发表机构
Delft Center for Systems and Control, TU Delft（代尔夫特理工大学德尔夫特系统与控制中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究开发了基于JAX的开源Python库“tnkm”，用于构建训练张量网络核机模型，该模型在非线性基准问题上兼具高预测精度与高效性，可支撑相关学习方法的可复现开发应用。
AI 中文摘要
开发兼具表达能力与计算效率的非线性模型，仍是机器学习与非线性系统辨识领域的挑战。张量网络核机（TNKM）通过将非线性特征表示与紧凑低秩张量网络参数化相结合，应对该挑战。然而，用于开发TNKM模型的实用且可扩展软件框架仍有限。本研究引入开源Python库“tnkm”，用于使用JAX构建和训练TNKM模型。该库提供统一接口，可组合不同特征映射、张量网络架构及优化策略，包括交替最小二乘法与基于梯度的方法。我们在非线性基准问题上展示“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，达到了有竞争力的预测精度。该框架促进了基于张量网络的学习方法的可复现开发与应用。
英文摘要
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.
Comments10 pages, 6 figures, 4 tables, 1 listing. Code available at: https://github.com/AlbMLpy/tnkm
