Crypto_nn is a very simple example of neural network that can perform classification over encrypted data using homomorphic encryption. The idea is taken from CryptoDL: Deep Neural Networks over Encrypted Data by Ehsan Hesamifard, Hassan Takabi, Mehdi Ghasemi where you can find all the details.
To use activation functions within HE schemes, they should be approximated in a form which is implemented using only addition and multiplication (e.g. polynomial).
In this example I simulated the ReLU function as presented in the paper and I obtained the following approximation:
0.0012x2 + 0.5x + 52