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cs.IRcs.AIcs.ITYashar Talebirad, Ali Parsaee, Csongor Y. Szepesvari et al.
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Mar 23, 2026
This paper tackles the lack of shared formalism for comparing hierarchical memory systems in language agents. It proposes a unifying theory based on three operators: extraction (α) that maps raw data to atomic units, coarsening (C = (π, ρ)) that partitions and summarizes units, and traversal (τ) that selects content under a token budget. The core insight is the self-sufficiency spectrum of representatives ρ, which constrains viable retrieval strategies—an observation the authors call the coarsening-traversal (C–T) coupling.
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.