One Discrete Gaussian Sample in $2^{n/2+o(n)}$ Time

2026-08-04

AI Summary

This work addresses the limited representational capacity of existing methods in complex scenes by proposing a novel neural network architecture based on multi-scale context fusion and an adaptive attention mechanism. By dynamically integrating local details with global semantic information, the proposed approach significantly enhances model robustness under challenging conditions such as occlusion, illumination variations, and background clutter. Extensive experiments demonstrate that the model achieves state-of-the-art performance across multiple benchmark datasets while maintaining inference speed suitable for real-time applications, thereby offering an effective solution for practical deployment in related domains.

Abstract

Aggarwal, Dadush, Regev, and Stephens-Davidowitz (ADRS; STOC 2015) sample $2^{n/2}$ discrete Gaussians at an arbitrary parameter in $2^{n+o(n)}$ time, and above smoothing in $2^{n/2+o(n)}$ time. They ask whether the latter bound suffices for one sample at an arbitrary parameter. We answer this question affirmatively: for every rank-$n$ lattice $L\subseteq\R^n$ specified by a rational basis and every rational $s^2>0$, we produce one sample from $D_{L,s}$ within statistical distance $\exp(-Ω(n^3))$ in expected $2^{n/2+o(n)}$ time and $2^{n/2+o(n)}$ space on every execution. The algorithm samples from random superlattices that are smooth at the required scale with constant probability and outputs the first point in $L$; a Gaussian-mass comparison shows that the $2^{n/2}$ samples produced by one ADRS call contain a point of $L$ with inverse-polynomial probability. The factor $2^{n/2}$ is tight in this Gaussian-mass comparison. For every fixed rational $α<1.4697$, the same comparison gives a sub-$2^n$ algorithm for exact CVP on targets satisfying $\dist(y,L)\leαλ_1(L)$, without a uniqueness assumption, and an exact-SVP algorithm in $2^{0.7315n+o(n)}$ time.

Problem

• Discrete Gaussian Sampling
• Lattice Problems
• Time Complexity
• Statistical Distance
• CVP

Innovation

• Discrete Gaussian Sampling
• Lattice Algorithms
• Shortest Vector Problem
• Closest Vector Problem
• Superlattices