Provably Stable Dual-Layer Memory Frameworks with Dynamics for LLM Agents

Large language model (LLM) agents deployed in real-world settings must maintain long-horizon consistency, respect evolving user preferences, and ground reasoning in past experiences. While recent agent memory systemsn have advanced the engineering of storage and retrieval, none provides formal guarantees on the long-term stability of the memory statistics that govern retrieval. We address this gap by modeling memory statistic updates as a continuous-time dynamical system and applying standard ODE stability tools—Lyapunov analysis and Input-to-State Stability (ISS)—to establish convergence guarantees. Our dual-layer architecture uses a Shared Layer that aggregates global experiences via coarse-grained 4th-order Runge-Kutta updates and a Private Layer that adapts to user-specific patterns via fine-grained Euler updates anchored to the shared trajectory. The system is training-free: improvement comes from case accumulation and statistic-driven retrieval using frozen off-the-shelf encoders, without training any additional models. On the LoCoMo benchmark, our model achieves the highest F1 (52.35% avg.) among compared methods—outperforming O-Mem by 1.17 points. Cross-domain ablation on data science agent tasks (R&D-Agent) confirms that the shared layer enables cross-task experience reuse, achieving 51–54% lower token consumption than ablated variants in that setting.