用张量网络构建高效非线性模型，支持快速训练与可复现开发。
Tensor Network Kernel Machines: A JAX Framework for Machine Learning and Nonlinear System Identification
- 结合张量网络与特征映射，实现参数紧凑的非线性建模
- 在基准测试中达到与主流方法相当的预测精度
- 提供统一接口，支持多种优化策略与架构组合
构建既具表达力又计算高效的非线性模型，仍是机器学习与非线性系统辨识中的挑战。张量网络核机（TNKM）通过将非线性特征表示与紧凑的低秩张量网络参数化相结合，应对该挑战。然而，实用且可扩展的TNKM开发软件框架仍有限。本文提出「tnkm」，一个基于JAX的开源Python库，用于构建和训练TNKM模型。该库提供统一接口，支持不同特征映射、张量网络架构及优化策略（包括交替最小二乘与基于梯度的方法）。我们在非线性基准问题上展示了「tnkm」的能力，结果表明所实现模型在保持紧凑参数化与高效训练的同时，达到具有竞争力的预测准确率。该框架促进了基于张量网络学习方法的可复现开发与应用。
原文摘要 · Abstract (English)
Developing nonlinear models that are both expressive and computationally efficient remains a challenge in machine learning and nonlinear system identification. Tensor network kernel machines (TNKM) address this challenge by combining nonlinear feature representations with compact low-rank tensor-network parameterizations. However, practical and extensible software frameworks for developing TNKM models remain limited. In this work, we introduce "tnkm", an open-source Python library for constructing and training TNKM models using JAX. The library provides a unified interface for combining different feature maps, tensor-network architectures, and optimization strategies, including alternating least squares and gradient-based methods. We demonstrate the capabilities of "tnkm" on nonlinear benchmark problems, showing that the implemented models achieve competitive prediction accuracy while retaining compact parameterizations and efficient training. The proposed framework facilitates reproducible development and application of tensor-network-based learning methods.
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