Related papers: Learning normalizing flows from Entropy-Kantorovic…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
Normalizing flows, diffusion normalizing flows and variational autoencoders are powerful generative models. This chapter provides a unified framework to handle these approaches via Markov chains. We consider stochastic normalizing flows as…
We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…
Reinforcement Learning (RL) of robotic manipulation skills, despite its impressive successes, stands to benefit from incorporating domain knowledge from control theory. One of the most important properties that is of interest is control…
Normalizing flows are machine-learned maps between different lattice theories which can be used as components in exact sampling and inference schemes. Ongoing work yields increasingly expressive flows on gauge fields, but it remains an open…
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…
The DC optimal power flow (DCOPF) problem is a fundamental problem in power systems operations and planning. With high penetration of uncertain renewable resources in power systems, DCOPF needs to be solved repeatedly for a large amount of…
We introduce in this work the normalizing field flows (NFF) for learning random fields from scattered measurements. More precisely, we construct a bijective transformation (a normalizing flow characterizing by neural networks) between a…
Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles,…
The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…
We derive the system of differential equations for the gradient flow characterizing the training process of linear in-context learning in full generality. Next, we explore the geometric structure of the gradient flows in two instances,…
The Schr\"{o}dinger Bridge Problem (SBP), which can be understood as an entropy-regularized optimal transport, seeks to compute stochastic dynamic mappings connecting two given distributions. SBP has shown significant theoretical importance…
Sampling-based motion planning is the predominant paradigm in many real-world robotic applications, but its performance is immensely dependent on the quality of the samples. The majority of traditional planners are inefficient as they use…
Offline reinforcement learning aims to train a policy on a pre-recorded and fixed dataset without any additional environment interactions. There are two major challenges in this setting: (1) extrapolation error caused by approximating the…
Traditional theories of optimization cannot describe the dynamics of optimization in deep learning, even in the simple setting of deterministic training. The challenge is that optimizers typically operate in a complex, oscillatory regime…
Training normalizing flow generative models can be challenging due to the need to calculate computationally expensive determinants of Jacobians. This paper studies the likelihood-free training of flows and proposes the energy objective, an…
This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory information. We introduce two-parameter flows that learn only…
This notebook tutorial demonstrates a method for sampling Boltzmann distributions of lattice field theories using a class of machine learning models known as normalizing flows. The ideas and approaches proposed in arXiv:1904.12072,…
The Monge-Kantorovich mass transfer problem is equivalently formulated as a convex optimization problem for a potential function. In the light of this formulation an interative algorithm is developed for determining the solution. It is a…
We develop a method for multidimensional optimisation using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimising functional correspond to fixed points of the…