Neural Lattice Reduction: A Self-Supervised Geometric Deep Learning Approach

Giovanni Luca Marchetti, Gabriele Cesa, Kumar Pratik, Arash Behboodi

Submission Track: Extended Abstract

Keywords: Lattice Reduction, Geometric Deep Learning, Equivariance, Self-Supervised

Abstract: 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.

Submission Number: 24