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

2026-01-02

arXiv.org

AI Summary

This work addresses the failure of bounded-context agents when intermediate reasoning exceeds working memory capacity by proposing an efficient reasoning framework that combines low-rank tensor compression with an external oracle. High-dimensional latent states are compressed into low-rank queries and delegated to the oracle, while state updates are performed via Riemannian optimization on a fixed-rank manifold. The approach is formalized as a constrained stochastic program, establishing connections to rate-distortion theory and the information bottleneck principle. The authors prove the optimality of spectral hard thresholding under specific distortion constraints and provide convergence guarantees for Riemannian stochastic approximation. Experiments demonstrate that the method significantly outperforms chain-of-thought baselines across 2,500 reasoning tasks and effectively balances knowledge gain against semantic drift on human cognitive mirroring benchmarks.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Stochastic Optimization
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• bounded-context reasoning
• working-memory budget
• compressed query delegation
• rate-distortion
• information bottleneck

Innovation

• Compressed Query Delegation
• Low-Rank Riemannian Optimization
• Rate-Distortion Theory
• Information Bottleneck
• Bounded-Context Reasoning