Toward a Theory of Hierarchical Memory for Language Agents
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914414263795712 |
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| author | Talebirad, Yashar Parsaee, Ali Szepesvari, Csongor Y. Nadiri, Amirhossein Zaiane, Osmar |
| author_facet | Talebirad, Yashar Parsaee, Ali Szepesvari, Csongor Y. Nadiri, Amirhossein Zaiane, Osmar |
| contents | 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 ($α$) maps raw data to atomic information units; coarsening ($C = (π, ρ)$) partitions units and assigns a representative to each group; and traversal ($τ$) selects which units to include in context given a query and budget. We identify a self-sufficiency spectrum for the representative function $ρ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21564 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Toward a Theory of Hierarchical Memory for Language Agents Talebirad, Yashar Parsaee, Ali Szepesvari, Csongor Y. Nadiri, Amirhossein Zaiane, Osmar Information Retrieval Artificial Intelligence Information Theory Social and Information Networks 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 ($α$) maps raw data to atomic information units; coarsening ($C = (π, ρ)$) partitions units and assigns a representative to each group; and traversal ($τ$) selects which units to include in context given a query and budget. We identify a self-sufficiency spectrum for the representative function $ρ$ 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. |
| title | Toward a Theory of Hierarchical Memory for Language Agents |
| topic | Information Retrieval Artificial Intelligence Information Theory Social and Information Networks |
| url | https://arxiv.org/abs/2603.21564 |