Building Deep Networks on Grassmann Manifolds

Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean network paradigm to Grassmann manifolds. In particular, we design full rank mapping layers to transform input Grassmannian data to more desirable ones, exploit re-orthonormalization layers to normalize the resulting matrices, study projection pooling layers to reduce the model complexity in the Grassmannian context, and devise projection mapping layers to respect Grassmannian geometry and meanwhile achieve Euclidean forms for regular output layers. To train the Grassmann networks, we exploit a stochastic gradient descent setting on manifolds of the connection weights, and study a matrix generalization of backpropagation to update the structured data. The evaluations on three visual recognition tasks show that our Grassmann networks have clear advantages over existing Grassmann learning methods, and achieve results comparable with state-of-the-art approaches.Comment: AAAI'18 pape

A Deep Learning Approach to Structured Signal Recovery

In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy algorithms, we introduce a deep learning framework that supports both linear and mildly nonlinear measurements, that learns a structured representation from training data, and that efficiently computes a signal estimate. In particular, we apply a stacked denoising autoencoder (SDA), as an unsupervised feature learner. SDA enables us to capture statistical dependencies between the different elements of certain signals and improve signal recovery performance as compared to the CS approach

Superpixel Convolutional Networks using Bilateral Inceptions

In this paper we propose a CNN architecture for semantic image segmentation. We introduce a new 'bilateral inception' module that can be inserted in existing CNN architectures and performs bilateral filtering, at multiple feature-scales, between superpixels in an image. The feature spaces for bilateral filtering and other parameters of the module are learned end-to-end using standard backpropagation techniques. The bilateral inception module addresses two issues that arise with general CNN segmentation architectures. First, this module propagates information between (super) pixels while respecting image edges, thus using the structured information of the problem for improved results. Second, the layer recovers a full resolution segmentation result from the lower resolution solution of a CNN. In the experiments, we modify several existing CNN architectures by inserting our inception module between the last CNN (1x1 convolution) layers. Empirical results on three different datasets show reliable improvements not only in comparison to the baseline networks, but also in comparison to several dense-pixel prediction techniques such as CRFs, while being competitive in time.Comment: European Conference on Computer Vision (ECCV), 201

Towards Faster Training of Global Covariance Pooling Networks by Iterative Matrix Square Root Normalization

Global covariance pooling in convolutional neural networks has achieved impressive improvement over the classical first-order pooling. Recent works have shown matrix square root normalization plays a central role in achieving state-of-the-art performance. However, existing methods depend heavily on eigendecomposition (EIG) or singular value decomposition (SVD), suffering from inefficient training due to limited support of EIG and SVD on GPU. Towards addressing this problem, we propose an iterative matrix square root normalization method for fast end-to-end training of global covariance pooling networks. At the core of our method is a meta-layer designed with loop-embedded directed graph structure. The meta-layer consists of three consecutive nonlinear structured layers, which perform pre-normalization, coupled matrix iteration and post-compensation, respectively. Our method is much faster than EIG or SVD based ones, since it involves only matrix multiplications, suitable for parallel implementation on GPU. Moreover, the proposed network with ResNet architecture can converge in much less epochs, further accelerating network training. On large-scale ImageNet, we achieve competitive performance superior to existing counterparts. By finetuning our models pre-trained on ImageNet, we establish state-of-the-art results on three challenging fine-grained benchmarks. The source code and network models will be available at http://www.peihuali.org/iSQRT-COVComment: Accepted to CVPR 201