Paper ID: 2311.08170

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

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

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.

Submitted: Nov 14, 2023