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

Grouping-matrix based Graph Pooling with Adaptive Number of Clusters

Graph pooling is a crucial operation for encoding hierarchical structures within graphs. Most existing graph pooling approaches formulate the problem as a node clustering task which effectively captures the graph topology. Conventional methods ask users to specify an appropriate number of clusters as a hyperparameter, then assume that all input graphs share the same number of clusters. In inductive settings where the number of clusters can vary, however, the model should be able to represent this variation in its pooling layers in order to learn suitable clusters. Thus we propose GMPool, a novel differentiable graph pooling architecture that automatically determines the appropriate number of clusters based on the input data. The main intuition involves a grouping matrix defined as a quadratic form of the pooling operator, which induces use of binary classification probabilities of pairwise combinations of nodes. GMPool obtains the pooling operator by first computing the grouping matrix, then decomposing it. Extensive evaluations on molecular property prediction tasks demonstrate that our method outperforms conventional methods.Comment: 10 pages, 3 figure

Learning Linear Dynamical Systems via Spectral Filtering

We present an efficient and practical algorithm for the online prediction of discrete-time linear dynamical systems with a symmetric transition matrix. We circumvent the non-convex optimization problem using improper learning: carefully overparameterize the class of LDSs by a polylogarithmic factor, in exchange for convexity of the loss functions. From this arises a polynomial-time algorithm with a near-optimal regret guarantee, with an analogous sample complexity bound for agnostic learning. Our algorithm is based on a novel filtering technique, which may be of independent interest: we convolve the time series with the eigenvectors of a certain Hankel matrix.Comment: Published as a conference paper at NIPS 201

New Deep Neural Networks for Unsupervised Feature Learning on Graph Data

Graph data are ubiquitous in the real world, such as social networks, biological networks. To analyze graph data, a fundamental task is to learn node features to benefit downstream tasks, such as node classification, community detection. Inspired by the powerful feature learning capability of deep neural networks on various tasks, it is important and necessary to explore deep neural networks for feature learning on graphs. Different from the regular image and sequence data, graph data encode the complicated relational information between different nodes, which challenges the classical deep neural networks. Moreover, in real-world applications, the label of nodes in graph data is usually not available, which makes the feature learning on graphs more difficult. To address these challenging issues, this thesis is focusing on designing new deep neural networks to effectively explore the relational information for unsupervised feature learning on graph data. First, to address the sparseness issue of the relational information, I propose a new proximity generative adversarial network which can discover the underlying relational information for learning better node representations. Meanwhile, a new self-paced network embedding method is designed to address the unbalance issue of the relational information when learning node representations. Additionally, to deal with rich attributes associated to nodes, I develop a new deep neural network to capture various relational information in both topological structure and node attributes for enhancing network embedding. Furthermore, to preserve the relational information in the hidden layers of deep neural networks, I develop a novel graph convolutional neural network (GCN) based on conditional random fields, which is the first algorithm applying this kind of graphical models to graph neural networks in an unsupervised manner

3D Generative Model Latent Disentanglement via Local Eigenprojection

Designing realistic digital humans is extremely complex. Most data-driven generative models used to simplify the creation of their underlying geometric shape do not offer control over the generation of local shape attributes. In this paper, we overcome this limitation by introducing a novel loss function grounded in spectral geometry and applicable to different neural-network-based generative models of 3D head and body meshes. Encouraging the latent variables of mesh variational autoencoders (VAEs) or generative adversarial networks (GANs) to follow the local eigenprojections of identity attributes, we improve latent disentanglement and properly decouple the attribute creation. Experimental results show that our local eigenprojection disentangled (LED) models not only offer improved disentanglement with respect to the state-of-the-art, but also maintain good generation capabilities with training times comparable to the vanilla implementations of the models. Our code and pre-trained models are available at github.com/simofoti/LocalEigenprojDisentangled