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Flow Annealed Importance Sampling Bootstrap (FAB)

Overview

Code for the paper Flow Annealed Importance Sampling Bootstrap (FAB).

FAB in JAX: See the JAX implementation of the FAB algorithm in the fab-jax repo. The fab-jax code is cleaner, faster and easier to use - hence we recommend it over the fab-torch code. Additionally, the fab-jax code applies FAB to some new problems, including the commonly used, challenging, 1600 dimensional log Gaussian Cox process [Møller et al., 1998, Arbel et al., 2021, Mathews et al., 2022, Zhang et at., 2023].

See About the code for further details on how to use the FAB codebase on new problems. Please contact us if you need any help running the code and replicating our experiments.

Methods of Installation

The package can be installed via pip by navigating in the repository directory and running

pip install --upgrade .

To run the alanine dipeptide experiments, you will need to install the OpenMM Library as well as openmmtools. This can be done via conda.

conda install -c conda-forge openmm openmmtools

Experiments

NB: See README within experiments/{problem-name} for further details on training and evaluation for each problem.

NB: Quickstart notebooks are simply to get up and running with the code with some visualisation of results after a little bit of training. To replicate the results from the paper run the python commands described below.

Gaussian Mixture Model

Quickstart (NB just for getting started, to replicate results from paper see python command below)

For this problem we use a mixture of 40 two dimensional Gaussian distributions. This allows for easy visualisation of the various methods for training the flow. We provide a colab notebook with an example of training a flow on the GMM problem, comparing FAB to training a flow with KL divergence minimisation. This can be run in a short period of time (10 min) and provides a clear visualisation of how FAB is able to discover new modes and fit them.

To run the experiment for the FAB with a prioritised replay buffer (for the first seed), use the following command:

python experiments/gmm/run.py training.use_buffer=True training.prioritised_buffer=True

To run the full set of experiments see the README for the GMM experiments.

The below plot shows samples from various trained models, with the GMM problem target contours in the background. Gaussian Mixture Model samples vs contours

Many Well distribution

Quickstart (NB just for getting started, to replicate results from paper see python command below)

The Many Well distribution is made up of multiple repeats of the Double Well distribution, from the original Boltzmann generators paper.

We provide a colab notebook comparing FAB to training a flow via KL divergence minimisation, on the 6 dimensional Many Well problem, where the difference between the two methods is apparent after a short (<5 min) training period. This experiment can be run locally on a laptop using just CPU.

Additionally, we provide the colab notebook <a href="https://colab.research.google.com/github/lollcat/fab-torch/blob/master/demo/many_well.ipynb" target="_parent"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> which demos inference with the flow trained with FAB (+prioritised buffer) on the 32 dim Many Well problem.

To run the experiment for the FAB with a prioritised replay buffer (for the first seed) on the 32 dimensional Many Well problem, use the following command:

python experiments/many_well/run.py training.use_buffer=True training.prioritised_buffer=True

To run the full set of experiments see the README for the Many Well experiments.

The below plot shows samples for our model (FAB) vs training a flow by reverse KL divergence minimisation, with the Many Well problem target contours in the background. This visualisation is for the marginal pairs of the distributions for the first four elements of the x. Many Well distribution FAB vs training by KL divergence minimisation

Alanine dipeptide

In our final experiment, we approximate the Boltzmann distribution of alanine dipeptide in an implicit solvent, which is a molecule with 22 atoms and a popular model system. The molecule is visualized in the figure below. The right figure shows the probability density of for the dihedral angle $\phi$ comparing the ground truth, which was obtrained with a molecular dynamics (MD) simulation, the models trained with our method as well as maximum likelihood on MD samples.

Alanine dipeptide and its dihedral angles; Comparison of probability densities

Furthermore, we compared the Ramachandran plots of the different methods in the following figure.

Ramachandran plot of alanine dipeptide

The weights for the flow model trained with FAB are available on huggingface. Additionally, we provide the colab notebook <a href="https://colab.research.google.com/github/lollcat/fab-torch/blob/master/demo/aldp.ipynb" target="_parent"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> which demos inference with this trained model.

To reproduce our experiment, use the experiments/aldp/train.py script. The respective configuration files are located in experiments/aldp/config. We used the seeds 0, 1, and 2 in our runs.

The data used to evaluate our models and to train the flow model with maximum likelihood is provided on Zenodo. If you want to use the configuration files in experiments/aldp/config as is, you should put the data in the experiment/aldp/data folder.

About the code

The main FAB loss can be found in core.py, and we provide a simple training loop to train a flow with this loss (or other flow - loss combinations that meet the spec) in train.py The FAB training algorithm with the prioritised buffer can be found in train_with_prioritised_buffer.py. Additionally, we provide the code for running the SNR/dimensionality analysis with p and q set to independent Gaussians. in the fab-jax-old repository. For training the CRAFT model on the GMM problem we forked the Annealed Flow Transport repository. This fork may be found here, and may be used for training the CRAFT model.

As we are still adding improvements to the efficiency and stability of the code, make sure you use the latest version. Additionally, if you spot any areas of the code that could be improved then make an issue and we will be more than happy to fix it. For the version of the code that was used in the paper see our releases.

Applying FAB to a new problem:

The most important thing to get right when applying FAB to a given problem is to make sure that AIS is returning reasonable samples, where by reasonable we just mean that the samples from AIS are closer to the target than the flow. Simply visualising the samples from the flow and AIS provides a good check for whether this is the case. Making sure that the transition kernel (e.g. HMC) is working well (e.g. has well tuned step size) is key for AIS to work well.

An additional source of instability can be if the target energy function gives spurious values to points that have extreme values. For example, evaluating the density of a zero-mean unit variance Gaussian on a point that has a value of 100 will give a spurious values. One can fix this by manually setting the log prob of the target to be -inf for regions that are known to be far outside of where samples from the target lie.

Feel free to contact us if you would like any help getting FAB to work nicely!

Normalizing Flow Libraries

We offer a simple wrapper that allows for various normalising flow libraries to be plugged into this repository. The main library we rely on is normflows.

Citation

If you use this code in your research, please cite it as:

Laurence I. Midgley, Vincent Stimper, Gregor N. C. Simm, Bernhard Schölkopf, José Miguel Hernández-Lobato. Flow Annealed Importance Sampling Bootstrap. The Eleventh International Conference on Learning Representations. 2023.

Bibtex

@inproceedings{
midgley2023flow,
title={Flow Annealed Importance Sampling Bootstrap},
author={Laurence Illing Midgley and Vincent Stimper and Gregor N. C. Simm and Bernhard Sch{\"o}lkopf and Jos{\'e} Miguel Hern{\'a}ndez-Lobato},
booktitle={The Eleventh International Conference on Learning Representations },
year={2023},
url={https://openreview.net/forum?id=XCTVFJwS9LJ}
}