When Does Typed Memory Help LLM Agents? A Subspace Perspective

LLM agents increasingly rely on typed external memory, but it remains unclear when typing should outperform a strong flat retriever. We define a type as a subspace of a frozen representation space and typed memory as a complementary decomposition of stored content. At matched effective rank, typing provides no intrinsic capacity advantage over an unconstrained target-aware selector; its benefit must instead arise from inductive bias. When the target covariance has effective rank $r_{\mathrm{eff}}\ll d$, blockwise spectral selection over label-free recovered subspaces incurs statistical dimension ${\max }_{\tau }{r}_{\mathrm{eff},\tau }$ rather than $r_{\mathrm{eff}}$, plus recovery and cross-block leakage costs. This gain belongs to the estimator rather than to physically separate stores: a flat retriever given the same blocks can obtain it without routing overhead, so store-specific benefits arise primarily from heterogeneous drift and per-type reliability. We instantiate these principles in , which learns write-time routing, complementary subspaces, per-type reliability and decay, and the effective number of types; provides the closed-form estimator covered by the analysis. Across seven text, image, and video benchmarks with a frozen encoder and matched rank $B=128$, achieves $55.4\%$ versus $53.4\%$ for target-aware flat and $50.0\%$ for similarity-flat memory, with a benchmark-bootstrap improvement of $[+1.1,+3.0]$ over target-aware flat. Its gain is largest in the low-data regime: $+5.6$ points at $n=25$, $+2.0$ at $n=200$, and $+1.2$ at $n=800$. A label-free drift-heterogeneity index correlates with the cost of shared decay (Spearman $\rho =0.89$, $n=7$). A risk-certificate heuristic, Type-If${}^0$, also separates most negative controls from all seven benchmarks, although its decisions are sensitive to the convention constant. All empirical results use one backbone with a frozen encoder at matched effective rank.