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.
Tensor networks are powerful formats for compressing large-scale data. However, their application to general data processing has been limited by the difficulty of performing nonlinear operations. Here, we introduce iterative tensor network transformations (ITNTs), a general algorithmic framework for the element-wise ev...
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This work presents a method to accelerate the optimization of learning high dimensional functions using deep neural network (DNN), and studies the effect of adding features which distill pretrained DNN into TNs using a discretize and decompose strategy.
This work introduces a general kernel-based encoder-decoder framework for operator learning that separates observation, representation, learning, and reconstruction, and develops this framework for multi-input, multi-output operator learning, where operators map between products of potentially distinct function spaces.
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Traditional model reduction techniques for neural network compression usually leverage existing matrix/tensor decomposition methods to explore the redundancy among model parameters, which may overlook the local structures of the models. In this work, we propose a novel low-rank approximation algorithm, called Dimension...
Yu-Chuan Tai, Cheng-Yu Sie, Che-Rung Lee· Annual International Compute...· 0 citations
This workshop aims to provide a forum for advancing tensor methods and applying them to various applications at the intersection of data mining and modern machine learning to foster an interactive environment for researchers to exchange ideas and build connections across communities.
Dawon Ahn, Yong-chan Park, Taehyung Kwon et al.· Proceedings of the 32nd ACM...· 0 citations
An efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format and observing that the proposed NTT fitting procedure exhibits drastically faster convergence than an alternative multiplicative update method that has been previously proposed...
Xun Tang, Rajat Vadiraj Dwaraknath, Le-Xing Ying· SIAM Journal on Scientific C...· 0 citations
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