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

Fuente: arXiv
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Autori principali: Alpay, Faruk, Kilictas, Bugra
Natura: Preprint
Pubblicazione: 2026
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author Alpay, Faruk
Kilictas, Bugra
author_facet Alpay, Faruk
Kilictas, Bugra
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_00938
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Rate-Distortion Analysis of Compressed Query Delegation with Low-Rank Riemannian Updates
Alpay, Faruk
Kilictas, Bugra
Computation and Language
Optimization and Control
68T50, 94A34, 15A69, 90C15
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.
title Rate-Distortion Analysis of Compressed Query Delegation with Low-Rank Riemannian Updates
topic Computation and Language
Optimization and Control
68T50, 94A34, 15A69, 90C15
url https://arxiv.org/abs/2601.00938