Fixed-kinetic Neural Hamiltonian Flows for enhanced interpretability and reduced complexity

Abstract

Normalizing Flows (NF) are Generative models which transform a simple prior distribution into the desired target. They however require the design of an invertible mapping whose Jacobian determinant has to be computable. Recently introduced, Neural Hamiltonian Flows (NHF) are Hamiltonian dynamics-based flows, which are continuous, volume-preserving and invertible and thus make for natural candidates for robust NF architectures. In particular, their similarity to classical Mechanics could lead to easier interpretability of the learned mapping. In this paper, we show that the current NHF architecture may still pose a challenge to interpretability. Inspired by Physics, we introduce a fixed-kinetic energy version of the model. This approach improves interpretability and robustness while requiring fewer parameters than the original model. We illustrate that on a 2D Gaussian mixture and on the MNIST and Fashion-MNIST datasets. Finally, we show how to adapt NHF to the context of Bayesian inference and illustrate the method on an example from cosmology.

References in corpus (10)

• Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples
• The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo
• Deep Unsupervised Learning using Nonequilibrium Thermodynamics
• NICE: Non-linear Independent Components Estimation
• Variational Inference with Normalizing Flows
• Towards Explainable Artificial Intelligence
• Hamiltonian Neural Networks
• Equivariant Hamiltonian Flows
• Bayesian Inference with Latent Hamiltonian Neural Networks
• Continuous Methods : Hamiltonian Domain Translation