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arXiv · 2603.21564

Toward a Theory of Hierarchical Memory for Language Agents

Yashar Talebirad·Ali Parsaee·Csongor Y. Szepesvari·Amirhossein Nadiri·Osmar Zaiane
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Abstract

Many recent long-context and agentic systems address context-length limitations by adding hierarchical memory: they extract atomic units from raw data, build multi-level representatives by grouping and compression, and traverse this structure to retrieve content under a token budget. Despite recurring implementations, there is no shared formalism for comparing design choices. We propose a unifying theory in terms of three operators. Extraction ($\alpha$) maps raw data to atomic information units; coarsening ($C = (\pi, \rho)$) partitions units and assigns a representative to each group; and traversal ($\tau$) selects which units to include in context given a query and budget. We identify a self-sufficiency spectrum for the representative function $\rho$ and show how it constrains viable retrieval strategies (a coarsening-traversal coupling). Finally, we instantiate the decomposition on eleven existing systems spanning document hierarchies, conversational memory, and agent execution traces, showcasing its generality.

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Yashar Talebirad, Ali Parsaee, Csongor Y. Szepesvari, Amirhossein Nadiri, Osmar Zaiane. 2026-03-23. Toward a Theory of Hierarchical Memory for Language Agents. https://arxiv.org/abs/2603.21564

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