用神经网络优化格量化器，提升高维压缩精度。
Gradient Based Method for the Fusion of Lattice Quantizers
- 引入家户算法与矩阵指数法，通过梯度优化格基矩阵。
- 在13至22维中均优于传统正交拼接方法，尤其高维更优。
- 适合做高效向量压缩与高维量化研究的工程师和学者。
实际应用中，格量化器利用离散格点逼近任意点。高效的格量化器能显著提升近似精度与效率。针对高维格量化问题，已有研究采用低维最优格量化器，并解决正交拼接中的最优长度比确定难题。值得注意的是，固定长度比与正交性在拼接低维格时表现次优。受此启发，我们提出使用梯度下降寻找最优格结构，进一步探索用神经网络发现优于正交拼接的矩阵。本文提出两种新方法：家户算法（Household Algorithm）与矩阵指数算法（Matrix Exp Algorithm）。实验结果表明，两者在维度13、15、17–19、21和22上均取得性能提升；其中矩阵指数算法在高维场景下表现更优。
原文摘要 · Abstract (English)
In practical applications, lattice quantizers leverage discrete lattice points to approximate arbitrary points in the lattice. An effective lattice quantizer significantly enhances both the accuracy and efficiency of these approximations. In the context of high-dimensional lattice quantization, previous work proposed utilizing low-dimensional optimal lattice quantizers and addressed the challenge of determining the optimal length ratio in orthogonal splicing. Notably, it was demonstrated that fixed length ratios and orthogonality yield suboptimal results when combining low-dimensional lattices. Building on this foundation, another approach employed gradient descent to identify optimal lattices, which inspired us to explore the use of neural networks to discover matrices that outperform those obtained from orthogonal splicing methods. We propose two novel approaches to tackle this problem: the Household Algorithm and the Matrix Exp Algorithm. Our results indicate that both the Household Algorithm and the Matrix Exp Algorithm achieve improvements in lattice quantizers across dimensions 13, 15, 17 to 19, 21, and 22. Moreover, the Matrix Exp Algorithm demonstrates superior efficacy in high-dimensional settings.
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