相关论文: Tensor-based Nonlinear Classifier for High-Order D…

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…

We introduce deep tensor networks, which are exponentially wide neural networks based on the tensor network representation of the weight matrices. We evaluate the proposed method on the image classification (MNIST, FashionMNIST) and…

A novel convolution neural network model, abbreviated NL-CNN is proposed, where nonlinear convolution is emulated in a cascade of convolution + nonlinearity layers. The code for its implementation and some trained models are made publicly…

Convolutional neural networks show outstanding results in a variety of computer vision tasks. However, a neural network architecture design usually faces a trade-off between model performance and computational/memory complexity. For some…

This paper investigates the learning of 3rd-order tensors representing the semantics of transitive verbs. The meaning representations are part of a type-driven tensor-based semantic framework, from the newly emerging field of compositional…

Recurrent Neural Networks (RNNs) and their variants, such as Long-Short Term Memory (LSTM) networks, and Gated Recurrent Unit (GRU) networks, have achieved promising performance in sequential data modeling. The hidden layers in RNNs can be…

Low-rankness is important in the hyperspectral image (HSI) denoising tasks. The tensor nuclear norm (TNN), defined based on the tensor singular value decomposition, is a state-of-the-art method to describe the low-rankness of HSI. However,…

The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so…

Learning hierarchical structures in sequential data -- from simple algorithmic patterns to natural language -- in a reliable, generalizable way remains a challenging problem for neural language models. Past work has shown that recurrent…

Tensor networks are factorisations of high rank tensors into networks of lower rank tensors and have primarily been used to analyse quantum many-body problems. Tensor networks have seen a recent surge of interest in relation to supervised…

We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient…

In this paper, we present connections between three models used in different research fields: weighted finite automata~(WFA) from formal languages and linguistics, recurrent neural networks used in machine learning, and tensor networks…

This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of…

Recently, hyperspectral image (HSI) classification approaches based on deep learning (DL) models have been proposed and shown promising performance. However, because of very limited available training samples and massive model parameters,…

This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…

In this manuscript, we introduce a tensor-based approach to Non-Negative Tensor Factorization (NTF). The method entails tensor dimension reduction through the utilization of the Einstein product. To maintain the regularity and sparsity of…

We propose a tensor neural network ($t$-NN) framework that offers an exciting new paradigm for designing neural networks with multidimensional (tensor) data. Our network architecture is based on the $t$-product (Kilmer and Martin, 2011), an…

Tensor Network (TN) decompositions have emerged as an indispensable tool in Big Data analytics owing to their ability to provide compact low-rank representations, thus alleviating the ``Curse of Dimensionality'' inherent in handling…

Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor…

Tensor factorization is a powerful tool to analyse multi-way data. Compared with traditional multi-linear methods, nonlinear tensor factorization models are capable of capturing more complex relationships in the data. However, they are…