benchmark settings. Within two evolution epochs, EMAS achieves relative gains of 6.30% and 20.10% in task-weighted accuracy on Kimi-K2-6 and Qwen3.6-27B, respectively. On MBPP with Qwen3.6-27B, EMAS raises accuracy from 55.09% to 89.12% while reducing token use per task by 62.2%. These results show that EMAS can turn experience from new samples into reusable updates to MAS topology and prompts.
Graph neural ordinary differential equations (Graph ODEs) extend graph learning from discrete message-passing layers to continuous-time representation flows. While it supports adaptive long-range propagation, we show that Graph ODEs with strictly positive irreducible mixing operators face an inherent \emph{monostability trap}: in the long-time regime, information leakage is unavoidable and the dynamics converge to a single global consensus attractor. We propose the \textbf{Hysteresis Graph ODE (HGODE)}, which couples feature evolution with a latent topological potential driven by a learned pairwise force. A double-well edge potential and bipolarized gate allow edge states to polarize into connected or insulated phases while preserving differentiability. We provide asymptotic analysis of the collapse mechanism and the proposed hysteretic topology dynamics, and validate HGODE on theory-driven synthetic diagnostics and real-world graph benchmarks.