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.