@inproceedings{
marchetti2023neural,
title={Neural Lattice Reduction: A Self-Supervised Geometric Deep Learning Approach},
author={Giovanni Luca Marchetti and Gabriele Cesa and Kumar Pratik and Arash Behboodi},
booktitle={NeurIPS 2023 Workshop on Symmetry and Geometry in Neural Representations},
year={2023},
url={https://openreview.net/forum?id=030cPt4d8i}
}
Lattice reduction is a combinatorial optimization problem aimed at finding the most orthogonal basis in a given lattice. In this work, we address lattice reduction via deep learning methods. We design a deep neural model outputting factorized unimodular matrices and train it in a self-supervised manner by penalizing non-orthogonal lattice bases. We incorporate the symmetries of lattice reduction into the model by making it invariant and equivariant with respect to appropriate continuous and discrete groups.
Neural Lattice Reduction: A Self-Supervised Geometric Deep Learning Approach
Giovanni Luca Marchetti Gabriele Cesa Kumar Pratik Arash Behboodi