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

Long-horizon language agents must operate under limited runtime memory, yet existing memory mechanisms often organize experience around descriptive criteria such as relevance, salience, or summary quality. For an agent, however, memory is valuable not because it faithfully describes the past, but because it preserves the distinctions between histories that must remain separated under a fixed budget to support good decisions. We cast this as a decision-centric rate-distortion problem, measuring memory quality by the loss in achievable decision quality induced by compression. This yields an exact forgetting boundary for what can be safely forgotten, and a memory-distortion frontier characterizing the optimal tradeoff between memory budget and decision quality. Motivated by this decision-centric view of memory, we propose DeMem, an online memory learner that refines its partition only when data certify that a shared state would induce decision conflict, and prove near-minimax regret guarantees. On both controlled synthetic diagnostics and long-horizon conversational benchmarks, DeMem yields consistent gains under the same runtime budget, supporting the principle that memory should preserve the distinctions that matter for decisions, not descriptions.

Current agentic memory systems (vector stores, retrieval-augmented generation, scratchpads, and context-window management) do not implement memory: they implement lookup. We argue that treating lookup as memory is a category error with provable consequences for agent capability, long-term learning, and security. Retrieval generalizes by similarity to stored cases; weight-based memory generalizes by applying abstract rules to inputs never seen before. Conflating the two produces agents that accumulate notes indefinitely without developing expertise, face a provable generalization ceiling on compositionally novel tasks that no increase in context size or retrieval quality can overcome, and are structurally vulnerable to persistent memory poisoning as injected content propagates across all future sessions. Drawing on Complementary Learning Systems theory from neuroscience, we show that biological intelligence solved this problem by pairing fast hippocampal exemplar storage with slow neocortical weight consolidation, and that current AI agents implement only the first half. We formalize these limitations, address four alternative views, and close with a co-existence proposal and a call to action for system builders, benchmark designers, and the memory community.

Memory for large language model (LLM) agents has rapidly evolved from simple retrieval-augmented mechanisms into a data management system that supports persistent information storage, retrieval, update, consolidation, and dynamic lifecycle governance throughout agent execution. Despite this evolution, existing evaluations still benchmark agent memory mainly through end-to-end task success metrics (e.g., F1, BLEU), while treating the underlying system as a monolithic black box. As a result, critical system-level concerns, including operational costs, architectural trade-offs across memory modules, and robustness under dynamic knowledge updates, remain insufficiently explored. In this paper, we present a systematic experimental study of agent memory from a data management perspective. We propose an analytical framework that decomposes agent memory into four core modules: memory representation and storage, extraction, retrieval and routing, and maintenance. Under this framework, we evaluate 12 representative memory systems and two reference baselines across five benchmark workloads spanning 11 datasets. Our extensive end-to-end evaluation shows that no single architecture dominates across all scenarios; instead, effectiveness depends heavily on how well the memory structure aligns with the workload bottleneck. Furthermore, through fine-grained ablation studies, we quantify their individual effects on representation fidelity, retrieval precision, update correctness, and long-horizon stability. Finally, we reveal cost-performance trade-offs under realistic workloads, showing localized maintenance is more cost-efficient than global reorganization. Based on these findings, we identify promising directions towards building truly agent-native memory systems. The code is publicly available at https://github.com/OpenDataBox/MemoryData.