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Building blocks for invertible neural networks in the Julia programming language.

• Memory efficient building blocks for invertible neural networks
• Hand-derived gradients, Jacobians $J$ , and $\log |J|$
• Flux integration
• Support for Zygote and ChainRules
• GPU support
• Includes various examples of invertible neural networks, normalizing flows, variational inference, and uncertainty quantification

InvertibleNetworks is registered and can be added like any standard Julia package with the command:

] add InvertibleNetworks

Due to its memory scaling InvertibleNetworks.jl has been particularily successful at Bayesian posterior sampling with simulation-based inference. To get started with this application please refer to a simple example (Conditional sampling for MNSIT inpainting) but please use this on your application and please reach out to us if you run into any trouble.

• 1x1 Convolutions using Householder transformations (example)

• Residual block (example)

• Invertible coupling layer from Dinh et al. (2017) (example)

• Invertible hyperbolic layer from Lensink et al. (2019) (example)

• Invertible coupling layer from Putzky and Welling (2019) (example)

• Invertible recursive coupling layer HINT from Kruse et al. (2020) (example)

• Activation normalization (Kingma and Dhariwal, 2018) (example)

• Various activation functions (Sigmoid, ReLU, leaky ReLU, GaLU)

• Objective and misfit functions (mean squared error, log-likelihood)

• Dimensionality manipulation: squeeze/unsqueeze (column, patch, checkerboard), split/cat

• Squeeze/unsqueeze using the wavelet transform

• Invertible recurrent inference machines (Putzky and Welling, 2019) (generic example)

• Generative models with maximum likelihood via the change of variable formula (example)

• Glow: Generative flow with invertible 1x1 convolutions (Kingma and Dhariwal, 2018) (generic example, source)

GPU support is supported via Flux/CuArray. To use the GPU, move the input and the network layer to GPU via |> gpu

using InvertibleNetworks, Flux

# Input
nx = 64
ny = 64
k = 10
batchsize = 4

# Input image: nx x ny x k x batchsize
X = randn(Float32, nx, ny, k, batchsize) |> gpu

# Activation normalization
AN = ActNorm(k; logdet=true) |> gpu

# Test invertibility
Y_, logdet = AN.forward(X)

If you use InvertibleNetworks.jl in your research, we would be grateful if you cite us with the following bibtex:

@article{orozco2023invertiblenetworks,
  title={InvertibleNetworks. jl: A Julia package for scalable normalizing flows},
  author={Orozco, Rafael and Witte, Philipp and Louboutin, Mathias and Siahkoohi, Ali and Rizzuti, Gabrio and Peters, Bas and Herrmann, Felix J},
  journal={arXiv preprint arXiv:2312.13480},
  year={2023}
}

The following publications use InvertibleNetworks.jl:

• "Reliable amortized variational inference with physics-based latent distribution correction"

  • paper: https://arxiv.org/abs/2207.11640
  • presentation
  • code: ReliableAVI.jl

• "Learning by example: fast reliability-aware seismic imaging with normalizing flows"

  • paper: https://arxiv.org/abs/2104.06255
  • presentation
  • code: ReliabilityAwareImaging.jl

• "Enabling uncertainty quantification for seismic data pre-processing using normalizing flows (NF)—an interpolation example"

  • paper
  • code: WavefieldRecoveryUQ.jl

• "Preconditioned training of normalizing flows for variational inference in inverse problems"

  • paper: https://arxiv.org/abs/2101.03709
  • presentation
  • code: FastApproximateInference.jl

• "Parameterizing uncertainty by deep invertible networks, an application to reservoir characterization"

  • paper: https://arxiv.org/abs/2004.07871
  • presentation
  • code: https://github.com/slimgroup/Software.SEG2020

• "Generalized Minkowski sets for the regularization of inverse problems"

  • paper: http://arxiv.org/abs/1903.03942
  • code: SetIntersectionProjection.jl

• Rafael Orozco, Georgia Institute of Technology [rorozco@gatech.edu]

• Philipp Witte, Georgia Institute of Technology (now Microsoft)

• Gabrio Rizzuti, Utrecht University

• Mathias Louboutin, Georgia Institute of Technology

• Ali Siahkoohi, Georgia Institute of Technology

This package uses functions from NNlib.jl, Flux.jl and Wavelets.jl