Tensor Network Structure Search Via Canonical Dimension Tree Enumeration

Abstract

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 challenging 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 decoupling topology enumeration from rank assignment search. We first represent the search space using canonical dimension trees, which encode potential network topology through nested index partitions and inherently rule out redundant and suboptimal topologies by construction. To mitigate the assessment bottleneck, we introduce a mechanism powered by the precomputation of a singular value map. By archiving the singular values of all feasible tensor matricizations, we transform the evaluation of any candidate dimension tree into a constraint-solving problem. This formulation yields an empirically near-optimal rank assignment via simple metadata lookups, allowing us to compute structural costs and bypass expensive tensor decompositions for all but the final selected candidate. Experimental results show that our approach accelerates the structure search by up to 10x while achieving highly competitive compression ratios, outperforming standard tensor trains and hierarchical tuckers by up to 10x, and matching or exceeding state-of-the-art structure search tools. Notably, our approach scales to larger tensors that are unattainable by prior work. Furthermore, the discovered topologies generalize well to similar data; they achieve compression ratios up to 2.4x better than tensor trains or hierarchical tuckers, while maintaining a search time of approximately 110 seconds for 6D tensors of 1-2GB disk size.