Gradient Boosting for Efficient Rank Discovery in Tensor Network Kernel Machines

arXiv:2611.08093v1 Announce Type: new Abstract: Tensor network kernel machines (TNKMs) combine nonlinear features with low-rank tensor representations to model complex relationships efficiently. However, selecting an appropriate tensor rank remains challenging, as conventional rank-search methods require training multiple candidate models, increasing computational costs. In this work, we focus on a canonical polyadic (CP) tensor network parameterization and propose GB-CPKM, a gradient boosting framework that builds a higher-capacity predictor by sequentially adding fixed-rank learners. This approach provides a new perspective on rank selection by incrementally increasing model capacity, with ensemble size selected based on validation performance rather than through explicit rank search. Experiments on real-world regression benchmarks show that GB-CPKM trains up to 6x faster and uses up to 2x less peak memory than a conventional rank-selection method based on cross-validation, while achieving comparable predictive performance. These results highlight the potential of gradient boosting to improve the computational efficiency and scalability of tensor-network learning.

Abstract:Tensor network kernel machines (TNKMs) combine nonlinear features with low-rank tensor representations to model complex relationships efficiently. However, selecting an appropriate tensor rank remains challenging, as conventional rank-search methods require training multiple candidate models, increasing computational costs. In this work, we focus on a canonical polyadic (CP) tensor network parameterization and propose GB-CPKM, a gradient boosting framework that builds a higher-capacity predictor by sequentially adding fixed-rank learners. This approach provides a new perspective on rank selection by incrementally increasing model capacity, with ensemble size selected based on validation performance rather than through explicit rank search. Experiments on real-world regression benchmarks show that GB-CPKM trains up to 6x faster and uses up to 2x less peak memory than a conventional rank-selection method based on cross-validation, while achieving comparable predictive performance. These results highlight the potential of gradient boosting to improve the computational efficiency and scalability of tensor-network learning.

13 pages, 3 figures, 1 table. Code available at: this https URL

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2611.08093 [cs.LG]

(or arXiv:2611.08093v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2611.08093 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Gradient Boosting for Efficient Rank Discovery in Tensor Network Kernel Machines

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