Search Results for author: Rongjie Lai

Found 23 papers, 5 papers with code

Deep Nonparametric Estimation of Intrinsic Data Structures by Chart Autoencoders: Generalization Error and Robustness

no code implementations17 Mar 2023 Hao liu, Alex Havrilla, Rongjie Lai, Wenjing Liao

Our paper establishes statistical guarantees on the generalization error of chart autoencoders, and we demonstrate their denoising capabilities by considering $n$ noisy training samples, along with their noise-free counterparts, on a $d$-dimensional manifold.


Semi-Supervised Manifold Learning with Complexity Decoupled Chart Autoencoders

no code implementations22 Aug 2022 Stefan C. Schonsheck, Scott Mahan, Timo Klock, Alexander Cloninger, Rongjie Lai

Our numerical experiments on synthetic and real-world data verify that the proposed model can effectively manage data with multi-class nearby but disjoint manifolds of different classes, overlapping manifolds, and manifolds with non-trivial topology.

Representation Learning

Bridging Mean-Field Games and Normalizing Flows with Trajectory Regularization

no code implementations30 Jun 2022 Han Huang, Jiajia Yu, Jie Chen, Rongjie Lai

In this work, we unravel the connections between MFGs and NFs by contextualizing the training of an NF as solving the MFG.

Learning Geometrically Disentangled Representations of Protein Folding Simulations

no code implementations20 May 2022 N. Joseph Tatro, Payel Das, Pin-Yu Chen, Vijil Chenthamarakshan, Rongjie Lai

Massive molecular simulations of drug-target proteins have been used as a tool to understand disease mechanism and develop therapeutics.

Protein Folding

Manifoldron: Direct Space Partition via Manifold Discovery

2 code implementations14 Jan 2022 Dayang Wang, Feng-Lei Fan, Bo-Jian Hou, Hao Zhang, Zhen Jia, Boce Zhou, Rongjie Lai, Hengyong Yu, Fei Wang

A neural network with the widely-used ReLU activation has been shown to partition the sample space into many convex polytopes for prediction.

BIG-bench Machine Learning

On Expressivity and Trainability of Quadratic Networks

1 code implementation12 Oct 2021 Feng-Lei Fan, Mengzhou Li, Fei Wang, Rongjie Lai, Ge Wang

Despite promising results so far achieved by networks of quadratic neurons, there are important issues not well addressed.

Unsupervised Geometric Disentanglement via CFAN-VAE

no code implementations ICLR Workshop GTRL 2021 Norman 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-Euclidean data such as 3D deformable models.

Disentanglement Pose Transfer

ProGAE: A Geometric Autoencoder-based Generative Model for Disentangling Protein Dynamics

no code implementations1 Jan 2021 Norman Joseph Tatro, Payel Das, Pin-Yu Chen, Vijil Chenthamarakshan, Rongjie Lai

Empowered by the disentangled latent space learning, the extrinsic latent embedding is successfully used for classification or property prediction of different drugs bound to a specific protein.

Optimizing Mode Connectivity via Neuron Alignment

1 code implementation NeurIPS 2020 N. Joseph Tatro, Pin-Yu Chen, Payel Das, Igor Melnyk, Prasanna Sattigeri, Rongjie Lai

Yet, current curve finding algorithms do not consider the influence of symmetry in the loss surface created by model weight permutations.

A Dual Iterative Refinement Method for Non-rigid Shape Matching

1 code implementation CVPR 2021 Rui Xiang, Rongjie Lai, Hongkai Zhao

The key idea is to use dual information, such as spatial and spectral, or local and global features, in a complementary and effective way, and extract more accurate information from current iteration to use for the next iteration.

Unsupervised Geometric Disentanglement for Surfaces via CFAN-VAE

no code implementations23 May 2020 N. Joseph Tatro, Stefan C. Schonsheck, Rongjie Lai

We also successfully detect a level of geometric disentanglement in mesh convolutional autoencoders that encode xyz-coordinates directly by registering its latent space to that of CFAN-VAE.

Disentanglement Pose Transfer

Efficient and Robust Shape Correspondence via Sparsity-Enforced Quadratic Assignment

no code implementations CVPR 2020 Rui Xiang, Rongjie Lai, Hongkai Zhao

To solve the resulting quadratic assignment problem efficiently, the two key ideas of our iterative algorithm are: 1) select pairs with good (approximate) correspondence as anchor points, 2) solve a regularized quadratic assignment problem only in the neighborhood of selected anchor points through sparsity control.

Quasi-Equivalence of Width and Depth of Neural Networks

no code implementations6 Feb 2020 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.

Classification General Classification

Chart Auto-Encoders for Manifold Structured Data

no code implementations20 Dec 2019 Stefan Schonsheck, Jie Chen, Rongjie Lai

CAE admits desirable manifold properties that auto-encoders with a flat latent space fail to obey, predominantly proximity of data.

Representation Learning

Optimizing Loss Landscape Connectivity via Neuron Alignment

no code implementations25 Sep 2019 N. Joseph Tatro, Pin-Yu Chen, Payel Das, Igor Melnyk, Prasanna Sattigeri, Rongjie Lai

Empirically, this initialization is critical for efficiently learning a simple, planar, low-loss curve between networks that successfully generalizes.

NPTC-net: Narrow-Band Parallel Transport Convolutional Neural Network on Point Clouds

no code implementations29 May 2019 Pengfei Jin, Tianhao Lai, Rongjie Lai, Bin Dong

Designing appropriate convolution neural networks on manifold-structured point clouds can inherit and empower recent advances of CNNs to analyzing and processing point cloud data.

General Classification Point Cloud Classification

Nonisometric Surface Registration via Conformal Laplace-Beltrami Basis Pursuit

no code implementations19 Sep 2018 Stefan C. Schonsheck, Michael M. Bronstein, Rongjie Lai

In this paper, we propose a variational model to align the Laplace-Beltrami (LB) eigensytems of two non-isometric genus zero shapes via conformal deformations.

Parallel Transport Convolution: A New Tool for Convolutional Neural Networks on Manifolds

no code implementations21 May 2018 Stefan C. Schonsheck, Bin Dong, Rongjie Lai

PTC allows for the construction of compactly supported filters and is also robust to manifold deformations.

Exact Reconstruction of Euclidean Distance Geometry Problem Using Low-rank Matrix Completion

no code implementations12 Apr 2018 Abiy Tasissa, Rongjie Lai

In this paper, this minimization program is recast as a matrix completion problem of a low-rank $r$ Gram matrix with respect to a suitable basis.

Low-Rank Matrix Completion

CT Image Reconstruction in a Low Dimensional Manifold

no code implementations16 Apr 2017 Wenxiang Cong, Ge Wang, Qingsong Yang, Jiang Hsieh, Jia Li, Rongjie Lai

In this paper, we propose a CT image reconstruction method based on the prior knowledge of the low-dimensional manifold of CT image.

Image Reconstruction

Manifold Based Low-rank Regularization for Image Restoration and Semi-supervised Learning

no code implementations9 Feb 2017 Rongjie Lai, Jia Li

Low-rank structures play important role in recent advances of many problems in image science and data science.

Image Inpainting Image Reconstruction +2

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