# Towards a Formal Definition of Agent Memory: Basis, Span, Optimality, and the Sequential Memory Problem

arXiv: https://arxiv.org/abs/2608.11654 · HTML: https://mlsanity.com/paper/2608.11654/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 33 references that are in the map.
- First posted on arXiv 12 Aug 2026.

## Builds on (most cited first, 28 of 28)

- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [MemGPT: Towards LLMs as Operating Systems](https://mlsanity.com/paper/2310.08560/) (2023)
- [A-MEM: Agentic Memory for LLM Agents](https://mlsanity.com/paper/2502.12110/) (2025)
- [Evaluating Very Long-Term Conversational Memory of LLM Agents](https://mlsanity.com/paper/2402.17753/) (2024)
- [Mem0: Building Production-Ready AI Agents with Scalable Long-Term Memory](https://mlsanity.com/paper/2504.19413/) (2025)
- [LongMemEval: Benchmarking Chat Assistants on Long-Term Interactive Memory](https://mlsanity.com/paper/2410.10813/) (2024)
- [MemoryBank: Enhancing Large Language Models with Long-Term Memory](https://mlsanity.com/paper/2305.10250/) (2023)
- [RAPTOR: Recursive Abstractive Processing for Tree-Organized Retrieval](https://mlsanity.com/paper/2401.18059/) (2024)
- [Titans: Learning to Memorize at Test Time](https://mlsanity.com/paper/2501.00663/) (2024)
- [HippoRAG: Neurobiologically Inspired Long-Term Memory for Large Language Models](https://mlsanity.com/paper/2405.14831/) (2024)
- [Evaluating Memory in LLM Agents via Incremental Multi-Turn Interactions](https://mlsanity.com/paper/2507.05257/) (2025)
- [MemAgent: Reshaping Long-Context LLM with Multi-Conv RL-based Memory Agent](https://mlsanity.com/paper/2507.02259/) (2025)
- [Memory-R1: Enhancing Large Language Model Agents to Manage and Utilize Memories via Reinforcement Learning](https://mlsanity.com/paper/2508.19828/) (2025)
- [From RAG to Memory: Non-Parametric Continual Learning for Large Language Models](https://mlsanity.com/paper/2502.14802/) (2025)
- [MemOS: A Memory OS for AI System](https://mlsanity.com/paper/2507.03724/) (2025)
- [Walking Down the Memory Maze: Beyond Context Limit through Interactive Reading](https://mlsanity.com/paper/2310.05029/) (2023)
- [MEMORYLLM: Towards Self-Updatable Large Language Models](https://mlsanity.com/paper/2402.04624/) (2024)
- [MemoryArena: Benchmarking Agent Memory in Interdependent Multi-Session Agentic Tasks](https://mlsanity.com/paper/2602.16313/) (2026)
- [Mem-Gallery: Benchmarking Multimodal Long-Term Conversational Memory for MLLM Agents](https://mlsanity.com/paper/2601.03515/) (2026)
- [AMA-Bench: Evaluating Long-Horizon Memory for Agentic Applications](https://mlsanity.com/paper/2602.22769/) (2026)
- [Memory3: Language Modeling with Explicit Memory](https://mlsanity.com/paper/2407.01178/) (2024)
- [Look Back to Reason Forward: Revisitable Memory for Long-Context LLM Agents](https://mlsanity.com/paper/2509.23040/) (2025)
- [Rethinking Memory in LLM based Agents: Representations, Operations, and Emerging Topics](https://mlsanity.com/paper/2505.00675/) (2025)
- [Mem2ActBench: A Benchmark for Evaluating Long-Term Memory Utilization in Task-Oriented Autonomous Agents](https://mlsanity.com/paper/2601.19935/) (2026)
- [DialSim: A Dialogue Simulator for Evaluating Long-Term Multi-Party Dialogue Understanding of Conversational Agents](https://mlsanity.com/paper/2406.13144/) (2024)
- [Evaluating Long-Term Memory for Long-Context Question Answering](https://mlsanity.com/paper/2510.23730/) (2025)

## Abstract (arXiv)

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 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.