迈向智能体记忆的形式化定义：基础、跨度、最优性与序列记忆问题
Towards a Formal Definition of Agent Memory: Basis, Span, Optimality, and the Sequential Memory Problem
- Tianjin University（天津大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出智能体记忆的形式化定义，定义最优记忆为容量受限的期望覆盖最大化器，实例化于《奥德赛》并将现有系统纳入框架，使记忆质量可度量。
AI中文摘要：
尽管记忆在大模型智能体中得到广泛部署，但尚未有关于记忆是什么或何时最优的统一形式化描述。本文为该描述迈出了第一步，核心思想是：记忆是一种基础，知识是其跨度，可回答性是一种覆盖问题——智能体存储从素材中提取的事件；生成算子将任意事件集转化为其蕴含的知识；查询可回答当且仅当跨度中的某一单个项覆盖该查询。最优记忆是容量受限的期望覆盖最大化器，其值追踪效用-容量前沿，这是可用于比较记忆系统的通用标准。接下来，考虑记忆中的噪声，讨论噪声下的覆盖与精度：记忆可能存储错误主张，因此写入策略必须推断所存储内容的真实性。通过类比通过持续经验形成的生物记忆，本文在覆盖多个层级的序列马尔可夫决策过程（MDP）中形式化了持续智能体记忆问题，其中记忆为状态，写作为动作，查询时确定的效用为驱动学习的延迟奖励。为使框架具体化，本文将其实例化于荷马的《奥德赛》，将前沿、压缩区及覆盖与精度的分歧转化为具体数值。最后，本文将现有系统置于该框架中，使“记忆有多好”可度量，并将构建与学习智能体记忆的开放问题重新表述为具体研究问题。
英文摘要：
Despite the wide deployment of memory in large-model agents, there is no unified formal account of what a memory is or when it is optimal. This paper takes a first step toward this account. The central idea is that memory is a basis, knowledge is its span, and answerability is a coverage problem: an agent stores events extracted from a material; a generation operator turns any event set into the knowledge it entails; and a query is answerable exactly when some single item in the span covers it. The optimal memory is then the capacity-constrained maximizer of expected coverage, and its value traces a utility--capacity frontier, the common yardstick on which memory systems can be compared. Next, we consider noise in the memory and discuss coverage versus precision under it: a memory may store false claims, so the write policy must infer the truth of what it stores. Drawing an analogy with biological memory, which is formed continuously through ongoing experience, we formalize the continual agent-memory problem in a sequential MDP that covers multiple levels, where memory is the state, writing is the action, and the utility settled at query time is the delayed reward that drives learning. To make the framework concrete, we instantiate it on Homer's \emph{Odyssey}, turning the frontier, the compression zone, and the divergence of coverage from precision into concrete numbers. Finally, we position existing systems within the framework, making ``how good is a memory'' measurable and recasting the open problems of constructing and learning agent memory as concrete research questions.
