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DeepEquilibriumNetworks.jl is a framework built on top of DifferentialEquations.jl and Lux.jl enabling the efficient training and inference for Deep Equilibrium Networks (Infinitely Deep Neural Networks).


using Pkg


using DeepEquilibriumNetworks, Lux, Random, NonlinearSolve, Zygote, SciMLSensitivity
# using LuxCUDA, LuxAMDGPU ## Install and Load for GPU Support. See

seed = 0
rng = Random.default_rng()
Random.seed!(rng, seed)

model = Chain(Dense(2 => 2),
    DeepEquilibriumNetwork(Parallel(+, Dense(2 => 2; use_bias=false),
            Dense(2 => 2; use_bias=false)), NewtonRaphson()))

gdev = gpu_device()
cdev = cpu_device()

ps, st = Lux.setup(rng, model) |> gdev
x = rand(rng, Float32, 2, 3) |> gdev
y = rand(rng, Float32, 2, 3) |> gdev

model(x, ps, st)

gs = only(Zygote.gradient(p -> sum(abs2, first(model(x, p, st)) .- y), ps))


If you are using this project for research or other academic purposes consider citing our paper:

  title={Continuous Deep Equilibrium Models: Training Neural ODEs Faster by Integrating Them to Infinity},
  author={Pal, Avik and Edelman, Alan and Rackauckas, Christopher},
  booktitle={2023 IEEE High Performance Extreme Computing Conference (HPEC)}, 

For specific algorithms, check the respective documentations and cite the corresponding papers.