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

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.

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Cite

Text

Marchetti et al. "Neural Lattice Reduction: A Self-Supervised Geometric Deep Learning Approach." NeurIPS 2023 Workshops: NeurReps, 2023.

Markdown

[Marchetti et al. "Neural Lattice Reduction: A Self-Supervised Geometric Deep Learning Approach." NeurIPS 2023 Workshops: NeurReps, 2023.](https://mlanthology.org/neuripsw/2023/marchetti2023neuripsw-neural/)

BibTeX

@inproceedings{marchetti2023neuripsw-neural,
  title     = {{Neural Lattice Reduction: A Self-Supervised Geometric Deep Learning Approach}},
  author    = {Marchetti, Giovanni Luca and Cesa, Gabriele and Pratik, Kumar and Behboodi, Arash},
  booktitle = {NeurIPS 2023 Workshops: NeurReps},
  year      = {2023},
  url       = {https://mlanthology.org/neuripsw/2023/marchetti2023neuripsw-neural/}
}