Distributions, bijections and normalizing flows using Equinox and JAX

• Includes a wide range of distributions and bijections.
• Distributions and bijections are PyTrees, registered through Equinox modules, making them compatible with JAX transformations.
• Includes many state of the art normalizing flow models.
• First class support for conditional distributions and density estimation.

Documentation

Available here.

Short example

As an example we will create and train a normalizing flow model to toy data in just a few lines of code:

from flowjax.flows import block_neural_autoregressive_flow
from flowjax.train import fit_to_data
from flowjax.distributions import Normal
import jax.random as jr
import jax.numpy as jnp

data_key, flow_key, train_key, sample_key = jr.split(jr.key(0), 4)

x = jr.uniform(data_key, (5000, 2))  # Toy data

flow = block_neural_autoregressive_flow(
    key=flow_key,
    base_dist=Normal(jnp.zeros(x.shape[1])),
)

flow, losses = fit_to_data(
    key=train_key,
    dist=flow,
    x=x,
    learning_rate=5e-3,
    max_epochs=200,
    )

# We can now evaluate the log-probability of arbitrary points
log_probs = flow.log_prob(x)

# And sample the distribution
samples = flow.sample(sample_key, (1000, ))

The package currently includes:

• Many simple bijections and distributions, implemented as Equinox modules.
• coupling_flow (Dinh et al., 2017) and masked_autoregressive_flow (Kingma et al., 2016, Papamakarios et al., 2017) normalizing flow architectures.
  • These can be used with arbitrary bijections as transformers, such as Affine or RationalQuadraticSpline (the latter used in neural spline flows; Durkan et al., 2019).
• block_neural_autoregressive_flow, as introduced by De Cao et al., 2019.
• planar_flow, as introduced by Rezende and Mohamed, 2015.
• triangular_spline_flow, introduced here.
• Training scripts for fitting by maximum likelihood, variational inference, or using contrastive learning for sequential neural posterior estimation (Greenberg et al., 2019; Durkan et al., 2020).
• A bisection search algorithm that allows inverting some bijections without a known inverse, allowing for example both sampling and density evaluation to be performed with block neural autoregressive flows.

Installation

pip install flowjax

Warning

This package is in its early stages of development and may undergo significant changes, including breaking changes, between major releases. Whilst ideally we should be on version 0.y.z to indicate its state, we have already progressed beyond that stage. Any breaking changes will be in the release notes for each major release.

Development

We can install a version for development as follows

git clone https://github.com/danielward27/flowjax.git
cd flowjax
pip install -e .[dev]
sudo apt-get install pandoc  # Required for building documentation

Related

• We make use of the Equinox package, which facilitates defining models using a PyTorch-like syntax with Jax.
• For applying parameterizations, we use paramax.

Citation

If you found this package useful in academic work, please consider citing it using the template below, filling in [version number] and [release year of version] to the appropriate values. Version specific DOIs can be obtained from zenodo if desired.

@software{ward2023flowjax,
  title = {FlowJAX: Distributions and Normalizing Flows in Jax},
  author = {Daniel Ward},
  url = {https://github.com/danielward27/flowjax},
  version = {[version number]},
  year = {[release year of version]},
  doi = {10.5281/zenodo.10402073},
}