Accelerating Regularized Attention Kernel Regression for Spectrum Cartography

TL;DR

This paper introduces LAKER, a learning-based preconditioning method that accelerates regularized attention kernel regression for spectrum cartography, significantly improving convergence speed while maintaining accuracy.

Contribution

LAKER is the first to learn a data-dependent preconditioner for attention kernel regression, effectively reducing condition numbers and speeding up convergence in spectrum cartography.

Findings

LAKER reduces condition numbers by up to three orders of magnitude.

LAKER accelerates convergence by over twenty times compared to baseline methods.

LAKER maintains high radio map reconstruction accuracy.

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.