Search Results for author:
Found 36 papers, 10 papers with code
Interpolation between CNNs and ResNets
Although ordinary differential equations (ODEs) provide insights for designing networks architectures, its relationship with the non-residual convolutional neural networks (CNNs) is still unclear.
Convection-Diffusion Equation: A Theoretically Certified Framework for Neural Networks
Neural network can be viewed as a map from a simple base model to a complicate function.
Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decay
The generalization error curve of certain kernel regression method aims at determining the exact order of generalization error with various source condition, noise level and choice of the regularization parameter rather than the minimax rate.
Neural Born Series Operator for Biomedical Ultrasound Computed Tomography
Ultrasound Computed Tomography (USCT) provides a radiation-free option for high-resolution clinical imaging.
Reconstruction of dynamical systems from data without time labels
In this paper, we study the method to reconstruct dynamical systems from data without time labels.
Addressing preferred orientation in single-particle cryo-EM through AI-generated auxiliary particles
The single-particle cryo-EM field faces the persistent challenge of preferred orientation, lacking general computational solutions.
An axiomatized PDE model of deep neural networks
Based on the convection-diffusion equation, we design a new training method for ResNets.
Non-Line-of-Sight Imaging With Signal Superresolution Network
This paper proposes a general learning-based pipeline for increasing imaging quality with only a few scanning points.
Few-shot Non-line-of-sight Imaging with Signal-surface Collaborative Regularization
In this work, we propose a signal-surface collaborative regularization (SSCR) framework that provides noise-robust reconstructions with a minimal number of measurements.
Non-line-of-sight imaging with arbitrary illumination and detection pattern
Non-line-of-sight (NLOS) imaging aims at reconstructing targets obscured from the direct line of sight.
Point normal orientation and surface reconstruction by incorporating isovalue constraints to Poisson equation
In this work, we bridge orientation and reconstruction in the implicit space and propose a novel approach to orient point cloud normals by incorporating isovalue constraints to the Poisson equation.
Semi-Supervised Clustering via Dynamic Graph Structure Learning
However, existing methods adopt a static affinity matrix to learn the low-dimensional representations of data points and do not optimize the affinity matrix during the learning process.
A scalable deep learning approach for solving high-dimensional dynamic optimal transport
In this work, we propose a deep learning based method to solve the dynamic optimal transport in high dimensional space.
BI-GreenNet: Learning Green's functions by boundary integral network
In addition, we also use the Green's function calculated by our method to solve a class of PDE, and also obtain high-precision solutions, which shows the good generalization ability of our method on solving PDEs.
M2N: Mesh Movement Networks for PDE Solvers
However, mesh movement methods, such as the Monge-Ampere method, require the solution of auxiliary equations, which can be extremely expensive especially when the mesh is adapted frequently.
Unsupervised Deep Learning Meets Chan-Vese Model
The Chan-Vese (CV) model is a classic region-based method in image segmentation.
Learning Modified Indicator Functions for Surface Reconstruction
We design a novel deep neural network to perform surface integral and learn the modified indicator functions from un-oriented and noisy point clouds.
Training Deep Neural Networks with Adaptive Momentum Inspired by the Quadratic Optimization
In this paper, to eliminate the effort for tuning the momentum-related hyperparameter, we propose a new adaptive momentum inspired by the optimal choice of the heavy ball momentum for quadratic optimization.
A framework of deep neural networks via the solution operator of partial differential equations
To show the effectiveness for general form of PDEs, we show that several effective networks can be interpreted by our general form of PDEs and design a training method motivated by PDEs theory to train DNN models for better robustness and less chance of overfitting.
A neural network framework for learning Green's function
Green's function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs).
Performance-Guaranteed ODE Solvers with Complexity-Informed Neural Networks
Traditionally, we provide technical parameters for ODE solvers, such as the order, the stepsize and the local error threshold.
Diffusion Mechanism in Residual Neural Network: Theory and Applications
In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data points and is a critical component for achieving high classification accuracy.
A Second-Order Nonlocal Approximation for Manifold Poisson Model with Dirichlet Boundary
Recently, we constructed a class of nonlocal Poisson model on manifold under Dirichlet boundary with global $\mathcal{O}(\delta^2)$ truncation error to its local counterpart, where $\delta$ denotes the nonlocal horizon parameter.
Numerical Analysis Numerical Analysis Analysis of PDEs
Deep Learning with Data Privacy via Residual Perturbation
Empirically, we show that residual perturbation outperforms the state-of-the-art DP stochastic gradient descent (DPSGD) in both membership privacy protection and maintaining the DL models' utility.
An Unsupervised Deep Learning Approach for Real-World Image Denoising
In the real-world case, the noise distribution is so complex that the simplified additive white Gaussian (AWGN) assumption rarely holds, which significantly deteriorates the Gaussian denoisers' performance.
Layer-wise Adversarial Defense: An ODE Perspective
Deep neural networks are observed to be fragile against adversarial attacks, which have dramatically limited their practical applicability.
Task-Oriented Feature Distillation
Moreover, an orthogonal loss is applied to the feature resizing layer in TOFD to improve the performance of knowledge distillation.
Interpolation between Residual and Non-Residual Networks
Although ordinary differential equations (ODEs) provide insights for designing network architectures, its relationship with the non-residual convolutional neural networks (CNNs) is still unclear.
CURE: Curvature Regularization For Missing Data Recovery
For that, we introduce a new regularization by combining the low dimension manifold regularization with a higher order Curvature Regularization, and we call this new regularization CURE for short.
ResNets Ensemble via the Feynman-Kac Formalism to Improve Natural and Robust Accuracies
However, both natural and robust accuracies, in classifying clean and adversarial images, respectively, of the trained robust models are far from satisfactory.
Deep Neural Nets with Interpolating Function as Output Activation
We replace the output layer of deep neural nets, typically the softmax function, by a novel interpolating function.
Weighted Nonlocal Total Variation in Image Processing
In this paper, a novel weighted nonlocal total variation (WNTV) method is proposed.
A Flow Model of Neural Networks
Based on a natural connection between ResNet and transport equation or its characteristic equation, we propose a continuous flow model for both ResNet and plain net.
Scalable low dimensional manifold model in the reconstruction of noisy and incomplete hyperspectral images
We present a scalable low dimensional manifold model for the reconstruction of noisy and incomplete hyperspectral images.
A Harmonic Extension Approach for Collaborative Ranking
We present a new perspective on graph-based methods for collaborative ranking for recommender systems.
Harmonic Extension
To tackle this problem, we propose a new method called the point integral method (PIM).
