Rate-Distortion Analysis of Compressed Query Delegation with Low-Rank Riemannian Updates

TL;DR

This paper introduces a rate-distortion framework for compressed query delegation in bounded-context agents, leveraging Riemannian optimization and spectral thresholding to improve reasoning efficiency and accuracy.

Contribution

It formulates compressed query delegation as a constrained stochastic program, connects it to classical information principles, and provides convergence guarantees for Riemannian stochastic approximation.

Findings

Achieved a 2,500-item reasoning benchmark showing improved performance.

Demonstrated the effectiveness of spectral hard-thresholding for optimal compression.

Provided empirical evidence of epistemic gain and semantic stability in human benchmarks.

Abstract

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.