---
title: "Gradient Boosting for Efficient Rank Discovery in Tensor Network Kernel Machines"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.08093v1"
permalink: "https://feed.astralor.com/items/itm_1820282658e333564f8d91ed"
published: "2026-11-05T14:36:46.000Z"
score: 57
channel: "tech"
tags: ["Gradient Boosting","Efficient Rank Discovery","Tensor Network Kernel","Machines Tensor","TNKMs","However","Tensor"]
---

# Gradient Boosting for Efficient Rank Discovery in Tensor Network Kernel Machines

## At a glance

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 co…

## Key points

- 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.

## Full text

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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