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Found 29 papers, 14 papers with code
Noise-Free Sampling Algorithms via Regularized Wasserstein Proximals
The score term is given in closed form by a regularized Wasserstein proximal, using a kernel convolution that is approximated by sampling.
Neural Collapse in Deep Linear Networks: From Balanced to Imbalanced Data
Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing.
Taming Hyperparameter Tuning in Continuous Normalizing Flows Using the JKO Scheme
Instead of tuning $\alpha$, we repeatedly solve the optimization problem for a fixed $\alpha$ effectively performing a JKO update with a time-step $\alpha$.
Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvature
Graph Neural Networks (GNNs) had been demonstrated to be inherently susceptible to the problems of over-smoothing and over-squashing.
Improving Generative Flow Networks with Path Regularization
Generative Flow Networks (GFlowNets) are recently proposed models for learning stochastic policies that generate compositional objects by sequences of actions with the probability proportional to a given reward function.
Neural ODE Control for Trajectory Approximation of Continuity Equation
As a corollary to this result, we establish that the continuity equation of the neural ODE is approximately controllable on the set of compactly supported probability measures that are absolutely continuous with respect to the Lebesgue measure.
How Does Momentum Benefit Deep Neural Networks Architecture Design? A Few Case Studies
As case studies, we consider how momentum can improve the architecture design for recurrent neural networks (RNNs), neural ordinary differential equations (ODEs), and transformers.
GRAND++: Graph Neural Diffusion with A Source Term
We propose GRAph Neural Diffusion with a source term (GRAND++) for graph deep learning with a limited number of labeled nodes, i. e., low-labeling rate.
Operator Splitting for Learning to Predict Equilibria in Convex Games
Systems of competing agents can often be modeled as games.
JFB: Jacobian-Free Backpropagation for Implicit Networks
Unlike traditional networks, implicit networks solve a fixed point equation to compute inferences.
Wasserstein Proximal of GANs
We introduce a new method for training generative adversarial networks by applying the Wasserstein-2 metric proximal on the generators.
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
Wasserstein-based Projections with Applications to Inverse Problems
To bridge this gap, we present a new algorithm that takes samples from the manifold of true data as input and outputs an approximation of the projection operator onto this manifold.
Differentially Private Federated Learning with Laplacian Smoothing
Federated learning aims to protect data privacy by collaboratively learning a model without sharing private data among users.
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.
Laplacian Smoothing Stochastic Gradient Markov Chain Monte Carlo
As an important Markov Chain Monte Carlo (MCMC) method, stochastic gradient Langevin dynamics (SGLD) algorithm has achieved great success in Bayesian learning and posterior sampling.
Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets
We prove that if the STE is properly chosen, the expected coarse gradient correlates positively with the population gradient (not available for the training), and its negation is a descent direction for minimizing the population loss.
Unnormalized Optimal Transport
We propose an extension of the computational fluid mechanics approach to the Monge-Kantorovich mass transfer problem, which was developed by Benamou-Brenier.
Optimization and Control
Decentralized Multi-Agents by Imitation of a Centralized Controller
In order to obtain multi-agents that act in a decentralized manner, we introduce a novel algorithm under the popular framework of centralized training, but decentralized execution.
Blended Coarse Gradient Descent for Full Quantization of Deep Neural Networks
We introduce the notion of coarse gradient and propose the blended coarse gradient descent (BCGD) algorithm, for training fully quantized neural networks.
Laplacian Smoothing Gradient Descent
We propose a class of very simple modifications of gradient descent and stochastic gradient descent.
BinaryRelax: A Relaxation Approach For Training Deep Neural Networks With Quantized Weights
We propose BinaryRelax, a simple two-phase algorithm, for training deep neural networks with quantized weights.
Stochastic Backward Euler: An Implicit Gradient Descent Algorithm for $k$-means Clustering
In this paper, we propose an implicit gradient descent algorithm for the classic $k$-means problem.
Deep Relaxation: partial differential equations for optimizing deep neural networks
In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs).
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.
Unsupervised Classification in Hyperspectral Imagery with Nonlocal Total Variation and Primal-Dual Hybrid Gradient Algorithm
In this paper, a graph-based nonlocal total variation method (NLTV) is proposed for unsupervised classification of hyperspectral images (HSI).
A Harmonic Extension Approach for Collaborative Ranking
We present a new perspective on graph-based methods for collaborative ranking for recommender systems.
A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-norm Fidelity
In this paper, we propose a variational multiphase image segmentation model based on fuzzy membership functions and L1-norm fidelity.
Sparse Recovery via Differential Inclusions
In this paper, we recover sparse signals from their noisy linear measurements by solving nonlinear differential inclusions, which is based on the notion of inverse scale space (ISS) developed in applied mathematics.
