Jie Chen

Han Huang, Jiajia Yu, Jie Chen et al.

Mean-field games (MFGs) are a modeling framework for systems with a large number of interacting agents. They have applications in economics, finance, and game theory. Normalizing flows (NFs) are a family of deep generative models that compute data likelihoods by using an invertible mapping, which is typically parameterized by using neural networks. They are useful for density modeling and data generation. While active research has been conducted on both models, few noted the relationship between the two. In this work, we unravel the connections between MFGs and NFs by contextualizing the training of an NF as solving the MFG. This is achieved by reformulating the MFG problem in terms of agent trajectories and parameterizing a discretization of the resulting MFG with flow architectures. With this connection, we explore two research directions. First, we employ expressive NF architectures to accurately solve high-dimensional MFGs, sidestepping the curse of dimensionality in traditional numerical methods. Compared with other deep learning approaches, our trajectory-based formulation encodes the continuity equation in the neural network, resulting in a better approximation of the population dynamics. Second, we regularize the training of NFs with transport costs and show the effectiveness on controlling the model's Lipschitz bound, resulting in better generalization performance. We demonstrate numerical results through comprehensive experiments on a variety of synthetic and real-life datasets.

Xiao Zang, Yi Xie, Siyu Liao et al.

Noise injection-based regularization, such as Dropout, has been widely used in image domain to improve the performance of deep neural networks (DNNs). However, efficient regularization in the point cloud domain is rarely exploited, and most of the state-of-the-art works focus on data augmentation-based regularization. In this paper, we, for the first time, perform systematic investigation on noise injection-based regularization for point cloud-domain DNNs. To be specific, we propose a series of regularization techniques, namely DropFeat, DropPoint and DropCluster, to perform noise injection on the point feature maps at the feature level, point level and cluster level, respectively. We also empirically analyze the impacts of different factors, including dropping rate, cluster size and dropping position, to obtain useful insights and general deployment guidelines, which can facilitate the adoption of our approaches across different datasets and DNN architectures. We evaluate our proposed approaches on various DNN models for different point cloud processing tasks. Experimental results show our approaches enable significant performance improvement. Notably, our DropCluster brings 1.5%, 1.3% and 0.8% higher overall accuracy for PointNet, PointNet++ and DGCNN, respectively, on ModelNet40 shape classification dataset. On ShapeNet part segmentation dataset, DropCluster brings 0.5%, 0.5% and 0.2% mean Intersection-over-union (IoU) increase for PointNet, PointNet++ and DGCNN, respectively. On S3DIS semantic segmentation dataset, DropCluster improves the mean IoU of PointNet, PointNet++ and DGCNN by 3.2%, 2.9% and 3.7%, respectively. Meanwhile, DropCluster also enables the overall accuracy increase for these three popular backbone DNNs by 2.4%, 2.2% and 1.8%, respectively.