忘却のタイミング：記憶管理の基本原理

Agent memory systems accumulate experience but currently lack a principled operational metric for memory quality governance -- deciding which memories to trust, suppress, or deprecate as the agent's task distribution shifts. Write-time importance scores are static; dynamic management systems use LLM judgment or structural heuristics rather than outcome feedback. This paper proposes Memory Worth (MW): a two-counter per-memory signal that tracks how often a memory co-occurs with successful versus failed outcomes, providing a lightweight, theoretically grounded foundation for staleness detection, retrieval suppression, and deprecation decisions. We prove that MW converges almost surely to the conditional success probability p+(m) = Pr[y_t = +1 | m in M_t] -- the probability of task success given that memory m is retrieved -- under a stationary retrieval regime with a minimum exploration condition. Importantly, p+(m) is an associational quantity, not a causal one: it measures outcome co-occurrence rather than causal contribution. We argue this is still a useful operational signal for memory governance, and we validate it empirically in a controlled synthetic environment where ground-truth utility is known: after 10,000 episodes, the Spearman rank-correlation between Memory Worth and true utilities reaches rho = 0.89 +/- 0.02 across 20 independent seeds, compared to rho = 0.00 for systems that never update their assessments. A retrieval-realistic micro-experiment with real text and neural embedding retrieval (all-MiniLM-L6-v2) further shows stale memories crossing the low-value threshold (MW = 0.17) while specialist memories remain high-value (MW = 0.77) across 3,000 episodes. The estimator requires only two scalar counters per memory unit and can be added to architectures that already log retrievals and episode outcomes.