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