Comb Tensor Networks vs. Matrix Product States: Enhanced Efficiency in High-Dimensional Spaces

2024/12/08 by Danylo Kolesnyk, Kolesnyk, Danylo, Yelyzaveta Vodovozova +1
Computer Science · #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Parallel Computing and Optimization Techniques #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2412.06857

openalex publication_date 2024/12/08 · openalex created_date 2024/12/12 · openalex updated_date 2026/07/28

Abstract

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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