# Prediction with FHE

This document explains how to perform encryption, execution, and decryption of Fully Homomorphic Encryption (FHE) using one function call of the Concrete ML API, or multiple function calls separately.

The APIs are different for the following:

* [Built-in models](#built-in-models)
* [Custom models](#custom-models)

## Built-in models

### Using one function

All Concrete ML built-in models have a single `predict` method that performs the encryption, FHE execution, and decryption with only one function call.

The following example shows how to create a synthetic data-set and how to use it to train a LogisticRegression model from Concrete ML.

```python
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from concrete.ml.sklearn import LogisticRegression
import numpy

# Create a synthetic data-set for a classification problem
x, y = make_classification(n_samples=100, class_sep=2, n_features=3, n_informative=3, n_redundant=0, random_state=42)

# Split the data-set into a train and test set
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=42)

# Instantiate and train the model
model = LogisticRegression()
model.fit(x_train,y_train)

# Simulate the predictions in the clear (optional)
y_pred_clear = model.predict(x_test)

# Compile the model on a representative set
fhe_circuit = model.compile(x_train)
```

Concrete ML models follow the same API as scikit-learn models, transparently performing the steps related to encryption for convenience.

```python
# Predict in FHE
y_pred_fhe = model.predict(x_test, fhe="execute")
```

Regarding this LogisticRegression model, as with scikit-learn, it is possible to predict the logits as well as the class probabilities by respectively using the `decision_function` or `predict_proba` methods instead.

### Using separate functions

Alternatively, you can execute key generation, quantization, encryption, FHE execution and decryption separately.

```python
# Generate the keys (set force to True in order to generate new keys at each execution)
fhe_circuit.keygen(force=True)

y_pred_fhe_step = []

for f_input in x_test:
    # Quantize an input (float)
    q_input = model.quantize_input([f_input])
    
    # Encrypt the input
    q_input_enc = fhe_circuit.encrypt(q_input)

    # Execute the linear product in FHE 
    q_y_enc = fhe_circuit.run(q_input_enc)

    # Decrypt the result (integer)
    q_y = fhe_circuit.decrypt(q_y_enc)

    # De-quantize the result
    y = model.dequantize_output(q_y)

    # Apply either the sigmoid if it is a binary classification task, which is the case in this 
    # example, or a softmax function in order to get the probabilities (in the clear)
    y_proba = model.post_processing(y)

    # Since this model does classification, apply the argmax to get the class predictions (in the clear)
    # Note that regression models won't need the following line
    y_class = numpy.argmax(y_proba, axis=1)

    y_pred_fhe_step += list(y_class)

y_pred_fhe_step = numpy.array(y_pred_fhe_step)

print("Predictions in clear:", y_pred_clear)
print("Predictions in FHE  :", y_pred_fhe_step)
print(f"Similarity: {int((y_pred_fhe_step == y_pred_clear).mean()*100)}%")
```

## Custom models

For custom models, the API to execute inference in FHE or simulation is as follows:

```python
from torch import nn
from brevitas import nn as qnn
from concrete.ml.torch.compile import compile_brevitas_qat_model

class FCSmall(nn.Module):
    """A small QAT NN."""

    def __init__(self, input_output):
        super().__init__()
        self.quant_input = qnn.QuantIdentity(bit_width=3)
        self.fc1 = qnn.QuantLinear(in_features=input_output, out_features=input_output, weight_bit_width=3, bias=True)
        self.quant_2 = qnn.QuantIdentity(bit_width=3)
        self.act_f = nn.ReLU()
        self.fc2 = qnn.QuantLinear(in_features=input_output, out_features=input_output, weight_bit_width=3, bias=True)

    def forward(self, x):
        return self.fc2(self.quant_2(self.act_f(self.fc1(self.quant_input(x)))))

torch_model = FCSmall(3)

quantized_module = compile_brevitas_qat_model(
    torch_model,
    x_train,
)

x_test_q = quantized_module.quantize_input(x_test)
y_pred = quantized_module.quantized_forward(x_test_q, fhe="simulate")
y_pred = quantized_module.dequantize_output(y_pred)

y_pred = numpy.argmax(y_pred, axis=1)
```


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