Last Updated: 12/13/2023 @ 18:00:09

Papers 📚, Slides 📊 etc.

• 📊 Slides (07/31/2023 @ Lattice 2023)
• 📕 Notebooks / Reports:
  • 📓 2D U(1) Example
    • 📙 2D U(1) Model (w/ fp16 or fp32 for training)
    • 📒 4D SU(3) Model (w/ complex128 + fp64 for training)
      • alt link (if github won’t load)
• 📝 Papers:
  • LeapfrogLayers: A Trainable Framework for Effective Topological Sampling, 2022
    
  • Accelerated Sampling Techniques for Lattice Gauge Theory @ BNL & RBRC: DWQ @ 25 (12/2021)
  • Training Topological Samplers for Lattice Gauge Theory from the ML for HEP, on and off the Lattice @ \mathrm{ECT}^{*} Trento (09/2021) (+ 📊 slides)
  • Deep Learning Hamiltonian Monte Carlo @ Deep Learning for Simulation (SimDL) Workshop ICLR 2021
    • 📚 : arXiv:2105.03418
      
    • 📊 : poster

\hspace{2pt} MLMC: Machine Learning Monte Carlo @ Lattice 2023 (07/2023)

Background

The L2HMC algorithm aims to improve upon HMC by optimizing a carefully chosen loss function which is designed to minimize autocorrelations within the Markov Chain, thereby improving the efficiency of the sampler.

A detailed description of the original L2HMC algorithm can be found in the paper:

Generalizing Hamiltonian Monte Carlo with Neural Network

with implementation available at brain-research/l2hmc/ by Daniel Levy, Matt D. Hoffman and Jascha Sohl-Dickstein.

Broadly, given an analytically described target distribution, π(x), L2HMC provides a statistically exact sampler that:

• Quickly converges to the target distribution (fast burn-in).
• Quickly produces uncorrelated samples (fast mixing).
• Is able to efficiently mix between energy levels.
• Is capable of traversing low-density zones to mix between modes (often difficult for generic HMC).

Installation

Warning

It is recommended to use / install l2hmc into a virtual environment¹

From source (RECOMMENDED)

git clone https://github.com/saforem2/l2hmc-qcd
cd l2hmc-qcd
# for development addons:
# python3 -m pip install -e ".[dev]"
python3 -m pip install -e .

From l2hmc on PyPI

python3 -m pip install l2hmc

Test install:

python3 -c 'import l2hmc ; print(l2hmc.__file__)'
# output: /path/to/l2hmc-qcd/src/l2hmc/__init__.py

Running the Code

Experiment configuration with Hydra

This project uses hydra for configuration management and supports distributed training for both PyTorch and TensorFlow.

In particular, we support the following combinations of framework + backend for distributed training:

• TensorFlow (+ Horovod for distributed training)
• PyTorch +
  • DDP
  • Horovod
  • DeepSpeed

The main entry point is src/l2hmc/main.py, which contains the logic for running an end-to-end Experiment.

An Experiment consists of the following sub-tasks:

1. Training
2. Evaluation
3. HMC (for comparison and to measure model improvement)

Running an Experiment

All configuration options can be dynamically overridden via the CLI at runtime, and we can specify our desired framework and backend combination via:

python3 main.py mode=debug framework=pytorch backend=deepspeed precision=fp16

to run a (non-distributed) Experiment with pytorch + deepspeed with fp16 precision.

The l2hmc/conf/config.yaml contains a brief explanation of each of the various parameter options, and values can be overriden either by modifying the config.yaml file, or directly through the command line, e.g.

cd src/l2hmc
./train.sh mode=debug framework=pytorch > train.log 2>&1 &
tail -f train.log $(tail -1 logs/latest)

Additional information about various configuration options can be found in:

• src/l2hmc/configs.py: Contains implementations of the (concrete python objects) that are adjustable for our experiment.
• src/l2hmc/conf/config.yaml: Starting point with default configuration options for a generic Experiment.

for more information on how this works I encourage you to read Hydra’s Documentation Page.

Running at ALCF

For running with distributed training on ALCF systems, we provide a complete src/l2hmc/train.sh script which should run without issues on either Polaris or ThetaGPU @ ALCF.

• ALCF:

  # Polaris --------------------------------
  if [[ "$(hostname)==x3*" ]]; then
    MACHINE="Polaris"
    CONDA_DATE="2023-10-02"
  # thetaGPU -------------------------------
  elif  [[ "$(hostname)==thetagpu*" ]]; then
    MACHINE="thetaGPU"
    CONDA_DATE="2023-01-11"
  else
    echo "Unknown machine"
    exit 1
  fi
  # Setup conda + build virtual env -----------------------------------------
  module load "conda/${CONDA_DATE}"
  conda activate base
  git clone https://github.com/saforem2/l2hmc-qcd
  cd l2hmc-qcd
  mkdir -p "venvs/${MACHINE}/${CONDA_DATE}"
  python3 -m venv "venvs/${MACHINE}/${CONDA_DATE}" --system-site-packages
  source "venvs/${MACHINE}/${CONDA_DATE}/bin/activate"
  python3 -m pip install --upgrade pip setuptools wheel
  # Install `l2hmc` ----------
  python3 -m pip install -e .
  # Train ----------------------------------------------------------------------
  cd src/l2hmc
  ./bin/train.sh mode=test framework=pytorch backend=deepspeed seed="${RANDOM}"

Details

Lattice Dynamics

Figure 1: A 2D view of the lattice, with an elementary plaquette, U_{\mu\nu}(x) illustrated.

Goal: Use L2HMC to efficiently generate gauge configurations for calculating observables in lattice QCD.

A detailed description of the (ongoing) work to apply this algorithm to simulations in lattice QCD (specifically, a 2D U(1) lattice gauge theory model) can be found in arXiv:2105.03418.

For a given target distribution, \pi(U) the Dynamics object (src/l2hmc/dynamics/) implements methods for generating proposal configurations

U_{0} \rightarrow U_{1} \rightarrow \cdots \rightarrow U_{n} \sim \pi(U)

using the generalized leapfrog update, as shown to the right in Figure 2.

This generalized leapfrog update takes as input a buffer of lattice configurations U² and generates a proposal configuration:

U^{\prime}= Dynamics(U)

by evolving the generalized L2HMC dynamics.

Network Architecture

We use networks with identical architectures, \Gamma^{\pm}³, \Lambda^{\pm}⁴ to update our momenta P and links U, respectively.

Figure 2: An illustration of the leapfrog layer updating (P, U) \rightarrow (P', U').

Figure 3: Overview of the L2HMC algorithm

Contact

Code author: Sam Foreman

Pull requests and issues should be directed to: saforem2

Posts

Citation

If you use this code or found this work interesting, please cite our work along with the original paper:

@misc{foreman2021deep,
      title={Deep Learning Hamiltonian Monte Carlo}, 
      author={Sam Foreman and Xiao-Yong Jin and James C. Osborn},
      year={2021},
      eprint={2105.03418},
      archivePrefix={arXiv},
      primaryClass={hep-lat}
}

@article{levy2017generalizing,
  title={Generalizing Hamiltonian Monte Carlo with Neural Networks},
  author={Levy, Daniel and Hoffman, Matthew D. and Sohl-Dickstein, Jascha},
  journal={arXiv preprint arXiv:1711.09268},
  year={2017}
}

Acknowledgement

Note
This research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under contract DE_AC02-06CH11357.
This work describes objective technical results and analysis.
Any subjective views or opinions that might be expressed in the work do not necessarily represent the views of the U.S. DOE or the United States Government.

Footnotes

1. A good way to do this is on top of a conda environment, e.g.:

   conda activate base;  # with either {pytorch, tensorflow}
   mkdir venv
   python3 -m venv venv --system-site-packages
   source venv/bin/activate
   # for development addons:
   # python3 -m pip install -e ".[dev]"
   python3 -m pip install -e .

2. Note that throughout the code, we refer to the link variables as x and the conjugate momenta as v.

3. referred to as vNet for the network used to update v

4. referred to as xNet for the network used to update x

Citation

BibTeX citation:

@online{foreman2023,
  author = {Foreman, Sam},
  title = {L2HMC-QCD},
  date = {2023-12-13},
  url = {https://saforem2.github.io/l2hmc-qcd/},
  langid = {en}
}

For attribution, please cite this work as:

Foreman, Sam. 2023. “L2HMC-QCD.” December 13, 2023. https://saforem2.github.io/l2hmc-qcd/.