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Found 26 papers, 5 papers with code
Unsupervised Solution Operator Learning for Mean-Field Games via Sampling-Invariant Parametrizations
To ensure the proposed parametrization is well-suited for operator learning, we introduce and prove the notion of sampling invariance for our model, establishing its convergence to a continuous operator in the sampling limit.
Emulating Complex Synapses Using Interlinked Proton Conductors
The memory consolidation from coupled storage components is revealed by both numerical simulations and experimental observations.
Generalization Error Guaranteed Auto-Encoder-Based Nonlinear Model Reduction for Operator Learning
The problem of operator learning, in this context, seeks to extract these physical processes from empirical data, which is challenging due to the infinite or high dimensionality of data.
Deep Nonparametric Estimation of Intrinsic Data Structures by Chart Autoencoders: Generalization Error and Robustness
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
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.
Bridging Mean-Field Games and Normalizing Flows with Trajectory Regularization
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
Massive molecular simulations of drug-target proteins have been used as a tool to understand disease mechanism and develop therapeutics.
Manifoldron: Direct Space Partition via Manifold Discovery
A neural network with the widely-used ReLU activation has been shown to partition the sample space into many convex polytopes for prediction.
On Expressivity and Trainability of Quadratic Networks
Despite promising results so far achieved by networks of quadratic neurons, there are important issues not well addressed.
$G^3$: Representation Learning and Generation for Geometric Graphs
A geometric graph is a graph equipped with geometric information (i. e., node coordinates).
Unsupervised Geometric Disentanglement via CFAN-VAE
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.
ProGAE: A Geometric Autoencoder-based Generative Model for Disentangling Protein Dynamics
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
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
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
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.
Efficient and Robust Shape Correspondence via Sparsity-Enforced Quadratic Assignment
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
While classic studies proved that wide networks allow universal approximation, recent research and successes of deep learning demonstrate the power of deep networks.
Chart Auto-Encoders for Manifold Structured Data
CAE admits desirable manifold properties that auto-encoders with a flat latent space fail to obey, predominantly proximity of data.
Optimizing Loss Landscape Connectivity via Neuron Alignment
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
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.
Nonisometric Surface Registration via Conformal Laplace-Beltrami Basis Pursuit
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.
Rational Neural Networks for Approximating Jump Discontinuities of Graph Convolution Operator
RatioanlNet is proposed to integrate rational function and neural networks.
Parallel Transport Convolution: A New Tool for Convolutional Neural Networks on Manifolds
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
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.
CT Image Reconstruction in a Low Dimensional Manifold
In this paper, we propose a CT image reconstruction method based on the prior knowledge of the low-dimensional manifold of CT image.
Manifold Based Low-rank Regularization for Image Restoration and Semi-supervised Learning
Low-rank structures play important role in recent advances of many problems in image science and data science.
