用梳状张量网络替代传统结构，提升高维数据建模效率
Comb Tensor Networks vs. Matrix Product States: Enhanced Efficiency in High-Dimensional Spaces
- 采用梳状张量网络结构优化高维数据的张量收缩
- 在数据维度和键维数超过阈值时，计算效率显著优于MPS
- 适合处理高维连续数据生成任务的研究者参考
当前基于张量网络的连续数据生成方法通过压缩层捕捉高维输入的关键特征，但普遍依赖传统的矩阵乘积态（MPS）架构。本文表明，在数据维度与键维数超过某一阈值后，梳状张量网络架构可实现比标准MPS更高效的张量收缩。这一结果表明，对于连续且高维的数据分布，从MPS转向梳状张量网络表示，可在保持精度的同时大幅降低计算开销。
原文摘要 · Abstract (English)
Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product States (MPS) architectures. Here, we demonstrate that beyond a certain threshold in data and bond dimensions, a comb-shaped tensor network architecture can yield more efficient contractions than a standard MPS. This finding suggests that for continuous and high-dimensional data distributions, transitioning from MPS to a comb tensor network representation can substantially reduce computational overhead while maintaining accuracy.
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