DeepEquilibriumNetworks.jl

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).

Installation

To install DeepEquilibriumNetworks.jl, use the Julia package manager:

using Pkg
Pkg.add("DeepEquilibriumNetworks")

Quick-start

using DeepEquilibriumNetworks, Lux, Random, NonlinearSolve, Zygote, SciMLSensitivity
using LuxCUDA  # For NVIDIA GPU support

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

res, st_ = model(x, ps, st)
st_.layer_2.solution

DeepEquilibriumSolution
 * Initial Guess: Float32[0.0 0.0 0.0; 0.0 0.0 0.0]
 * Steady State: Float32[-0.219407 0.637479 -0.744242; 1.50412 -0.962679 3.12426]
 * Residual: Float32[-4.47035f-8 -5.96046f-8 -5.96046f-8; -1.19209f-7 5.96046f-8 -2.38419f-7]
 * Jacobian Loss: 0.0
 * NFE: 3

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

(layer_1 = (weight = Float32[-4.6991134 -8.227526; -13.163104 -20.53097], bias = Float32[-11.837078, -31.839073]), layer_2 = (model = (layer_1 = (weight = Float32[15.304397 -58.909546; -21.828897 81.71437],), layer_2 = (weight = Float32[17.71767 3.5711353; -23.398441 -5.474779],)), init = nothing))

Citation

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

@article{pal2022continuous,
  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)}, 
  year={2023}
}

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

Contributing

Please refer to the SciML ColPrac: Contributor's Guide on Collaborative Practices for Community Packages for guidance on PRs, issues, and other matters relating to contributing to SciML.
See the SciML Style Guide for common coding practices and other style decisions.
There are a few community forums:
- The #diffeq-bridged and #sciml-bridged channels in the Julia Slack
- The #diffeq-bridged and #sciml-bridged channels in the Julia Zulip
- On the Julia Discourse forums
- See also SciML Community page

Reproducibility

The documentation of this SciML package was built using these direct dependencies,

Status `/var/lib/buildkite-agent/builds/gpuci-9/julialang/deepequilibriumnetworks/docs/Project.toml`
  [6748aba7] DeepEquilibriumNetworks v2.3.0 `/var/lib/buildkite-agent/builds/gpuci-9/julialang/deepequilibriumnetworks`
  [e30172f5] Documenter v1.7.0
  [daee34ce] DocumenterCitations v1.3.3
  [7ed4a6bd] LinearSolve v2.34.0
  [b2108857] Lux v1.0.1
  [d0bbae9a] LuxCUDA v0.3.3
  [eb30cadb] MLDatasets v0.7.17
  [f1d291b0] MLUtils v0.4.4
  [8913a72c] NonlinearSolve v3.14.0
  [0b1bfda6] OneHotArrays v0.2.5
  [3bd65402] Optimisers v0.3.3
  [1dea7af3] OrdinaryDiffEq v6.89.0
  [1ed8b502] SciMLSensitivity v7.66.2
  [efcf1570] Setfield v1.1.1
  [e88e6eb3] Zygote v0.6.70
  [ade2ca70] Dates
  [de0858da] Printf
  [9a3f8284] Random

and using this machine and Julia version.

Julia Version 1.10.5
Commit 6f3fdf7b362 (2024-08-27 14:19 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 48 × AMD EPYC 7402 24-Core Processor
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
Threads: 3 default, 0 interactive, 1 GC (on 2 virtual cores)
Environment:
  JULIA_CPU_THREADS = 2
  JULIA_DEBUG = Documenter
  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/018c7dba-9a5f-4ad5-a288-1442edf3444d
  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64

A more complete overview of all dependencies and their versions is also provided.

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⌅ [f50d1b31] Rmath_jll v0.4.3+0
  [477f73a3] libaec_jll v1.1.2+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+4
  [05823500] OpenLibm_jll v0.8.1+2
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

You can also download the manifest file and the project file.