相关论文: Deep tensor networks with matrix product operators

Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…

Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…

It is well known that tensor network regression models operate on an exponentially large feature space, but questions remain as to how effectively they are able to utilize this space. Using a polynomial featurization, we propose the…

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…

Deep neural networks have been extremely successful at various image, speech, video recognition tasks because of their ability to model deep structures within the data. However, they are still prohibitively expensive to train and apply for…

Our proposed deeply-supervised nets (DSN) method simultaneously minimizes classification error while making the learning process of hidden layers direct and transparent. We make an attempt to boost the classification performance by studying…

Deep neural networks have achieved strong performance in image classification tasks due to their ability to learn complex patterns from high-dimensional data. However, their large computational and memory requirements often limit deployment…

Deep neural network models owe their representational power to the high number of learnable parameters. It is often infeasible to run these largely parametrized deep models in limited resource environments, like mobile phones. Network…

To what extent is the success of deep visualization due to the training? Could we do deep visualization using untrained, random weight networks? To address this issue, we explore new and powerful generative models for three popular deep…

Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal…

Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned via gradient descent or similar optimization methods. However,…

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…

Recurrent Neural Networks (RNNs) produce state-of-art performance on many machine learning tasks but their demand on resources in terms of memory and computational power are often high. Therefore, there is a great interest in optimizing the…

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…

Tensor network methods have been a key ingredient of advances in condensed matter physics and have recently sparked interest in the machine learning community for their ability to compactly represent very high-dimensional objects. Tensor…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

This paper is the first to explore an automatic way to detect bias in deep convolutional neural networks by simply looking at their weights. Furthermore, it is also a step towards understanding neural networks and how they work. We show…

We study the quantification of uncertainty of Convolutional Neural Networks (CNNs) based on gradient metrics. Unlike the classical softmax entropy, such metrics gather information from all layers of the CNN. We show for the EMNIST digits…

Tensor networks, a model that originated from quantum physics, has been gradually generalized as efficient models in machine learning in recent years. However, in order to achieve exact contraction, only tree-like tensor networks such as…

Beyond their origin in modeling many-body quantum systems, tensor networks have emerged as a promising class of models for solving machine learning problems, notably in unsupervised generative learning. While possessing many desirable…