Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network structure search a difficult problem. Existing solutions typically rely on sampling and compressing numerous candidate structures; these procedures are computationally expensive and therefore limiting for practical applications. We address this challenge by viewing tensor network structure search as a program synthesis problem and introducing an efficient constraint-based assessment method that avoids costly tensor decomposition. Specifically, we establish a correspondence between transformation programs and network structures. We also design a novel operation named output-directed splits to reduce the search space without hindering expressiveness. We then propose a synthesis algorithm to identify promising network candidates through constraint solving, and avoid tensor decomposition for all but the most promising candidates. Experimental results show that our approach improves search speed by up to $10\times$ and achieves compression ratios $1.5\times$ to $3\times$ better than state-of-the-art. Notably, our approach scales to larger tensors that are unattainable by prior work. Furthermore, the discovered topologies generalize well to similar data, yielding compression ratios up to $ 2.4\times$ better than a generic structure while the runtime remains around $110$ seconds.

翻译：张量网络为多维数据压缩提供了强大的框架。针对给定数据张量的最优张量网络结构取决于数据特征和特定的最优性准则，这使得张量网络结构搜索成为一个难题。现有解决方案通常依赖对大量候选结构进行采样和压缩；这些过程计算成本高昂，从而限制了实际应用。我们通过将张量网络结构搜索视为程序合成问题，引入一种高效的基于约束的评估方法以避免昂贵的张量分解，从而应对这一挑战。具体而言，我们建立了变换程序与网络结构之间的对应关系。我们还设计了一种名为输出导向分裂（output-directed splits）的新型操作，在不影响表达能力的前提下缩小搜索空间。随后，我们提出一种通过约束求解来识别有前景的网络候选结构的合成算法，并仅对最有前景的候选结构进行张量分解。实验结果表明，我们的方法将搜索速度提升至多$10\times$，压缩比相比现有最优方法提高$1.5\times$到$3\times$。值得注意的是，我们的方法可扩展至先前工作无法处理的大张量。此外，发现的拓扑结构对相似数据具有良好的泛化能力，其压缩比相比通用结构提升至多$2.4\times$，而运行时间保持在约$110$秒。