ST-UNet: A Spatio-Temporal U-Network for Graph-structured Time Series Modeling

The spatio-temporal graph learning is becoming an increasingly important object of graph study. Many application domains involve highly dynamic graphs where temporal information is crucial, e.g. traffic networks and financial transaction graphs. Despite the constant progress made on learning structured data, there is still a lack of effective means to extract dynamic complex features from spatio-temporal structures. Particularly, conventional models such as convolutional networks or recurrent neural networks are incapable of revealing the temporal patterns in short or long terms and exploring the spatial properties in local or global scope from spatio-temporal graphs simultaneously. To tackle this problem, we design a novel multi-scale architecture, Spatio-Temporal U-Net (ST-UNet), for graph-structured time series modeling. In this U-shaped network, a paired sampling operation is proposed in spacetime domain accordingly: the pooling (ST-Pool) coarsens the input graph in spatial from its deterministic partition while abstracts multi-resolution temporal dependencies through dilated recurrent skip connections; based on previous settings in the downsampling, the unpooling (ST-Unpool) restores the original structure of spatio-temporal graphs and resumes regular intervals within graph sequences. Experiments on spatio-temporal prediction tasks demonstrate that our model effectively captures comprehensive features in multiple scales and achieves substantial improvements over mainstream methods on several real-world datasets.

3D Graph Convolutional Networks with Temporal Graphs: A Spatial Information Free Framework For Traffic Forecasting

Spatio-temporal prediction plays an important role in many application areas especially in traffic domain. However, due to complicated spatio-temporal dependency and high non-linear dynamics in road networks, traffic prediction task is still challenging. Existing works either exhibit heavy training cost or fail to accurately capture the spatio-temporal patterns, also ignore the correlation between distant roads that share the similar patterns. In this paper, we propose a novel deep learning framework to overcome these issues: 3D Temporal Graph Convolutional Networks (3D-TGCN). Two novel components of our model are introduced. (1) Instead of constructing the road graph based on spatial information, we learn it by comparing the similarity between time series for each road, thus providing a spatial information free framework. (2) We propose an original 3D graph convolution model to model the spatio-temporal data more accurately. Empirical results show that 3D-TGCN could outperform state-of-the-art baselines.

Tangent-Normal Adversarial Regularization for Semi-supervised Learning

The ever-increasing size of modern datasets combined with the difficulty of obtaining label information has made semi-supervised learning of significant practical importance in modern machine learning applications. Compared with supervised learning, the key difficulty in semi-supervised learning is how to make full use of the unlabeled data. In order to utilize manifold information provided by unlabeled data, we propose a novel regularization called the tangent-normal adversarial regularization, which is composed by two parts. The two terms complement with each other and jointly enforce the smoothness along two different directions that are crucial for semi-supervised learning. One is applied along the tangent space of the data manifold, aiming to enforce local invariance of the classifier on the manifold, while the other is performed on the normal space orthogonal to the tangent space, intending to impose robustness on the classifier against the noise causing the observed data deviating from the underlying data manifold. Both of the two regularizers are achieved by the strategy of virtual adversarial training. Our method has achieved state-of-the-art performance on semi-supervised learning tasks on both artificial dataset and FashionMNIST dataset.

Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting

Timely accurate traffic forecast is crucial for urban traffic control and guidance. Due to the high nonlinearity and complexity of traffic flow, traditional methods cannot satisfy the requirements of mid-and-long term prediction tasks and often neglect spatial and temporal dependencies. In this paper, we propose a novel deep learning framework, Spatio-Temporal Graph Convolutional Networks (STGCN), to tackle the time series prediction problem in traffic domain. Instead of applying regular convolutional and recurrent units, we formulate the problem on graphs and build the model with complete convolutional structures, which enable much faster training speed with fewer parameters. Experiments show that our model STGCN effectively captures comprehensive spatio-temporal correlations through modeling multi-scale traffic networks and consistently outperforms state-of-the-art baselines on various real-world traffic datasets.

The Anisotropic Noise in Stochastic Gradient Descent: Its Behavior of Escaping from Minima and Regularization Effects

Understanding the behavior of stochastic gradient descent (SGD) in the context of deep neural networks has raised lots of concerns recently. Along this line, we theoretically study a general form of gradient based optimization dynamics with unbiased noise, which unifies SGD and standard Langevin dynamics. Through investigating this general optimization dynamics, we analyze the behavior of SGD on escaping from minima and its regularization effects. A novel indicator is derived to characterize the efficiency of escaping from minima through measuring the alignment of noise covariance and the curvature of loss function. Based on this indicator, two conditions are established to show which type of noise structure is superior to isotropic noise in term of escaping efficiency. We further show that the anisotropic noise in SGD satisfies the two conditions, and thus helps to escape from sharp and poor minima effectively, towards more stable and flat minima that typically generalize well. We verify our understanding through comparing this anisotropic diffusion with full gradient descent plus isotropic diffusion (i.e. Langevin dynamics) and other types of position-dependent noise.

Load Balanced GANs for Multi-view Face Image Synthesis

Multi-view face synthesis from a single image is an ill-posed problem and often suffers from serious appearance distortion. Producing photo-realistic and identity preserving multi-view results is still a not well defined synthesis problem. This paper proposes Load Balanced Generative Adversarial Networks (LB-GAN) to precisely rotate the yaw angle of an input face image to any specified angle. LB-GAN decomposes the challenging synthesis problem into two well constrained subtasks that correspond to a face normalizer and a face editor respectively. The normalizer first frontalizes an input image, and then the editor rotates the frontalized image to a desired pose guided by a remote code. In order to generate photo-realistic local details, the normalizer and the editor are trained in a two-stage manner and regulated by a conditional self-cycle loss and an attention based L2 loss. Exhaustive experiments on controlled and uncontrolled environments demonstrate that the proposed method not only improves the visual realism of multi-view synthetic images, but also preserves identity information well.

The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems

We propose a deep learning based method, the Deep Ritz Method, for numerically solving variational problems, particularly the ones that arise from partial differential equations. The Deep Ritz method is naturally nonlinear, naturally adaptive and has the potential to work in rather high dimensions. The framework is quite simple and fits well with the stochastic gradient descent method used in deep learning. We illustrate the method on several problems including some eigenvalue problems.