Inspired by coarse-graining approaches used in physics, we show how similar algorithms can be adapted for data. The resulting algorithms are based on layered tree tensor networks and scale linearly with both the dimension of the input and the training set size. Computing most of the layers with an unsupervised algorithm, then optimizing just the top layer for supervised classification of the MNIST and fashion MNIST data sets gives very good results. We also discuss mixing a prior guess for supervised weights together with an unsupervised representation of the data, yielding a smaller number of features nevertheless able to give good performance.
Another related line of work is the study of convolutional arithmetic circuits or ConvACs @cite_45 @cite_40 @cite_30 , a type of neural network constructed from a tree tensor network @cite_63 . The present work could be viewed as a proposal for an unsupervised, adaptive algorithm for training ConvAC neural networks, along with variations such as replacing the upper layers with an MPS.
@cite_30 @cite_40 @cite_45 @cite_63
2766931946 2964055354 2525098248 2756815061
We propose a generalization of convolutional neural networks (CNNs) to irregular domains, through the use of an inferred graph structure. In more details, we introduce a three-step methodology to create convolutional layers that are adapted to the signals to process: 1) From a training set of signals, infer a graph representing the topology on which they evolve; 2) Identify translation operators in the vertex domain; 3) Emulate a convolution operator by translating a localized kernel on the graph. Using these layers, a convolutional neural network is built, and is trained on the initial signals to perform a classification task. Contributions are twofold. First, we adapt a definition of translations on graphs to make them more robust to irregularities, and to take into account locality of the kernel. Second, we introduce a procedure to build CNNs from data. We apply our methodology on a scrambled version of the CIFAR-10 and Haxby datasets. Without using any knowledge on the signals, we significantly outperform existing methods. Moreover, our approach extends classical CNNs on images in the sense that such networks are a particular case of our approach when the inferred graph is a grid. In this paper, we make two contributions to unsupervised domain adaptation (UDA) using the convolutional neural network (CNN). First, our approach transfers knowledge in all the convolutional layers through attention alignment. Most previous methods align high-level representations, e.g., activations of the fully connected (FC) layers. In these methods, however, the convolutional layers which underpin critical low-level domain knowledge cannot be updated directly towards reducing domain discrepancy. Specifically, we assume that the discriminative regions in an image are relatively invariant to image style changes. Based on this assumption, we propose an attention alignment scheme on all the target convolutional layers to uncover the knowledge shared by the source domain. Second, we estimate the posterior label distribution of the unlabeled data for target network training. Previous methods, which iteratively update the pseudo labels by the target network and refine the target network by the updated pseudo labels, are vulnerable to label estimation errors. Instead, our approach uses category distribution to calculate the cross-entropy loss for training, thereby ameliorating the error accumulation of the estimated labels. The two contributions allow our approach to outperform the state-of-the-art methods by +2.6 on the Office-31 dataset. Convolutional neural networks (CNNs) have achieved remarkable performance in a wide range of computer vision tasks, typically at the cost of massive computational complexity. The low speed of these networks may hinder real-time applications especially when computational resources are limited. In this paper, an efficient and effective approach is proposed to accelerate the test-phase computation of CNNs based on low-rank and group sparse tensor decomposition. Specifically, for each convolutional layer, the kernel tensor is decomposed into the sum of a small number of low multilinear rank tensors. Then we replace the original kernel tensors in all layers with the approximate tensors and fine-tune the whole net with respect to the final classification task using standard backpropagation. Comprehensive experiments on ILSVRC-12 demonstrate significant reduction in computational complexity, at the cost of negligible loss in accuracy. For the widely used VGG-16 model, our approach obtains a 6.6 @math speed-up on PC and 5.91 @math speed-up on mobile device of the whole network with less than 1 increase on top-5 error. Convolutional Neural Network (CNN) image classifiers are traditionally designed to have sequential convolutional layers with a single output layer. This is based on the assumption that all target classes should be treated equally and exclusively. However, some classes can be more difficult to distinguish than others, and classes may be organized in a hierarchy of categories. At the same time, a CNN is designed to learn internal representations that abstract from the input data based on its hierarchical layered structure. So it is natural to ask if an inverse of this idea can be applied to learn a model that can predict over a classification hierarchy using multiple output layers in decreasing order of class abstraction. In this paper, we introduce a variant of the traditional CNN model named the Branch Convolutional Neural Network (B-CNN). A B-CNN model outputs multiple predictions ordered from coarse to fine along the concatenated convolutional layers corresponding to the hierarchical structure of the target classes, which can be regarded as a form of prior knowledge on the output. To learn with B-CNNs a novel training strategy, named the Branch Training strategy (BT-strategy), is introduced which balances the strictness of the prior with the freedom to adjust parameters on the output layers to minimize the loss. In this way we show that CNN based models can be forced to learn successively coarse to fine concepts in the internal layers at the output stage, and that hierarchical prior knowledge can be adopted to boost CNN models' classification performance. Our models are evaluated to show that the B-CNN extensions improve over the corresponding baseline CNN on the benchmark datasets MNIST, CIFAR-10 and CIFAR-100.