Add to ORKGGiven a desired target distribution and an initial guess of that distribution, composed of finitely many samples, what is the best way to evolve the locations of the samples so that they more accurately represent the desired distribution A classical solution to this problem is to allow the samples to evolve according to Langevin dynamics, the stochastic particle method corresponding to the Fokker-Planck equation. In todayâ s talk, I will contrast this classical approach with a deterministic particle method corresponding to the porous medium equation. This method corresponds exactly to the mean-field dynamics of training a two layer neural network for a radial basis function activation function. We prove that, as the number of samples incre...
Introduction The work reported here began with the desire to find a network architecture that shared...
Machine learning, and in particular neural network models, have revolutionized fields such as image,...
Nowadays neural networks are a powerful tool, even if there are few mathematical results that explai...
As a counterpoint to classical stochastic particle methods for linear diffusion equations, we develo...
The method of choice for integrating the time-dependent Fokker-Planck equation in high-dimension is ...
As a counterpoint to classical stochastic particle methods for diffusion, we develop a deterministic...
We present a method for solving population density equations (PDEs)–-a mean-field technique describi...
We present a novel method for solving population density equations (PDEs) - a mean field technique d...
The quest for biologically plausible deep learning is driven, not just by the desire to explain expe...
The formation of pattern in biological systems may be modeled by a set of reaction-diffusion equatio...
textabstractIn this paper we show some further experiments with neural network sampling, a class of ...
Approximate Bayesian inference estimates descriptors of an intractable target distribution - in esse...
Finding the dynamical law of observable quantities lies at the core of physics. Within the particula...
Recently, a series of papers proposed deep learning-based approaches to sample from unnormalized tar...
Modern machine learning models are complex, hierarchical, and large-scale and are trained using non-...
Introduction The work reported here began with the desire to find a network architecture that shared...
Machine learning, and in particular neural network models, have revolutionized fields such as image,...
Nowadays neural networks are a powerful tool, even if there are few mathematical results that explai...
As a counterpoint to classical stochastic particle methods for linear diffusion equations, we develo...
The method of choice for integrating the time-dependent Fokker-Planck equation in high-dimension is ...
As a counterpoint to classical stochastic particle methods for diffusion, we develop a deterministic...
We present a method for solving population density equations (PDEs)–-a mean-field technique describi...
We present a novel method for solving population density equations (PDEs) - a mean field technique d...
The quest for biologically plausible deep learning is driven, not just by the desire to explain expe...
The formation of pattern in biological systems may be modeled by a set of reaction-diffusion equatio...
textabstractIn this paper we show some further experiments with neural network sampling, a class of ...
Approximate Bayesian inference estimates descriptors of an intractable target distribution - in esse...
Finding the dynamical law of observable quantities lies at the core of physics. Within the particula...
Recently, a series of papers proposed deep learning-based approaches to sample from unnormalized tar...
Modern machine learning models are complex, hierarchical, and large-scale and are trained using non-...
Introduction The work reported here began with the desire to find a network architecture that shared...
Machine learning, and in particular neural network models, have revolutionized fields such as image,...
Nowadays neural networks are a powerful tool, even if there are few mathematical results that explai...