Tensor Network Structure Search with Program Synthesis
Zheng Guo, Aditya Deshpande, Brian Kiedrowski, Xinyu Wang, Alex Gorodetsky

TL;DR
This paper introduces a novel program synthesis approach to tensor network structure search, significantly improving efficiency and compression performance while enabling scaling to larger tensors.
Contribution
It formulates tensor network structure search as a program synthesis problem, proposing a constraint-based assessment method and new operations to efficiently find optimal structures.
Findings
Search speed improved by up to 10x
Achieves 1.5x to 3x better compression ratios than state-of-the-art
Scales to larger tensors unattainable by prior methods
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 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…
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Taxonomy
TopicsComputational Physics and Python Applications · Parallel Computing and Optimization Techniques · Distributed and Parallel Computing Systems
