Accelerating Regularized Attention Kernel Regression for Spectrum Cartography

This repository provides code for regularized attention kernel regression and an efficient learning-based solver for spectrum cartography. It addresses the ill-conditioning of attention-based exponential kernels. Numerical experiments demonstrate accelerated convergence and accurate radio map reconstruction. For more details, please refer to our paper "Accelerating Regularized Attention Kernel Regression for Spectrum Cartography" (https://doi.org/10.48550/arXiv.2604.25138)

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Installation

The following software and libraries are required:

• Python 3.11
• PyTorch 2.5.1
• CVXPY
• NVIDIA Sionna RT

Repository Structure

This repository contains the following example scripts:

• example_spectrum_of_attention_kernel_in_model.py
  Demonstrates the spectral properties of the attention kernel used in the model.

• numerical_example_in_algorithm_with_sionna.py
  Provides a numerical example illustrating the radio map reconstruction process in the algorithm using NVIDIA Sionna.

• sc_radiomap_kernel_in_introduction_with_sionna_munich.py
  Implements kernel-based radio map reconstruction in a realistic Munich urban environment simulated with NVIDIA Sionna.

Usage

Running the Python script

Python scripts, such as numerical_example_in_algorithm_with_sionna.py, can be executed in two ways:

1. Direct Execution

Open the file in a Python IDE (e.g., PyCharm) and run it directly.

2. Command-Line Execution

From a terminal, navigate to the script directory and run:

python numerical_example_in_algorithm_with_sionna.py

Citation

@article{tao2026accelerating,
  title={Accelerating Regularized Attention Kernel Regression for Spectrum Cartography},
  author={Tao, Liping and Tan, Chee Wei},
  journal={arXiv preprint arXiv:2604.25138},
  year={2026}
}