The Convolution Exponential and Generalized Sylvester Flows

This paper introduces a new method to build linear flows, by taking the exponential of a linear transformation. This linear transformation does not need to be invertible itself, and the exponential has the following desirable properties: it is guaranteed to be invertible, its inverse is straightforward to compute and the log Jacobian determinant is equal to the trace of the linear transformation. An important insight is that the exponential can be computed implicitly, which allows the use of convolutional layers. Using this insight, we develop new invertible transformations named convolution exponentials and graph convolution exponentials, which retain the equivariance of their underlying transformations. In addition, we generalize Sylvester Flows and propose Convolutional Sylvester Flows which are based on the generalization and the convolution exponential as basis change. Empirically, we show that the convolution exponential outperforms other linear transformations in generative flows on CIFAR10 and the graph convolution exponential improves the performance of graph normalizing flows. In addition, we show that Convolutional Sylvester Flows improve performance over residual flows as a generative flow model measured in log-likelihood

Scalable Deep Traffic Flow Neural Networks for Urban Traffic Congestion Prediction

Tracking congestion throughout the network road is a critical component of Intelligent transportation network management systems. Understanding how the traffic flows and short-term prediction of congestion occurrence due to rush-hour or incidents can be beneficial to such systems to effectively manage and direct the traffic to the most appropriate detours. Many of the current traffic flow prediction systems are designed by utilizing a central processing component where the prediction is carried out through aggregation of the information gathered from all measuring stations. However, centralized systems are not scalable and fail provide real-time feedback to the system whereas in a decentralized scheme, each node is responsible to predict its own short-term congestion based on the local current measurements in neighboring nodes. We propose a decentralized deep learning-based method where each node accurately predicts its own congestion state in real-time based on the congestion state of the neighboring stations. Moreover, historical data from the deployment site is not required, which makes the proposed method more suitable for newly installed stations. In order to achieve higher performance, we introduce a regularized Euclidean loss function that favors high congestion samples over low congestion samples to avoid the impact of the unbalanced training dataset. A novel dataset for this purpose is designed based on the traffic data obtained from traffic control stations in northern California. Extensive experiments conducted on the designed benchmark reflect a successful congestion prediction