no code implementations • 17 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.
no code implementations • 22 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.
no code implementations • 30 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.
no code implementations • 20 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.
2 code implementations • 14 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.
1 code implementation • 12 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.
no code implementations • 29 Sep 2021 • Han Huang, Stefan C Schonsheck, Rongjie Lai, Jie Chen
A geometric graph is a graph equipped with geometric information (i. e., node coordinates).
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.
no code implementations • 1 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.
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.
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.
no code implementations • 23 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.
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.
no code implementations • 6 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.
no code implementations • 20 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.
no code implementations • 25 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.
no code implementations • 29 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.
no code implementations • 19 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.
1 code implementation • 30 Aug 2018 • Zhiqian Chen, Feng Chen, Rongjie Lai, Xuchao Zhang, Chang-Tien Lu
RatioanlNet is proposed to integrate rational function and neural networks.
no code implementations • 21 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.
no code implementations • 12 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.
no code implementations • 16 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.
no code implementations • 9 Feb 2017 • Rongjie Lai, Jia Li
Low-rank structures play important role in recent advances of many problems in image science and data science.