The Hamiltonian formalism plays a central role in classical and quantum
physics. Hamiltonians are the main tool for modelling the continuous time
evolution of systems with conserved quantities, and they come equipped with
many useful properties, like time reversibility and smooth interpolation in
time. These properties are important for many machine learning problems - from
sequence prediction to reinforcement learning and density modelling - but are
not typically provided out of the box by standard tools such as recurrent
neural networks. In this paper, we introduce the Hamiltonian Generative Network
(HGN), the first approach capable of consistently learning Hamiltonian dynamics
from high-dimensional observations (such as images) without restrictive domain
assumptions. Once trained, we can use HGN to sample new trajectories, perform
rollouts both forward and backward in time and even speed up or slow down the
learned dynamics. We demonstrate how a simple modification of the network
architecture turns HGN into a powerful normalising flow model, called Neural
Hamiltonian Flow (NHF), that uses Hamiltonian dynamics to model expressive
densities. We hope that our work serves as a first practical demonstration of
the value that the Hamiltonian formalism can bring to deep learning.

本文介绍了哈密顿生成网络 (HGN) 和神经哈密顿流 (NHF)，这是第一种能够从高维度观察中连续地学习哈密顿动力学而无需限制性条件的方法，它能够可靠地从机器学习的角度解决很多问题。