Rate-Distortion Analysis of Compressed Query Delegation with Low-Rank Riemannian Updates
This addresses memory constraints in AI agents for reasoning tasks, but it is incremental as it builds on existing rate-distortion and information bottleneck principles.
The paper tackles the problem of bounded-context agents failing due to memory limits by proposing compressed query delegation (CQD), which compresses reasoning states into low-rank queries and updates them via Riemannian optimization, achieving optimal spectral hard-thresholding and convergence guarantees with empirical benchmarks on 2,500 reasoning tasks and a human study with N=200.
Bounded-context agents fail when intermediate reasoning exceeds an effective working-memory budget. We study compressed query delegation (CQD): (i) compress a high-dimensional latent reasoning state into a low-rank tensor query, (ii) delegate the minimal query to an external oracle, and (iii) update the latent state via Riemannian optimization on fixed-rank manifolds. We give a math-first formulation: CQD is a constrained stochastic program with a query-budget functional and an oracle modeled as a noisy operator. We connect CQD to classical rate-distortion and information bottleneck principles, showing that spectral hard-thresholding is optimal for a natural constrained quadratic distortion problem, and we derive convergence guarantees for Riemannian stochastic approximation under bounded oracle noise and smoothness assumptions. Empirically, we report (A) a 2,500-item bounded-context reasoning suite (BBH-derived tasks plus curated paradox instances) comparing CQD against chain-of-thought baselines under fixed compute and context; and (B) a human "cognitive mirror" benchmark (N=200) measuring epistemic gain and semantic drift across modern oracles.