Generalization and Equilibrium in Generative Adversarial Nets (GANs)

We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However, generalization does occur for a weaker metric called neural net distance. It is also shown that an approximate pure equilibrium exists in the discriminator/generator game for a special class of generators with natural training objectives when generator capacity and training set sizes are moderate. This existence of equilibrium inspires MIX+GAN protocol, which can be combined with any existing GAN training, and empirically shown to improve some of them.Comment: This is an updated version of an ICML'17 paper with the same title. The main difference is that in the ICML'17 version the pure equilibrium result was only proved for Wasserstein GAN. In the current version the result applies to most reasonable training objectives. In particular, Theorem 4.3 now applies to both original GAN and Wasserstein GA

Diastereoselective three-component synthesis of beta-amino carbonyl compounds using diazo compounds, boranes, and acyl imines under catalyst-free conditions

Diazo compounds, boranes, and acyl imines undergo a three-component Mannich condensation reaction under catalyst-free conditions to give the anti β-amino carbonyl compounds in high diastereoselectivity. The reaction tolerates a variety of functional groups, and an asymmetric variant was achieved using the (−)-phenylmenthol as chiral auxiliary in good yield and selectivity. These β-amino carbonyl compounds are valuable intermediates, which can be transformed to many potential bioactive molecules.We gratefully acknowledge Philip N. Moquist for editorial review of the manuscript. Preliminary experiments were performed by Y.L. at Boston University. Completion of the work was accomplished under the direction of G.W. at the University of Science and Technology Beijing, China. S.E.S. and Y.L. gratefully acknowledge the NIH for support (NIGMS R01 GM078240). Y.L., J.Y., and G.W. thank the Innovative Foundation from China National Petroleum Corporation (Grant No. 2012D-5006-0504) for financial support. Y.L. also thanks the Beijing Natural Science Foundation (Grant No. 2144052) and China Postdoctoral Science Foundation (2013M540859) for financial support. (NIGMS R01 GM078240 - NIH; 2012D-5006-0504 - Innovative Foundation from China National Petroleum Corporation; 2144052 - Beijing Natural Science Foundation; 2013M540859 - China Postdoctoral Science Foundation)Published versio

Weighted Bayesian Gaussian Mixture Model for Roadside LiDAR Object Detection

Background modeling is widely used for intelligent surveillance systems to detect moving targets by subtracting the static background components. Most roadside LiDAR object detection methods filter out foreground points by comparing new data points to pre-trained background references based on descriptive statistics over many frames (e.g., voxel density, number of neighbors, maximum distance). However, these solutions are inefficient under heavy traffic, and parameter values are hard to transfer from one scenario to another. In early studies, the probabilistic background modeling methods widely used for the video-based system were considered unsuitable for roadside LiDAR surveillance systems due to the sparse and unstructured point cloud data. In this paper, the raw LiDAR data were transformed into a structured representation based on the elevation and azimuth value of each LiDAR point. With this high-order tensor representation, we break the barrier to allow efficient high-dimensional multivariate analysis for roadside LiDAR background modeling. The Bayesian Nonparametric (BNP) approach integrates the intensity value and 3D measurements to exploit the measurement data using 3D and intensity info entirely. The proposed method was compared against two state-of-the-art roadside LiDAR background models, computer vision benchmark, and deep learning baselines, evaluated at point, object, and path levels under heavy traffic and challenging weather. This multimodal Weighted Bayesian Gaussian Mixture Model (GMM) can handle dynamic backgrounds with noisy measurements and substantially enhances the infrastructure-based LiDAR object detection, whereby various 3D modeling for smart city applications could be created