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

• URL: http://arxiv.org/abs/2601.00938v1
• Date: Fri, 02 Jan 2026 14:04:58 GMT
• Title: Rate-Distortion Analysis of Compressed Query Delegation with Low-Rank Riemannian Updates
• Abstract summary: We study compressed query delegation (CQD)<n>CQD is a constrained program with a query-budget functional and an oracle modeled as a noisy operator.
• Score: 0.5729426778193398
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Central Limit Theorem for Two-Time-Scale Approximate Distributionally Robust RL [8.809468023364703]
  Design of robust reinforcement learning algorithms poses fundamental challenges.<n>We propose an approximate DRRL framework based on a first-order expansion of the relevant robust functional.<n>To learn the fixed point of this approximate equation, we propose Mean-Variance Approximation (MVSA)
  arXiv  Detail & Related papers  (2026-05-08T19:24:28Z)
• Bridging the Gap Between Average and Discounted TD Learning [14.556544278062793]
  We introduce a novel algorithm designed explicitly for policy evaluation in the average-reward setting.<n>Our proposed method overcomes previous limitations by guaranteeing convergence to the unique solution of a properly defined Bellman equation.
  arXiv  Detail & Related papers  (2026-05-03T23:54:36Z)
• The Query Channel: Information-Theoretic Limits of Masking-Based Explanations [0.17188280334580197]
  Masking-based post-hoc explanation methods, such as KernelSHAP and LIME, estimate local feature importance by querying a black-box model.<n>This paper formulates this procedure as communication over a query channel, where the latent explanation acts as a message.
  arXiv  Detail & Related papers  (2026-04-17T20:46:25Z)
• Active Bipartite Ranking with Smooth Posterior Distributions [1.9838140219494644]
  Bipartite ranking is a statistical learning problem involved in many applications and widely studied in the passive context.<n>We propose a novel algorithm, referred to as smooth-rank and designed for the continuous setting, which aims to minimise the distance between the ROC curve of the estimated ranking rule and the optimal one w.r.t. the $sup$ norm.<n>We provide a problem dependent upper bound on the expected sampling time of smooth-rank and establish a problem dependent lower bound on the expected sampling time of any PAC$(,)$ algorithm.
  arXiv  Detail & Related papers  (2026-02-27T18:32:08Z)
• Sharp Convergence Rates for Masked Diffusion Models [53.117058231393834]
  We develop a total-variation based analysis for the Euler method that overcomes limitations.<n>Our results relax assumptions on score estimation, improve parameter dependencies, and establish convergence guarantees.<n>Overall, our analysis introduces a direct TV-based error decomposition along the CTMC trajectory and a decoupling-based path-wise analysis for FHS.
  arXiv  Detail & Related papers  (2026-02-26T00:47:51Z)
• GTS: Inference-Time Scaling of Latent Reasoning with a Learnable Gaussian Thought Sampler [54.10960908347221]
  We model latent thought exploration as conditional sampling from learnable densities and instantiate this idea as a Gaussian Thought Sampler (GTS)<n>GTS predicts context-dependent perturbation distributions over continuous reasoning states and is trained with GRPO-style policy optimization while keeping the backbone frozen.
  arXiv  Detail & Related papers  (2026-02-15T09:57:47Z)
• QUARK: Robust Retrieval under Non-Faithful Queries via Query-Anchored Aggregation [2.505352949111876]
  QUARK is a training-free framework for robust retrieval under non-faithful queries.<n>The design enables QUARK to improve recall and ranking quality without sacrificing robustness.
  arXiv  Detail & Related papers  (2026-01-28T21:14:49Z)
• RI-Loss: A Learnable Residual-Informed Loss for Time Series Forecasting [13.117430904377905]
  Time series forecasting relies on predicting future values from historical data.<n>MSE has two fundamental weaknesses: its point-wise error fails to capture temporal relationships, and it does not account for inherent noise in the data.<n>We introduce the Residual-Informed Loss (RI-Loss), a novel objective function based on the Hilbert-Schmidt Independence Criterion (HSIC)
  arXiv  Detail & Related papers  (2025-11-13T09:36:00Z)
• Efficient Thought Space Exploration through Strategic Intervention [54.35208611253168]
  We propose a novel Hint-Practice Reasoning (HPR) framework that operationalizes this insight through two synergistic components.<n>The framework's core innovation lies in Distributional Inconsistency Reduction (DIR), which dynamically identifies intervention points.<n> Experiments across arithmetic and commonsense reasoning benchmarks demonstrate HPR's state-of-the-art efficiency-accuracy tradeoffs.
  arXiv  Detail & Related papers  (2025-11-13T07:26:01Z)
• Supervised Optimism Correction: Be Confident When LLMs Are Sure [91.7459076316849]
  We establish a novel theoretical connection between supervised fine-tuning and offline reinforcement learning.<n>We show that the widely used beam search method suffers from unacceptable over-optimism.<n>We propose Supervised Optimism Correction, which introduces a simple yet effective auxiliary loss for token-level $Q$-value estimations.
  arXiv  Detail & Related papers  (2025-04-10T07:50:03Z)
• Semiparametric Double Reinforcement Learning with Applications to Long-Term Causal Inference [33.14076284663493]
  Long-term causal effects must be estimated from short-term data.<n>MDPs provide a natural framework for capturing such long-term dynamics.<n>Nonparametric implementations require strong intertemporal overlap assumptions.<n>We introduce a novel plug-in estimator based on isotonic Bellman calibration.
  arXiv  Detail & Related papers  (2025-01-12T20:35:28Z)
• Non-Convex Robust Hypothesis Testing using Sinkhorn Uncertainty Sets [18.46110328123008]
  We present a new framework to address the non-robust hypothesis testing problem. The goal is to seek the optimal detector that minimizes the maximum numerical risk.
  arXiv  Detail & Related papers  (2024-03-21T20:29:43Z)
• Optimal Multi-Distribution Learning [88.3008613028333]
  Multi-distribution learning seeks to learn a shared model that minimizes the worst-case risk across $k$ distinct data distributions.<n>We propose a novel algorithm that yields an varepsilon-optimal randomized hypothesis with a sample complexity on the order of (d+k)/varepsilon2.
  arXiv  Detail & Related papers  (2023-12-08T16:06:29Z)
• Last-Iterate Convergence of Adaptive Riemannian Gradient Descent for Equilibrium Computation [52.73824786627612]
  This paper establishes new convergence results for textitgeodesic strongly monotone games.<n>Our key result shows that RGD attains last-iterate linear convergence in a textitgeometry-agnostic fashion.<n>Overall, this paper presents the first geometry-agnostic last-iterate convergence analysis for games beyond the Euclidean settings.
  arXiv  Detail & Related papers  (2023-06-29T01:20:44Z)
• Large deviations rates for stochastic gradient descent with strongly convex functions [11.247580943940916]
  We provide a formal framework for the study of general high probability bounds with gradient descent. We find an upper large deviations bound for SGD with strongly convex functions.
  arXiv  Detail & Related papers  (2022-11-02T09:15:26Z)
• Accelerated and instance-optimal policy evaluation with linear function approximation [17.995515643150657]
  Existing algorithms fail to match at least one of these lower bounds. We develop an accelerated, variance-reduced fast temporal difference algorithm that simultaneously matches both lower bounds and attains a strong notion of instance-optimality.
  arXiv  Detail & Related papers  (2021-12-24T17:21:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.