Related papers: Semi-Tensor-Product Based Convolutional Neural Net…

In convolutional neural networks (CNNs), padding plays a pivotal role in preserving spatial dimensions throughout the layers. Traditional padding techniques do not explicitly distinguish between the actual image content and the padded…

The $\star_M$-family of tensor-tensor products is a framework which generalizes many properties from linear algebra to third order tensors. Here, we investigate positive semidefiniteness and semidefinite programming under the…

When applying a convolutional kernel to an image, if the output is to remain the same size as the input then some form of padding is required around the image boundary, meaning that for each layer of convolution in a convolutional neural…

The current methods for learning representations with auto-encoders almost exclusively employ vectors as the latent representations. In this work, we propose to employ a tensor product structure for this purpose. This way, the obtained…

The tensor-tensor product (t-product) [M. E. Kilmer and C. D. Martin, 2011] is a natural generalization of matrix multiplication. Based on t-product, many operations on matrix can be extended to tensor cases, including tensor SVD, tensor…

Convolutional neural networks (CNNs) have enabled the state-of-the-art performance in many computer vision tasks. However, little effort has been devoted to establishing convolution in non-linear space. Existing works mainly leverage on the…

Although the convolutional neural networks (CNNs) have become popular for various image processing and computer vision task recently, it remains a challenging problem to reduce the storage cost of the parameters for resource-limited…

DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of…

Convolutional neural networks (CNNs) have been used in many machine learning fields. In practical applications, the computational cost of convolutional neural networks is often high with the deepening of the network and the growth of data…

Deep Learning methods, specifically convolutional neural networks (CNNs), have seen a lot of success in the domain of image-based data, where the data offers a clearly structured topology in the regular lattice of pixels. This…

Matrix product states (MPS), a tensor network designed for one-dimensional quantum systems, has been recently proposed for generative modeling of natural data (such as images) in terms of `Born machine'. However, the exponential decay of…

Vision Transformers have achieved state-of-the-art performance in a wide range of computer vision tasks, but their practical deployment is limited by high computational and memory costs. In this paper, we introduce a novel tensor-based…

Convolutional Neural Networks (CNNs) have become indispensable for solving machine learning tasks in speech recognition, computer vision, and other areas that involve high-dimensional data. A CNN filters the input feature using a network…

We discuss basic concepts of convolutional neural networks (CNNs) and outline uses in manufacturing. We begin by discussing how different types of data objects commonly encountered in manufacturing (e.g., time series, images, micrographs,…

An equivalence of matrices via semi-tensor product (STP) is proposed. Using this equivalence, the quotient space is obtained. Parallel and sequential arrangements of the natural projection on different shapes of matrices leads to the…

Automated visual inspection in the semiconductor industry aims to detect and classify manufacturing defects utilizing modern image processing techniques. While an earliest possible detection of defect patterns allows quality control and…

Convolutional neural networks (CNNs) are among the most widely used machine learning models for computer vision tasks, such as image classification. To improve the efficiency of CNNs, many CNNs compressing approaches have been developed.…

We introduce the Convolutional Conditional Neural Process (ConvCNP), a new member of the Neural Process family that models translation equivariance in the data. Translation equivariance is an important inductive bias for many learning…

Current practice in convolutional neural networks (CNN) remains largely bottom-up and the role of top-down process in CNN for pattern analysis and visual inference is not very clear. In this paper, we propose a new method for structured…

The convolution operator at the core of many modern neural architectures can effectively be seen as performing a dot product between an input matrix and a filter. While this is readily applicable to data such as images, which can be…