Memory systems for LLM agents struggle to determine what information deserves retention.Existing approaches rely on predefined heuristics such as importance scores, emotional tags, or factual templates, encoding designer intuition rather than learning from the data itself.Inspired by cognitive ideas, we propose NEMORI, an adaptive memory distillation framework that casts the assessment of the experience's future utility as a matter of predictability.Specifically, NEMORI comprises two cascading modules: Episodic Memory Integration transforms raw interactions into coherent narratives, and Semantic Knowledge Distillation extracts insights via prediction error.Centering on distillation, the framework remains agnostic to downstream management.Extensive experiments confirm that NEMORI achieves strong performance, efficiency, and storage reduction.Our work suggests that observing the intrinsic properties of interaction sequences offers a viable, data-driven alternative to heuristic-based memory design.Code at