A Julia package for robust neural networks built from the Recurrent Equilibrium Network (REN) and Lipschitz-Bounded Deep Network (LBDN) model classes. Please visit the docs page for detailed documentation
To install the package, type the following into the REPL.
] add RobustNeuralNetworks
You should now be able to construct robust neural network models. The following example constructs a contracting REN and evalutates it given a batch of random initial states x0 and inputs u0.
using Random
using RobustNeuralNetworks
# Setup
rng = Xoshiro(42)
batches = 10
nu, nx, nv, ny = 4, 2, 20, 1
# Construct a REN
contracting_ren_ps = ContractingRENParams{Float64}(nu, nx, nv, ny; rng)
ren = REN(contracting_ren_ps)
# Some random inputs
x0 = init_states(ren, batches; rng)
u0 = randn(rng, ren.nu, batches)
# Evaluate the REN over one timestep
x1, y1 = ren(x0, u0)
println(round.(y1;digits=2))The output should be:
[-1.49 0.75 1.34 -0.23 -0.84 0.38 0.79 -0.1 0.72 0.54]If you use RobustNeuralNetworks.jl for any research or publications, please cite our work as necessary.
@article{barbara2025robustneuralnetworksjl,
title = {RobustNeuralNetworks.jl: a Package for Machine Learning and Data-Driven Control with Certified Robustness},
author = {Nicholas H. Barbara and Max Revay and Ruigang Wang and Jing Cheng and Ian R. Manchester},
journal = {Proceedings of the JuliaCon Conferences},
publisher = {The Open Journal},
year = {2025},
volume = {7},
number = {68},
pages = {163},
doi = {10.21105/jcon.00163},
url = {https://doi.org/10.21105/jcon.00163},
}Please contact Nic Barbara ([email protected]) with any questions.