Accelerating Regularized Attention Kernel Regression for Spectrum Cartography

2026-04-27

AI Summary

This work addresses the severe spectral imbalance in attention-based kernel regression for radio map reconstruction, which stems from the use of exponential kernels and manifests as an excessively large condition number that compromises iterative solvers. To overcome this limitation, the authors propose Learnable Attention Kernel Regression (LAKER), a novel algorithm that introduces, for the first time, a data-driven preconditioner into the attention kernel system. By approximating the inverse spectral structure of the kernel matrix, LAKER enables efficient solution of the regularized regression problem via preconditioned conjugate gradient methods. The approach dramatically alleviates the condition number bottleneck—reducing it by up to three orders of magnitude—and accelerates convergence by over 20×, all while preserving high-fidelity reconstruction accuracy of wireless signal maps.

Abstract

Spectrum cartography reconstructs spatial radio fields from sparse and heterogeneous wireless measurements, underpinning many sensing and optimization tasks in wireless networks. Attention mechanisms have recently enabled adaptive measurement aggregation via attention kernel-based formulations. However, the resulting exponential kernels exhibit severe spectral imbalance, inducing large condition numbers that render standard iterative solvers ineffective for regularized attention kernel regression. This paper proposes a Learning-based Attention Kernel Regression (LAKER) algorithm for accelerating regularized attention kernel regression in spectrum cartography. The key idea is to learn a data-dependent preconditioner that captures the inverse spectral structure of the attention kernel system, directly reducing the condition number bottleneck. The preconditioner is obtained by solving a regularized maximum-likelihood estimation problem via a shrinkage-regularized convex--concave procedure, and is integrated with a preconditioned conjugate gradient solver for efficient optimization, whose solution is used for radio map reconstruction. Extensive experiments demonstrate that LAKER significantly reduces condition numbers by up to three orders of magnitude, accelerates convergence by over twenty-fold compared to baselines, and maintains high reconstruction accuracy, establishing learning-based preconditioning as an effective approach for attention kernel regression in spectrum cartography.

Problem

• spectrum cartography
• attention kernel regression
• spectral imbalance
• condition number
• regularized regression

Innovation

• learning-based preconditioning
• attention kernel regression
• spectrum cartography
• condition number reduction
• radio map reconstruction