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Found 31 papers, 23 papers with code
PyHySCO: GPU-Enabled Susceptibility Artifact Distortion Correction in Seconds
Over the past decade, reversed Gradient Polarity (RGP) methods have become a popular approach for correcting susceptibility artifacts in Echo-Planar Imaging (EPI).
Differential Equations for Continuous-Time Deep Learning
This short, self-contained article seeks to introduce and survey continuous-time deep learning approaches that are based on neural ordinary differential equations (neural ODEs).
Learning Control Policies of Hodgkin-Huxley Neuronal Dynamics
In this setting, control policies aim to optimize therapeutic outcomes by tailoring the parameters of a DBS system, typically via electrical stimulation, in real time based on the patient's ongoing neuronal activity.
Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference
PCP-Map models conditional transport maps as the gradient of a partially input convex neural network (PICNN) and uses a novel numerical implementation to increase computational efficiency compared to state-of-the-art alternatives.
Alternating Minimization for Regression with Tropical Rational Functions
We propose an alternating minimization heuristic for regression over the space of tropical rational functions with fixed exponents.
Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generation
We thereby intend to obtain diffusion models that generalize across different resolution levels and improve the efficiency of the training process.
Improving Graph Neural Networks with Learnable Propagation Operators
Graph Neural Networks (GNNs) are limited in their propagation operators.
Multivariate Quantile Function Forecaster
We propose Multivariate Quantile Function Forecaster (MQF$^2$), a global probabilistic forecasting method constructed using a multivariate quantile function and investigate its application to multi-horizon forecasting.
slimTrain -- A Stochastic Approximation Method for Training Separable Deep Neural Networks
In the absence of theoretical guidelines or prior experience on similar tasks, this requires solving many training problems, which can be time-consuming and demanding on computational resources.
An Introduction to Deep Generative Modeling
Developing DGMs has become one of the most hotly researched fields in artificial intelligence in recent years.
Avoiding The Double Descent Phenomenon of Random Feature Models Using Hybrid Regularization
To close this gap, the hybrid method considered in our paper combines the respective strengths of the two most common forms of regularization: early stopping and weight decay.
MGIC: Multigrid-in-Channels Neural Network Architectures
We present a multigrid-in-channels (MGIC) approach that tackles the quadratic growth of the number of parameters with respect to the number of channels in standard convolutional neural networks (CNNs).
A Neural Network Approach Applied to Multi-Agent Optimal Control
Our approach is grid-free and scales efficiently to dimensions where grids become impractical or infeasible.
Optimization and Control
Train Like a (Var)Pro: Efficient Training of Neural Networks with Variable Projection
To solve the optimization problem more efficiently, we propose the use of variable projection (VarPro), a method originally designed for separable nonlinear least-squares problems.
Multigrid-in-Channels Architectures for Wide Convolutional Neural Networks
We present a multigrid approach that combats the quadratic growth of the number of parameters with respect to the number of channels in standard convolutional neural networks (CNNs).
OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transport
On five high-dimensional density estimation and generative modeling tasks, OT-Flow performs competitively to state-of-the-art CNFs while on average requiring one-fourth of the number of weights with an 8x speedup in training time and 24x speedup in inference.
PNKH-B: A Projected Newton-Krylov Method for Large-Scale Bound-Constrained Optimization
We present an interior point method to solve the quadratic projection problem efficiently.
Numerical Analysis Numerical Analysis
Discretize-Optimize vs. Optimize-Discretize for Time-Series Regression and Continuous Normalizing Flows
Neural ODEs are ordinary differential equations (ODEs) with neural network components.
A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems
State-of-the-art numerical methods for solving such problems utilize spatial discretization that leads to a curse-of-dimensionality.
LeanConvNets: Low-cost Yet Effective Convolutional Neural Networks
In practice, the input data and the hidden features consist of a large number of channels, which in most CNNs are fully coupled by the convolution operators.
LeanResNet: A Low-cost Yet Effective Convolutional Residual Networks
Convolutional Neural Networks (CNNs) filter the input data using spatial convolution operators with compact stencils.
IMEXnet: A Forward Stable Deep Neural Network
Deep convolutional neural networks have revolutionized many machine learning and computer vision tasks, however, some remaining key challenges limit their wider use.
ADMM-SOFTMAX : An ADMM Approach for Multinomial Logistic Regression
Solution of the least-squares problem can be be accelerated by pre-computing a factorization or preconditioner, and the separability in the smooth, convex problem can be easily parallelized across examples.
Never look back - A modified EnKF method and its application to the training of neural networks without back propagation
Further, we provide numerical examples that demonstrate the potential of our method for training deep neural networks.
Deep Neural Networks Motivated by Partial Differential Equations
In the latter area, PDE-based approaches interpret image data as discretizations of multivariate functions and the output of image processing algorithms as solutions to certain PDEs.
Ranked #69 on
Image Classification
on STL-10
Reversible Architectures for Arbitrarily Deep Residual Neural Networks
In this work, we interpret deep residual networks as ordinary differential equations (ODEs), which have long been studied in mathematics and physics with rich theoretical and empirical success.
Ranked #49 on
Image Classification
on STL-10
LAP: a Linearize and Project Method for Solving Inverse Problems with Coupled Variables
LAP is most promising for cases when the subproblem corresponding to one of the variables is considerably easier to solve than the other.
Stable Architectures for Deep Neural Networks
While our new architectures restrict the solution space, several numerical experiments show their competitiveness with state-of-the-art networks.
A Lagrangian Gauss-Newton-Krylov Solver for Mass- and Intensity-Preserving Diffeomorphic Image Registration
We use an optimal control formulation, in which the velocity field of a hyperbolic PDE needs to be found such that the distance between the final state of the system (the transformed/transported template image) and the observation (the reference image) is minimized.
Learning across scales - A multiscale method for Convolution Neural Networks
In this work we establish the relation between optimal control and training deep Convolution Neural Networks (CNNs).
jInv -- a flexible Julia package for PDE parameter estimation
Estimating parameters of Partial Differential Equations (PDEs) from noisy and indirect measurements often requires solving ill-posed inverse problems.
Mathematical Software
