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

TL;DR

This paper introduces a fixed-kinetic energy variant of Neural Hamiltonian Flows, enhancing interpretability and robustness while reducing complexity, demonstrated on various datasets and adapted for Bayesian inference in cosmology.

Contribution

The paper proposes a fixed-kinetic energy version of NHF that improves interpretability, robustness, and reduces parameter count compared to the original model.

Findings

Improved interpretability of NHF models.

Enhanced robustness with fewer parameters.

Successful application to Bayesian inference in cosmology.

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.