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.

翻译：格基约简是一类旨在给定格中寻找最正交基的组合优化问题。本文通过深度学习方法解决格基约简问题，设计了一种可输出分解幺模矩阵的深度神经模型，并以自监督方式通过惩罚非正交格基进行训练。通过使模型对相应连续群与离散群具有不变性和等变性，我们将格基约简的对称性融入模型中。