Related papers: Machine Learning Trivializing Maps: A First Step T…
General-purpose Markov Chain Monte Carlo sampling algorithms suffer from a dramatic reduction in efficiency as the system being studied is driven towards a critical point. Recently, a series of seminal studies suggested that normalizing…
The so-called trivializing flows were proposed to speed up Hybrid Monte Carlo simulations, where the Wilson flow was used as an approximation of a trivializing map, a transformation of the gauge fields which trivializes the theory. It was…
Normalizing flows (NF) use a continuous generator to map a simple latent (e.g. Gaussian) distribution, towards an empirical target distribution associated with a training data set. Once trained by minimizing a variational objective, the…
Normalizing flows learn a diffeomorphic mapping between the target and base distribution, while the Jacobian determinant of that mapping forms another real-valued function. In this paper, we show that the Jacobian determinant mapping is…
The recent introduction of machine learning techniques, especially normalizing flows, for the sampling of lattice gauge theories has shed some hope on improving the sampling efficiency of the traditional HMC algorithm. Naive use of…
Efficient gradient computation of the Jacobian determinant term is a core problem in many machine learning settings, and especially so in the normalizing flow framework. Most proposed flow models therefore either restrict to a function…
We propose a unifying approach that starts from the perturbative construction of trivializing maps by L\"uscher and then improves on it by learning. The resulting continuous normalizing flow model can be implemented using common tools of…
The recent introduction of Machine Learning techniques, especially Normalizing Flows, for the sampling of lattice gauge theories has shed some hope on improving the sampling efficiency of the traditional Hybrid Monte Carlo (HMC) algorithm.…
Flow matching learns a velocity field that transports a base distribution to data. We study how small latent perturbations propagate through these flows and show that Jacobian-vector products (JVPs) provide a practical lens on dependency…
Normalizing flows are constructed from a base distribution with a known density and a diffeomorphism with a tractable Jacobian. The base density of a normalizing flow can be parameterised by a different normalizing flow, thus allowing maps…
Through examples of coordinate and probability transformation between different distributions, the basic principle of normalizing flow is introduced in a simple and concise manner. From the perspective of the distribution of random variable…
Data-carving methods perform selective inference by conditioning the distribution of data on the observed selection event. However, existing data-carving approaches typically require an analytically tractable characterization of the…
Transport maps can ease the sampling of distributions with non-trivial geometries by transforming them into distributions that are easier to handle. The potential of this approach has risen with the development of Normalizing Flows (NF)…
We construct an approximate trivializing map by using a Schwinger-Dyson equation. The advantage of this method is that: (1) The basis for the flow kernel can be chosen arbitrarily by hand. (2) It can be applied to the general action of…
Learning expressive probabilistic models correctly describing the data is a ubiquitous problem in machine learning. A popular approach for solving it is mapping the observations into a representation space with a simple joint distribution,…
Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…
Alongside optimization-based planners, sampling-based approaches are often used in trajectory planning for autonomous driving due to their simplicity. Model predictive path integral control is a framework that builds upon optimization…
Applications of normalizing flows to the sampling of field configurations in lattice gauge theory have so far been explored almost exclusively in two space-time dimensions. We report new algorithmic developments of gauge-equivariant flow…
Normalizing flows are a widely used class of latent-variable generative models with a tractable likelihood. Affine-coupling (Dinh et al, 2014-16) models are a particularly common type of normalizing flows, for which the Jacobian of the…
We test a recent proposal to use approximate trivializing maps in a field theory to speed up Hybrid Monte Carlo simulations. Simulating the CP^{N-1} model, we find a small improvement with the leading order transformation, which is however…