## Quick Start

First define your computation as a `nn.Module` and wrap it using
`auto_LiRPA.BoundedModule()`. Then, you can call the `compute_bounds` function
to obtain certified lower and upper bounds under input perturbations:

```python
from auto_LiRPA import BoundedModule, BoundedTensor, PerturbationLpNorm

# Define computation as a nn.Module.
class MyModel(nn.Module):
    def forward(self, x):
        # Define your computation here.

model = MyModel()
my_input = load_a_batch_of_data()
# Wrap the model with auto_LiRPA.
model = BoundedModule(model, my_input)
# Define perturbation. Here we add Linf perturbation to input data.
ptb = PerturbationLpNorm(norm=np.inf, eps=0.1)
# Make the input a BoundedTensor with the pre-defined perturbation.
my_input = BoundedTensor(my_input, ptb)
# Regular forward propagation using BoundedTensor works as usual.
prediction = model(my_input)
# Compute LiRPA bounds using the backward mode bound propagation (CROWN).
lb, ub = model.compute_bounds(x=(my_input,), method="backward")
```

Checkout
[examples/vision/simple_verification.py](examples/vision/simple_verification.py)
for a complete but very basic example.

<a href="http://PaperCode.cc/AutoLiRPA-Demo"><img align="left" width=64 height=64 src="https://colab.research.google.com/img/colab_favicon_256px.png"></a>
We also provide a [Google Colab Demo](http://PaperCode.cc/AutoLiRPA-Demo) including an example of computing verification
bounds for a 18-layer ResNet model on CIFAR-10 dataset. Once the ResNet model
is defined as usual in Pytorch, obtaining provable output bounds is as easy as
obtaining gradients through autodiff. Bounds are efficiently computed on GPUs.