# Accelerating Regularized Attention Kernel Regression for Spectrum Cartography

arXiv: https://arxiv.org/abs/2604.25138 · HTML: https://mlsanity.com/paper/2604.25138/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 50 references that are in the map.
- First posted on arXiv 28 Apr 2026.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks](https://mlsanity.com/paper/2002.02561/) (2020)
- [RadioUNet: Fast Radio Map Estimation with Convolutional Neural Networks](https://mlsanity.com/paper/1911.09002/) (2019)
- [Faster Kernel Ridge Regression Using Sketching and Preconditioning](https://mlsanity.com/paper/1611.03220/) (2016)
- [Radio Map Estimation: A Data-Driven Approach to Spectrum Cartography](https://mlsanity.com/paper/2202.03269/) (2022)
- [Disciplined Convex-Concave Programming](https://mlsanity.com/paper/1604.02639/) (2016)
- [Solving Attention Kernel Regression Problem via Pre-conditioner](https://mlsanity.com/paper/2308.14304/) (2023)
- [RadioNet: Transformer based Radio Map Prediction Model For Dense Urban Environments](https://mlsanity.com/paper/2105.07158/) (2021)
- [Learning Power Spectrum Maps from Quantized Power Measurements](https://mlsanity.com/paper/1606.02679/) (2016)
- [Regularized Tyler's Scatter Estimator: Existence, Uniqueness, and Algorithms](https://mlsanity.com/paper/1407.3079/) (2014)
- [Spectrum Surveying: Active Radio Map Estimation with Autonomous UAVs](https://mlsanity.com/paper/2201.04125/) (2022)
- [Radio Map Prediction from Aerial Images and Application to Coverage Optimization](https://mlsanity.com/paper/2410.17264/) (2024)
- [Robust, randomized preconditioning for kernel ridge regression](https://mlsanity.com/paper/2304.12465/) (2023)
- [Location-free Spectrum Cartography](https://mlsanity.com/paper/1812.11539/) (2018)
- [A Comprehensive Analysis on the Learning Curve in Kernel Ridge Regression](https://mlsanity.com/paper/2410.17796/) (2024)
- [Fast and Accurate Gaussian Kernel Ridge Regression Using Matrix Decompositions for Preconditioning](https://mlsanity.com/paper/1905.10587/) (2019)
- [Spatial Transformers for Radio Map Estimation](https://mlsanity.com/paper/2411.01211/) (2024)
- [RMTransformer: Accurate Radio Map Construction and Coverage Prediction](https://mlsanity.com/paper/2501.05190/) (2025)
- [Radio Map Prediction from Noisy Environment Information and Sparse Observations](https://mlsanity.com/paper/2602.11950/) (2026)

## Built on by (most cited first, 1 of 1)

- [Difference-of-Convex Regularization for Graph Learning by Differentiable Programming](https://mlsanity.com/paper/2608.12757/) (2026)

## Abstract (arXiv)

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.