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Tensor networks, originally designed to address computational problems in quantum many-body physics, have recently been applied to machine learning tasks. However, compared to quantum physics, where the reasons for the success of tensor network approaches over the last 30 years is well understood, very little is yet known about why these techniques work for machine learning. The goal of this paper is to investigate entanglement properties of tensor network models in a current machine learning application, in order to uncover general principles that may guide future developments. We revisit the use of tensor networks for supervised image classification using the MNIST data set of handwritten digits, as pioneered by Stoudenmire and Schwab [Adv. in Neur. Inform. Proc. Sys. 29, 4799 (2016)]. Firstly we hypothesize about which state the tensor network might be learning during training. For that purpose, we propose a plausible candidate state $|Sigma_{ell}rangle$ (built as a superposition of product states corresponding to images in the training set) and investigate its entanglement properties. We conclude that $|Sigma_{ell}rangle$ is so robustly entangled that it cannot be approximated by the tensor network used in that work, which must therefore be representing a very different state. Secondly, we use tensor networks with a block product structure, in which entanglement is restricted within small blocks of $n times n$ pixels/qubits. We find that these states are extremely expressive (e.g. training accuracy of $99.97 %$ already for $n=2$), suggesting that long-range entanglement may not be essential for image classification. However, in our current implementation, optimization leads to over-fitting, resulting in test accuracies that are not competitive with other current approaches.
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Topic modeling based on latent Dirichlet allocation (LDA) has been a framework of choice to perform scene recognition and annotation. Recently, a new type of topic model called the Document Neural Autoregressive Distribution Estimator (DocNADE) was proposed and demonstrated state-of-the-art performance for document modeling. In this work, we show how to successfully apply and extend this model to the context of visual scene modeling. Specifically, we propose SupDocNADE, a supervised extension of DocNADE, that increases the discriminative power of the hidden topic features by incorporating label information into the training objective of the model. We also describe how to leverage information about the spatial position of the visual words and how to embed additional image annotations, so as to simultaneously perform image classification and annotation. We test our model on the Scene15, LabelMe and UIUC-Sports datasets and show that it compares favorably to other topic models such as the supervised variant of LDA.
Recent advances in semi-supervised learning methods rely on estimating the categories of unlabeled data using a model trained on the labeled data (pseudo-labeling) and using the unlabeled data for various consistency-based regularization. In this work, we propose to explicitly leverage the structure of the data manifold based on a Manifold Graph constructed over the image instances within the feature space. Specifically, we propose an architecture based on graph networks that jointly optimizes feature extraction, graph connectivity, and feature propagation and aggregation to unlabeled data in an end-to-end manner. Further, we present a novel Prototype Generator for producing a diverse set of prototypes that compactly represent each category, which supports feature propagation. To evaluate our method, we first contribute a strong baseline that combines two consistency-based regularizers that already achieves state-of-the-art results especially with fewer labels. We then show that when combined with these regularizers, the proposed method facilitates the propagation of information from generated prototypes to image data to further improve results. We provide extensive qualitative and quantitative experimental results on semi-supervised benchmarks demonstrating the improvements arising from our design and show that our method achieves state-of-the-art performance when compared with existing methods using a single model and comparable with ensemble methods. Specifically, we achieve error rates of 3.35% on SVHN, 8.27% on CIFAR-10, and 33.83% on CIFAR-100. With much fewer labels, we surpass the state of the arts by significant margins of 41% relative error decrease on average.
Convolutional neural networks (CNNs) have achieved state-of-the-art results on many visual recognition tasks. However, current CNN models still exhibit a poor ability to be invariant to spatial transformations of images. Intuitively, with sufficient layers and parameters, hierarchical combinations of convolution (matrix multiplication and non-linear activation) and pooling operations should be able to learn a robust mapping from transformed input images to transform-invariant representations. In this paper, we propose randomly transforming (rotation, scale, and translation) feature maps of CNNs during the training stage. This prevents complex dependencies of specific rotation, scale, and translation levels of training images in CNN models. Rather, each convolutional kernel learns to detect a feature that is generally helpful for producing the transform-invariant answer given the combinatorially large variety of transform levels of its input feature maps. In this way, we do not require any extra training supervision or modification to the optimization process and training images. We show that random transformation provides significant improvements of CNNs on many benchmark tasks, including small-scale image recognition, large-scale image recognition, and image retrieval. The code is available at https://github.com/jasonustc/caffe-multigpu/tree/TICNN.
Machine Learning provides powerful tools for a variety of applications, including disease diagnosis through medical image classification. In recent years, quantum machine learning techniques have been put forward as a way to potentially enhance performance in machine learning applications, both through quantum algorithms for linear algebra and quantum neural networks. In this work, we study two different quantum neural network techniques for medical image classification: first by employing quantum circuits in training of classical neural networks, and second, by designing and training quantum orthogonal neural networks. We benchmark our techniques on two different imaging modalities, retinal color fundus images and chest X-rays. The results show the promises of such techniques and the limitations of current quantum hardware.
Supervised classification and representation learning are two widely used classes of methods to analyze multivariate images. Although complementary, these methods have been scarcely considered jointly in a hierarchical modeling. In this paper, a method coupling these two approaches is designed using a matrix cofactorization formulation. Each task is modeled as a factorization matrix problem and a term relating both coding matrices is then introduced to drive an appropriate coupling. The link can be interpreted as a clustering operation over a low-dimensional representation vectors. The attribution vectors of the clustering are then used as features vectors for the classification task, i.e., the coding vectors of the corresponding factorization problem. A proximal gradient descent algorithm, ensuring convergence to a critical point of the objective function, is then derived to solve the resulting non-convex non-smooth optimization problem. An evaluation of the proposed method is finally conducted both on synthetic and real data in the specific context of hyperspectral image interpretation, unifying two standard analysis techniques, namely unmixing and classification.
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