← 研踪 PaperTrailarXiv:2611.08093 · v1
Gradient Boosting for Efficient Rank Discovery in Tensor Network Kernel Machines
首次提交 2026-11-05 22:36
版本更新 2026-11-05 22:36
雷达观测 2026-11-06 12:09
摘要
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.
作者备注：13 pages, 3 figures, 1 table. Code available at: https://github.com/AlbMLpy/boosting-tnkm
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v1 · 2026-11-05 22:36 · 最新观测版本
Gradient Boosting for Efficient Rank Discovery in Tensor Network Kernel Machines
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.
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