StarChild

StarChild is a library for leveraging the interactive theorem proving and SMT checking abilities of F* to verify properties of neural networks. It currently supports feedforward neural networks using ReLU, sigmoid, and softmax activation functions. Networks are written as follows:

val layer1 : layer 2 1
let layer1 = { weights    = [[228300.0R /. 13.0R]; [228300.0R /. 13.0R]]
             ; biases     = [~.337910.0R /. 13.0R]
             ; activation = Sigmoid
             }

val model : network 2 1 1
let model = NLast layer1

Properties of the model can then be checked using F* assertions. Let’s check if the model correctly implements the AND gate:

let _ = assert (run_network model [1.0R; 1.0R] == [1.0R])
let _ = assert (run_network model [0.0R; 1.0R] == [0.0R])
let _ = assert (run_network model [1.0R; 0.0R] == [0.0R])
let _ = assert (run_network model [0.0R; 0.0R] == [0.0R])

Yes! It correctly implements the AND gate! However, is it robust? What do we mean by robust? That’s generally not an easy question. For this AND gate, let’s take robustness to mean that if the input is within some epsilon of a 0.0 or 1.0, the gate still works:

let epsilon  = 0.24R
let truthy x = dist x 1.0R <=. epsilon
let falsy  x = dist x 0.0R <=. epsilon

let _ = assert (forall x1 x2. truthy x1 && truthy x2 ==> run_network model [x1; x2] == [1.0R])
let _ = assert (forall x1 x2. falsy  x1 && truthy x2 ==> run_network model [x1; x2] == [0.0R])
let _ = assert (forall x1 x2. truthy x1 && falsy  x2 ==> run_network model [x1; x2] == [0.0R])
let _ = assert (forall x1 x2. falsy  x1 && falsy  x2 ==> run_network model [x1; x2] == [0.0R])

The network we defined is robust around truthy and falsy inputs!

StarChild ships with a script which can help you convert a subset of Keras models to F* files. It’s called convert.py, and you invoke it like this:

python convert.py \
  -i models/Fashion_MNIST_PCA_100_ReLU_64_Softmax_10.h5 \
  -o models/Fashion_MNIST_PCA_100_ReLU_64_Softmax_10.fst

Make sure to install the requirements first!¹

StarChild also comes with two example models, trained on the Fashion MNIST dataset, using the train_*.py scripts. Currently, F* chokes up when type checking the larger of the models.

You may also be interested in StarChild’s friend, Lazuli!

<a name="pip">1</a>: Run pip install -r requirements.txt.