210 citations · 416 across the 36 of their papers we have counts for
36 papers
Exact Total Variation Minimizers as Non-Oscillatory Limiters in High-Order Methods for Conservation Laws
Gabriel P. Langlois, Jerome Darbon, Rongjie Lai +2
High-order numerical methods for conservation laws can generate spurious oscillations near discontinuities. We propose to suppress these oscillations by post-processing the numeric…
Deep Nonparametric Estimation of Intrinsic Data Structures by Chart Autoencoders: Generalization Error and Robustness
Hao Liu, Alex Havrilla, Rongjie Lai +1
Autoencoders have demonstrated remarkable success in learning low-dimensional latent features of high-dimensional data across various applications. Assuming that data are sampled n…
Semi-Supervised Manifold Learning with Complexity Decoupled Chart Autoencoders
Stefan C. Schonsheck, Scott Mahan, Timo Klock +2
Autoencoding is a popular method in representation learning. Conventional autoencoders employ symmetric encoding-decoding procedures and a simple Euclidean latent space to detect h…
Bridging Mean-Field Games and Normalizing Flows with Trajectory Regularization
Han Huang, Jiajia Yu, Jie Chen +1
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 f…
Computational Mean-field Games on Manifolds
Jiajia Yu, Rongjie Lai, Wuchen Li +1
Conventional Mean-field games/control study the behavior of a large number of rational agents moving in the Euclidean spaces. In this work, we explore the mean-field games on Riema…
Learning Geometrically Disentangled Representations of Protein Folding Simulations
N. Joseph Tatro, Payel Das, Pin-Yu Chen +2
Massive molecular simulations of drug-target proteins have been used as a tool to understand disease mechanism and develop therapeutics. This work focuses on learning a generative…
Manifoldron: Direct Space Partition via Manifold Discovery
Dayang Wang, Feng-Lei Fan, Bo-Jian Hou +6
A neural network with the widely-used ReLU activation has been shown to partition the sample space into many convex polytopes for prediction. However, the parameterized way a neura…
On Expressivity and Trainability of Quadratic Networks
Feng-Lei Fan, Mengzhou Li, Fei Wang +2
Inspired by the diversity of biological neurons, quadratic artificial neurons can play an important role in deep learning models. The type of quadratic neurons of our interest repl…
A Fast Proximal Gradient Method and Convergence Analysis for Dynamic Mean Field Planning
Jiajia Yu, Rongjie Lai, Wuchen Li +1
In this paper, we propose an efficient and flexible algorithm to solve dynamic mean-field planning problems based on an accelerated proximal gradient method. Besides an easy-to-imp…
Optimizing Mode Connectivity via Neuron Alignment
N. Joseph Tatro, Pin-Yu Chen, Payel Das +3
The loss landscapes of deep neural networks are not well understood due to their high nonconvexity. Empirically, the local minima of these loss functions can be connected by a lear…
A Dual Iterative Refinement Method for Non-rigid Shape Matching
Rui Xiang, Rongjie Lai, Hongkai Zhao
In this work, a simple and efficient dual iterative refinement (DIR) method is proposed for dense correspondence between two nearly isometric shapes. The key idea is to use dual in…
Unsupervised Geometric Disentanglement for Surfaces via CFAN-VAE
N. Joseph Tatro, Stefan C. Schonsheck, Rongjie Lai
Geometric disentanglement, the separation of latent codes for intrinsic (i.e. identity) and extrinsic(i.e. pose) geometry, is a prominent task for generative models of non-Euclidea…
Efficient and Robust Shape Correspondence via Sparsity-Enforced Quadratic Assignment
Rui Xiang, Rongjie Lai, Hongkai Zhao
In this work, we introduce a novel local pairwise descriptor and then develop a simple, effective iterative method to solve the resulting quadratic assignment through sparsity cont…
Quasi-Equivalence of Width and Depth of Neural Networks
Feng-Lei Fan, Rongjie Lai, Ge Wang
While classic studies proved that wide networks allow universal approximation, recent research and successes of deep learning demonstrate the power of deep networks. Based on a sym…
Generalized Unnormalized Optimal Transport and its fast algorithms
Wonjun Lee, Rongjie Lai, Wuchen Li +1
We introduce fast algorithms for generalized unnormalized optimal transport. To handle densities with different total mass, we consider a dynamic model, which mixes the optim…
Chart Auto-Encoders for Manifold Structured Data
Stefan Schonsheck, Jie Chen, Rongjie Lai
Deep generative models have made tremendous advances in image and signal representation learning and generation. These models employ the full Euclidean space or a bounded subset as…
Shape Analysis via Functional Map Construction and Bases Pursuit
Omri Azencot, Rongjie Lai
We propose a method to simultaneously compute scalar basis functions with an associated functional map for a given pair of triangle meshes. Unlike previous techniques that put emph…
NPTC-net: Narrow-Band Parallel Transport Convolutional Neural Network on Point Clouds
Pengfei Jin, Tianhao Lai, Rongjie Lai +1
Convolution plays a crucial role in various applications in signal and image processing, analysis, and recognition. It is also the main building block of convolution neural network…
Low-rank Matrix Completion in a General Non-orthogonal Basis
Abiy Tasissa, Rongjie Lai
This paper considers theoretical analysis of recovering a low rank matrix given a few expansion coefficients with respect to any basis. The current approach generalizes the existin…
Nonisometric Surface Registration via Conformal Laplace-Beltrami Basis Pursuit
Stefan C. Schonsheck, Michael M. Bronstein, Rongjie Lai
Surface registration is one of the most fundamental problems in geometry processing. Many approaches have been developed to tackle this problem in cases where the surfaces are near…
Rational Neural Networks for Approximating Jump Discontinuities of Graph Convolution Operator
Zhiqian Chen, Feng Chen, Rongjie Lai +2
For node level graph encoding, a recent important state-of-art method is the graph convolutional networks (GCN), which nicely integrate local vertex features and graph topology in…
Parallel Transport Convolution: A New Tool for Convolutional Neural Networks on Manifolds
Stefan C. Schonsheck, Bin Dong, Rongjie Lai
Convolution has been playing a prominent role in various applications in science and engineering for many years. It is the most important operation in convolutional neural networks…
Exact Reconstruction of Euclidean Distance Geometry Problem Using Low-rank Matrix Completion
Abiy Tasissa, Rongjie Lai
The Euclidean distance geometry problem arises in a wide variety of applications, from determining molecular conformations in computational chemistry to localization in sensor netw…
Triangulated Surface Denoising using High Order Regularization with Dynamic Weights
Zheng Liu, Rongjie Lai, Huayan Zhang +1
Recovering high quality surfaces from noisy triangulated surfaces is a fundamental important problem in geometry processing. Sharp features including edges and corners can not be w…