Lattice Basis Reduction

Lattice basis reduction is a computational problem focused on finding the most orthogonal basis within a given lattice, a regular arrangement of points in space. Recent research explores applying deep learning models, often incorporating group symmetries for improved efficiency, and leveraging algorithms like the Lenstra-Lenstra-Lovász (LLL) method to solve this problem in various contexts. These advancements are impacting diverse fields, including signal processing (e.g., non-Gaussian component analysis) and data analysis (e.g., identifying hidden structures in datasets), where lattice reduction offers efficient solutions to otherwise computationally challenging problems. The development of statistically query lower bounds further clarifies the computational limits and potential advantages of lattice-based algorithms compared to other approaches.