Concrete-ML provides several of the most popular classification and regression tree models that can be found in Scikit-learn:

In addition to support for scikit-learn, Concrete-ML also supports XGBoost 's XGBClassifier:

Example

Here's an example of how to use this model in FHE on a popular data-set using some of scikit-learn's pre-processing tools. A more complete example can be found in the XGBClassifier notebook.

from sklearn.datasets import load_breast_cancer
from sklearn.decomposition import PCA
from sklearn.model_selection import GridSearchCV, train_test_split
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler

from concrete.ml.sklearn.xgb import XGBClassifier


# Get data-set and split into train and test
X, y = load_breast_cancer(return_X_y=True)

# Split the train and test set
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)

# Define our model
model = XGBClassifier(n_jobs=1, n_bits=3)

# Define the pipeline
# We will normalize the data and apply a PCA before fitting the model
pipeline = Pipeline(
    [("standard_scaler", StandardScaler()), ("pca", PCA(random_state=0)), ("model", model)]
)

# Define the parameters to tune
param_grid = {
    "pca__n_components": [2, 5, 10, 15],
    "model__max_depth": [2, 3, 5],
    "model__n_estimators": [5, 10, 20],
}

# Instantiate the grid search with 5-fold cross validation on all available cores
grid = GridSearchCV(pipeline, param_grid, cv=5, n_jobs=-1, scoring="accuracy")

# Launch the grid search
grid.fit(X_train, y_train)

# Print the best parameters found
print(f"Best parameters found: {grid.best_params_}")

# Output:
#  Best parameters found: {'model__max_depth': 5, 'model__n_estimators': 10, 'pca__n_components': 5}

# Currently we only focus on model inference in FHE
# The data transformation will be done in clear (client machine)
# while the model inference will be done in FHE on a server.
# The pipeline can be split into 2 parts:
#   1. data transformation
#   2. estimator
best_pipeline = grid.best_estimator_
data_transformation_pipeline = best_pipeline[:-1]
model = best_pipeline[-1]

# Transform test set
X_train_transformed = data_transformation_pipeline.transform(X_train)
X_test_transformed = data_transformation_pipeline.transform(X_test)

# Evaluate the model on the test set in clear
y_pred_clear = model.predict(X_test_transformed)
print(f"Test accuracy in clear: {(y_pred_clear == y_test).mean():0.2f}")

# Output:
#  Test accuracy: 0.98

# Compile the model to FHE
model.compile(X_train_transformed)

# Perform the inference in FHE
# Warning: this will take a while. It is recommended to run this with a very small batch of
# example first (e.g. N_TEST_FHE = 1)
# Note that here the encryption and decryption is done behind the scene.
N_TEST_FHE = 1
y_pred_fhe = model.predict(X_test_transformed[:N_TEST_FHE], execute_in_fhe=True)

# Assert that FHE predictions are the same as the clear predictions
print(f"{(y_pred_fhe == y_pred_clear[:N_TEST_FHE]).sum()} "
      f"examples over {N_TEST_FHE} have a FHE inference equal to the clear inference.")

# Output:
#  1 examples over 1 have a FHE inference equal to the clear inference

Using the above example, we can then plot how the model classifies the inputs and then compare those results with the XGBoost model executed in clear. A 6-bits model is also given in order to better understand the impact of quantization on classification. Similar plots can be found in the Classifier Comparison notebook.

This graph shows the impact of quantization over the decision boundaries in the Concrete-ML FHE decision tree models. In the 3-bits model, only a rough, highly-discrete decision function is observed. This results in a small decrease of accuracy of about 7% compared to the initial XGBoost classifier. Besides, using 6-bits of quantization makes the model reach 93% accuracy, drastically reducing this difference to only 1.7 percentage points.

In fact, the quantization process may sometimes create some artifacts that could lead to a decrease in performance. Still, as the quantization is done individually on each input feature, the artifacts are minor when considering small tree-based models with 5-6 bits quantization. Thus, FHE tree-based models reach similar scores as their equivalent floating point ones.

The following graph shows that using 5-6 bits of quantization is usually sufficient to reach the performance of a non-quantized XGBoost model on floating point data. The metrics plotted are accuracy and F1-score on the spambase data-set.

Concrete-ML models can be easily deployed in a client/server setting, enabling the creation of privacy-preserving services in the cloud.

As seen in the , a Concrete-ML model, once compiled to FHE, generates machine code that performs the inference on private data. Furthermore, secret encryption keys are needed so that the user can securely encrypt their data and decrypt the inference result. An evaluation key is also needed for the server to securely process the user's encrypted data.

Keys are generated by the user once for each service they use, based on the model the service provides and its cryptographic parameters.

The overall communications protocol to enable cloud deployment of machine learning services can be summarized in the following diagram:

The steps detailed above are as follows:

1. The model developer deploys the compiled machine learning model to the server. This model includes the cryptographic parameters. The server is now ready to provide private inference.

2. The client requests the cryptographic parameters (also called "client specs"). Once it gets them from the server, the secret and evaluation keys are generated.

3. The client sends the evaluation key to the server. The server is now ready to accept requests from this client. The client sends their encrypted data.

4. The server uses the evaluation key to securely run inference on the user's data and sends back the encrypted result.

5. The client now decrypts the result and can send back new requests.

Concrete-ML provides several of the most popular linear models for regression or classification that can be found in :

Using these models in FHE is extremely similar to what can be done with scikit-learn's , making it easy for data scientists who are used to this framework to get started with Concrete-ML.

Models are also compatible with some of scikit-learn's main workflows, such as Pipeline() or GridSearch().

Example

Here's an example of how to use this model in FHE on a simple data-set below. A more complete example can be found in the .

We can clearly observe the impact of quantization over the decision boundaries in the FHE model, separating the initial lines into broken lines with steps. However, this does not change the overall score as both models output the same accuracy (90%).

In fact, the quantization process may sometimes create some artifacts that could lead to a decrease in performance. Still, the impact of those artifacts is often minor when considering linear models as FHE models reach similar scores as their equivalent clear ones.

Depending on your OS, Concrete-ML may be installed with Docker or with pip:

Also, only some versions of python are supported: in the current release, these are 3.7 (linux only), 3.8 and 3.9.

Most of these limits are shared with the rest of the Concrete stack (namely Concrete-Numpy and Concrete-Compiler). Support for more platforms will be added in the future.

Using PyPi

Requirements

Installing Concrete-ML using PyPi requires a Linux-based OS or macOS running on an x86 CPU. For Apple Silicon, Docker is the only currently supported option (see ).

Installing on Windows can be done using Docker or WSL. On WSL, Concrete-ML will work as long as the package is not installed in the /mnt/c/ directory, which corresponds to the host OS filesystem.

Installation

To install Concrete-ML from PyPi, run the following:

This will automatically install all dependencies, notably Concrete-Numpy.

Using Docker

Concrete-ML can be installed using Docker by either pulling the latest image or a specific version:

The image can then be used via the following command:

This will launch a Concrete-ML enabled Jupyter server in Docker that can be accessed directly from a browser.

Alternatively, a shell can be lauched in Docker, with or without volumes:

Concrete-ML is built on top of Concrete-Numpy, which enables Numpy programs to be converted into FHE circuits.

Lifecycle of a Concrete-ML model

I. Model Development

1. Training. A model is trained using plaintext, non-encrypted, training data.

2. Quantization. The model is converted into an integer equivalent using quantization. Concrete-ML performs this step either during training (Quantization-Aware Training) or after training (Post-Training Quantization), depending on model type. Quantization converts inputs, model weights and all intermediate values of the inference computation to integers. More information is available .

3. Simulation using the Virtual Library. Testing FHE models on very large datasets can take a long time. Furthermore, not all models are compatible with FHE constraints out-of-the-box. Simulation using the Virtual Library allows you to execute a model that was quantized, to measure the accuracy it would have in FHE, but also to determine the modifications required to make it FHE compatible. Simulation is described in more details .

4. Compilation. Once the model is quantized, simulation can confirm it has good accuracy in FHE. The model then needs to be compiled using Concrete's FHE compiler to produce an equivalent FHE circuit. This circuit is represented as an MLIR program consisting of low level cryptographic operations. You can read more about FHE compilation , MLIR and about the low-level Concrete library .

5. Inference. The compiled model can then be executed on encrypted data, once the proper keys have been generated. The model can also be deployed to a server and used to run private inference on encrypted inputs.

You can see some examples of the model development workflow .

II. Model deployment

1. Client/Server deployment. In a client/server setting, the model can be exported in a way that:

   • allows the client to generate keys, encrypt and decrypt.

   • provides a compiled model that can run on the server to perform inference on encrypted data

2. Key generation. The data owner (client) needs to generate a pair of private keys (to encrypt/decrypt their data and results) and a public evaluation key (for the model's FHE evaluation on the server).

You can see an example of the model deployment workflow .

Cryptography concepts

Concrete-ML and Concrete-Numpy are tools that hide away the details of the underlying cryptography scheme, called TFHE. However, some cryptography concepts are still useful when using these two toolkits:

1. Encryption/Decryption. These operations transform plaintext, i.e. human-readable information, into ciphertext, i.e. data that contains a form of the original plaintext that is unreadable by a human or computer without the proper key to decrypt it. Encryption takes plaintext and an encryption key and produces ciphertext, while decryption is the inverse operation.

2. Encrypted inference. FHE allows a third party to execute (i.e. run inference or predict) a machine learning model on encrypted data (a ciphertext). The result of the inference is also encrypted and can only be read by the person who gets the decryption key.

3. Keys. A key is a series of bits used within an encryption algorithm for encrypting data so that the corresponding ciphertext appears random.

4. Key generation. Cryptographic keys need to be generated using random number generators. Their size may be large and key generation may take a long time. However, keys only need to be generated once for each model a client uses.

5. Guaranteed correctness of encrypted computations. To achieve security, TFHE, the underlying encryption scheme, adds random noise as ciphertexts. This can induce errors during processing of encrypted data, depending on noise parameters. By default, Concrete-ML uses parameters that ensure the correctness of the encrypted computation, so you do not need to take into account the noise parametrization. Therefore, results on encrypted data will be the same as the results of simulation on clear data.

Model accuracy considerations under FHE constraints

To respect FHE constraints, all numerical programs over encrypted data must have all inputs, constants and intermediate values represented with integers of a maximum of 8 bits.

Concrete-ML provides simple neural networks models with a Scikit-learn interface through the NeuralNetClassifier and NeuralNetRegressor classes.

The neural network models are built with , which provides a scikit-learn like interface to Torch models (more ).

These models use a stack of linear layers and the activation function and the number of neurons in each layer is configurable. This approach is similar to what is available in Scikit-learn using the MLPClassifier/MLPRegressor classes. The built-in, fully connected neural network (FCNN) models train easily with a single call to .fit(), which will automatically quantize the weights and activations. These models use Quantization Aware Training, allowing good performance for low precision (down to 2-3 bit) weights and activations.

While NeuralNetClassifier and NeuralNetClassifier provide scikit-learn like models, their architecture is somewhat restricted in order to make training easy and robust. If you need more advanced models, you can convert custom neural networks as described in the .

Example usage

To create an instance of a Fully Connected Neural Network you need to instantiate one of the NeuralNetClassifier and NeuralNetRegressor classes and configure a number of parameters that are passed to their constructor. Note that some parameters need to be prefixed by module__, while others don't. Basically, the parameters that are related to the model, i.e. the underlying nn.Module, must have the prefix. The parameters that are related to training options do not require the prefix.

The figure above shows, on the right, the Concrete-ML neural network, trained with Quantization Aware Training, in a FHE-compatible configuration. The figure compares this network to the floating point equivalent, trained with scikit-learn.

Architecture parameters

• module__n_layers: number of layers in the FCNN, must be at least 1. Note that this is the total number of layers. For a single hidden layer NN model, set module__n_layers=2

• module__n_outputs: number of outputs (classes or targets)

• module__input_dim: dimensionality of the input

Quantization parameters

• n_w_bits (default 3): number of bits for weights

• n_a_bits (default 3): number of bits for activations and inputs

Training parameters (from Skorch)

• max_epochs: The number of epochs to train the network (default 10)

• verbose: Whether to log loss/metrics during training (default: False)

• lr: Learning rate (default 0.001)

Advanced parameters

Network input/output

When you have training data in the form of a NumPy array, and targets in a NumPy 1d array, you can set:

Class weights

You can give weights to each class to use in training. Note that this must be supported by the underlying PyTorch loss function.

Overflow errors

The n_hidden_neurons_multiplier parameter influences training accuracy as it controls the number of non-zero neurons that are allowed in each layer. Increasing n_hidden_neurons_multiplier improves accuracy, but should take into account precision limitations to avoid overflow in the accumulator. The default value is a good compromise that avoids overflow, in most cases, but you may want to change the value of this parameter to reduce the breadth of the network if you have overflow errors. A value of 1 should be completely safe with respect to overflow.

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Concrete-ML is an open-source privacy-preserving machine learning inference framework based on fully homomorphic encryption (FHE). It enables data scientists without any prior knowledge of cryptography to automatically turn machine learning models into their FHE equivalent, using familiar APIs from Scikit-learn and PyTorch (see how it looks for , and ).

Fully Homomorphic Encryption (FHE) is an encryption technique that allows computing directly on encrypted data, without needing to decrypt it. With FHE, you can build private-by-design applications without compromising on features. You can learn more about FHE in , or by joining the community.

Example usage

This example shows the typical flow of a Concrete-ML model:

• The model is trained on unencrypted (plaintext) data using scikit-learn. As FHE operates over integers, Concrete-ML quantizes the model to use only integers during inference.

• The quantized model is compiled to a FHE equivalent. Under the hood, the model is first converted to a Concrete-Numpy program, then compiled.

Current limitations

To make a model work with FHE, the only constraint is to make it run within the supported precision limitations of Concrete-ML (currently 8-bit integers). Thus, machine learning models are required to be quantized, which sometimes leads to a loss of accuracy versus the original model operating on plaintext.

Additionally, Concrete-ML currently only supports FHE inference. On the other hand, training has to be done on unencrypted data, producing a model which is then converted to a FHE equivalent that can perform encrypted inference, i.e. prediction over encrypted data.

Finally, in Concrete-ML there is currently no support for pre-processing model inputs and for post-processing model outputs. These processing stages may involve text to numerical feature transformation, dimensionality reduction, KNN or clustering, featurization, normalization, and the mixing of results of ensemble models.

All of these issues are currently being addressed and significant improvements are expected to be released in the coming months.

Concrete Stack

Online demos and tutorials.

More generally, if you have built awesome projects using Concrete-ML, feel free to let us know and we'll link to it!

Additional resources

Looking for support? Ask our team!

In addition to Concrete-ML models and to custom models in torch, it is also possible to directly compile ONNX models. This can be particularly appealing, notably to import models trained with Keras.

ONNX models can be compiled by directly importing models that are already quantized with Quantization Aware Training (QAT). or by performing Post-Training Quantization (PTQ) with Concrete-ML.

Simple example

The following example shows how to compile an ONNX model using PTQ. The model was initially trained using Keras before being exported to ONNX. The training code is not shown here.

import numpy
import onnx
import tensorflow
import tf2onnx

from concrete.ml.torch.compile import compile_onnx_model
from concrete.numpy.compilation import Configuration


class FC(tensorflow.keras.Model):
    """A fully-connected model."""

    def __init__(self):
        super().__init__()
        hidden_layer_size = 10
        output_size = 5

        self.dense1 = tensorflow.keras.layers.Dense(
            hidden_layer_size,
            activation=tensorflow.nn.relu,
        )
        self.dense2 = tensorflow.keras.layers.Dense(output_size, activation=tensorflow.nn.relu6)
        self.flatten = tensorflow.keras.layers.Flatten()

    def call(self, inputs):
        """Forward function."""
        x = self.flatten(inputs)
        x = self.dense1(x)
        x = self.dense2(x)
        return self.flatten(x)


n_bits = 6
input_output_feature = 2
input_shape = (input_output_feature,)
num_inputs = 1
n_examples = 5000

# Define the Keras model
keras_model = FC()
keras_model.build((None,) + input_shape)
keras_model.compute_output_shape(input_shape=(None, input_output_feature))

# Create random input
input_set = numpy.random.uniform(-100, 100, size=(n_examples, *input_shape))

# Convert to ONNX
tf2onnx.convert.from_keras(keras_model, opset=14, output_path="tmp.model.onnx")

onnx_model = onnx.load("tmp.model.onnx")
onnx.checker.check_model(onnx_model)

# Compile
quantized_numpy_module = compile_onnx_model(
    onnx_model, input_set, n_bits=2
)

# Create test data from the same distribution and quantize using
# learned quantization parameters during compilation
x_test = tuple(numpy.random.uniform(-100, 100, size=(1, *input_shape)) for _ in range(num_inputs))
qtest = quantized_numpy_module.quantize_input(x_test)

y_clear = quantized_numpy_module(*qtest)
y_fhe = quantized_numpy_module.forward_fhe.encrypt_run_decrypt(*qtest)

print("Execution in clear: ", y_clear)
print("Execution in FHE:   ", y_fhe)
print("Equality:           ", numpy.sum(y_clear == y_fhe), "over", numpy.size(y_fhe), "values")

Quantization Aware Training

QAT models contain quantizers in the ONNX graph. These quantizers ensure that the inputs to the Linear/Dense and Conv layers are quantized. Since these QAT models have quantizers that are configured during training to a specific number of bits, the ONNX graph will need to be imported using the same settings:

n_bits_qat = 3  # number of bits for weights and activations during training

quantized_numpy_module = compile_onnx_model(
    onnx_model,
    input_set,
    n_bits=n_bits_qat,
)

Supported operators

The following operators are supported for evaluation and conversion to an equivalent FHE circuit. Other operators were not implemented either due to FHE constraints, or because they are rarely used in PyTorch activations or scikit-learn models.

• Abs

• Acos

• Acosh

• Add

• Asin

• Asinh

• Atan

• Atanh

• AveragePool

• BatchNormalization

• Cast

• Celu

• Clip

• Constant

• Conv

• Cos

• Cosh

• Div

• Elu

• Equal

• Erf

• Exp

• Flatten

• Floor

• Gemm

• Greater

• GreaterOrEqual

• HardSigmoid

• HardSwish

• Identity

• LeakyRelu

• Less

• LessOrEqual

• Log

• MatMul

• Max

• Min

• Mul

• Neg

• Not

• Or

• PRelu

• Pad

• Pow

• ReduceSum

• Relu

• Reshape

• Round

• Selu

• Sigmoid

• Sign

• Sin

• Sinh

• Softplus

• Sub

• Tan

• Tanh

• ThresholdedRelu

• Transpose

• Where

• onnx.brevitas.Quant

This section provides a set of tools and guidelines to help users build optimized FHE-compatible models.

Virtual library

The Virtual Lib in Concrete-ML is a prototype that provides drop-in replacements for Concrete-Numpy's compiler, allowing users to simulate what would happen when converting a model to FHE without the current bit-width constraint. Additionally, it quickly simulates the behavior with 8 bits or less without actually doing the FHE computations.

The Virtual Lib can be useful when developing and iterating on an ML model implementation. For example, you can check that your model is compatible in terms of operands (all integers) with the Virtual Lib compilation. Then, you can check how many bits your ML model would require, which can give you hints as to how it should be modified if you want to compile it to an actual FHE Circuit (not a simulated one) that only supports 8 bits of integer precision.

The Virtual Lib, being pure Python and not requiring crypto key generation, can be much faster than the actual compilation and FHE execution, thus allowing for faster iterations, debugging and FHE simulation, regardless of the bit-width used. For example, this was used for the red/blue contours in the Classifier Comparison notebook, as computing in FHE for the whole grid and all the classifiers would take significant time.

The following example shows how to use the Virtual Lib in Concrete-ML. Simply add use_virtual_lib = True and enable_unsafe_features = True in a Configuration. The result of the compilation will then be a simulated circuit that allows for more precision or simulated FHE execution.

from sklearn.datasets import fetch_openml, make_circles
from concrete.ml.sklearn import RandomForestClassifier
from concrete.numpy import Configuration
debug_config = Configuration(
    enable_unsafe_features=True,
    use_insecure_key_cache=True,
    insecure_key_cache_location="~/.cml_keycache",
)

n_bits = 2
X, y = make_circles(n_samples=1000, noise=0.1, factor=0.6, random_state=0)
concrete_clf = RandomForestClassifier(
    n_bits=n_bits, n_estimators=10, max_depth=5
)
concrete_clf.fit(X, y)

concrete_clf.compile(X, debug_config, use_virtual_lib=True)

y_preds_clear = concrete_clf.predict(X)

Compilation debugging

The following example produces a neural network that is not FHE-compatible:

import numpy
import torch

from torch import nn
from concrete.ml.torch.compile import compile_torch_model

N_FEAT = 2
class SimpleNet(nn.Module):
    """Simple MLP with PyTorch"""

    def __init__(self, n_hidden=30):
        super().__init__()
        self.fc1 = nn.Linear(in_features=N_FEAT, out_features=n_hidden)
        self.fc2 = nn.Linear(in_features=n_hidden, out_features=n_hidden)
        self.fc3 = nn.Linear(in_features=n_hidden, out_features=2)


    def forward(self, x):
        """Forward pass."""
        x = torch.relu(self.fc1(x))
        x = torch.relu(self.fc2(x))
        x = self.fc3(x)
        return x


torch_input = torch.randn(100, N_FEAT)
torch_model = SimpleNet(120)
try:
    quantized_numpy_module = compile_torch_model(
        torch_model,
        torch_input,
        n_bits = 3,
    )
except RuntimeError as err:
    print(err)

Upon execution, the compiler will raise the following error:

%0 = [[-1 -3] [ ... ] [-2  2]]        # ClearTensor<int3, shape=(120, 2)>
 %1 = [[ 1  3 -2 ...  1  2  0]]        # ClearTensor<int3, shape=(120, 120)>
 %2 = [[ 2  0  3 ... -2 -2 -1]]        # ClearTensor<int3, shape=(2, 120)>
 %3 = _onnx__Gemm_0                    # EncryptedTensor<uint5, shape=(1, 2)>
 %4 = -15                              # ClearScalar<int5>
 %5 = add(%3, %4)                      # EncryptedTensor<int6, shape=(1, 2)>
 %6 = subgraph(%5)                     # EncryptedTensor<int3, shape=(1, 2)>
 %7 = matmul(%6, %2)                   # EncryptedTensor<int6, shape=(1, 120)>
 %8 = subgraph(%7)                     # EncryptedTensor<uint3, shape=(1, 120)>
 %9 = matmul(%8, %1)                   # EncryptedTensor<int9, shape=(1, 120)>
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ only up to 8-bit integers are supported
%10 = subgraph(%9)                     # EncryptedTensor<uint3, shape=(1, 120)>
%11 = matmul(%10, %0)                  # EncryptedTensor<int8, shape=(1, 2)>
%12 = subgraph(%11)                    # EncryptedTensor<uint5, shape=(1, 2)>
return %12

Knowing that a linear/dense layer is implemented as a matrix multiplication, it can determine which parts of the op-graph listing in the exception message above correspond to which layers.

Layer weights initialization:

%0 = [[-1 -3] [ ... ] [-2  2]]        # ClearTensor<int3, shape=(120, 2)>
 %1 = [[ 1  3 -2 ...  1  2  0]]        # ClearTensor<int3, shape=(120, 120)>
 %2 = [[ 2  0  3 ... -2 -2 -1]]        # ClearTensor<int3, shape=(2, 120)>

Input processing and quantization:

 %3 = _onnx__Gemm_0                    # EncryptedTensor<uint5, shape=(1, 2)>
 %4 = -15                              # ClearScalar<int5>
 %5 = add(%3, %4)                      # EncryptedTensor<int6, shape=(1, 2)>
 %6 = subgraph(%5)                     # EncryptedTensor<int3, shape=(1, 2)>

First dense layer and activation function:

%7 = matmul(%6, %2)                   # EncryptedTensor<int6, shape=(1, 120)>
%8 = subgraph(%7)                     # EncryptedTensor<uint3, shape=(1, 120)>

Second dense layer and activation function:

%9 = matmul(%8, %1)                   # EncryptedTensor<int9, shape=(1, 120)>
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ only up to 8-bit integers are supported
%10 = subgraph(%9)                     # EncryptedTensor<uint3, shape=(1, 120)>

Third dense layer and output quantization:

%11 = matmul(%10, %0)                  # EncryptedTensor<int8, shape=(1, 2)>
%12 = subgraph(%11)                    # EncryptedTensor<uint5, shape=(1, 2)>
return %12

We can see here that the error is in the second layer. Reducing the number of neurons in this layer will resolve the error and make the network FHE-compatible:

torch_model = SimpleNet(50)
try:
    quantized_numpy_module = compile_torch_model(
        torch_model,
        torch_input,
        n_bits = 3,
    )
except RuntimeError as err:
    print(err)

Complexity analysis

In FHE, univariate functions are encoded as table lookups, which are then implemented using Programmable Bootstrapping (PBS). PBS is a powerful technique but will require significantly more computing resources, and thus time, than simpler encrypted operations such matrix multiplications, convolution or additions.

Furthermore, the cost of PBS will depend on the bit-width of the compiled circuit. Every additional bit in the maximum bit-width raises the complexity of the PBS by a significant factor. It may be of interest to the model developer, then, to determine the bit-width of the circuit and the amount of PBS it performs.

This can be done by inspecting the MLIR code produced by the compiler:

Concrete-ML Model

torch_model = SimpleNet(50)
try:
    quantized_numpy_module = compile_torch_model(
        torch_model,
        torch_input,
        n_bits = 3,
        show_mlir=True,
    )
except RuntimeError as err:
    print(err)

Compiled MLIR model

%cst = arith.constant dense<...> : tensor<50x2xi9>
%cst_0 = arith.constant dense<...>
%cst_1 = arith.constant dense<...> : tensor<2x50xi9>
%c-14_i9 = arith.constant -14 : i9
%c128_i9 = arith.constant 128 : i9
%c128_i9_2 = arith.constant 128 : i9
%c128_i9_3 = arith.constant 128 : i9
%c128_i9_4 = arith.constant 128 : i9
%hack_0_c-14_i9 = tensor.from_elements %c-14_i9 : tensor<1xi9>
%0 = "FHELinalg.add_eint_int"(%arg0, %hack_0_c-14_i9) : (tensor<1x2x!FHE.eint<8>>, tensor<1xi9>) -> tensor<1x2x!FHE.eint<8>>
%hack_1_c128_i9_4 = tensor.from_elements %c128_i9_4 : tensor<1xi9>
%1 = "FHELinalg.add_eint_int"(%0, %hack_1_c128_i9_4) : (tensor<1x2x!FHE.eint<8>>, tensor<1xi9>) -> tensor<1x2x!FHE.eint<8>>
%cst_5 = arith.constant dense<...> : tensor<256xi64>
%2 = "FHELinalg.apply_lookup_table"(%1, %cst_5) : (tensor<1x2x!FHE.eint<8>>, tensor<256xi64>) -> tensor<1x2x!FHE.eint<8>>

%3 = "FHELinalg.matmul_eint_int"(%2, %cst_1) : (tensor<1x2x!FHE.eint<8>>, tensor<2x50xi9>) -> tensor<1x50x!FHE.eint<8>>
%hack_4_c128_i9_3 = tensor.from_elements %c128_i9_3 : tensor<1xi9>
%4 = "FHELinalg.add_eint_int"(%3, %hack_4_c128_i9_3) : (tensor<1x50x!FHE.eint<8>>, tensor<1xi9>) -> tensor<1x50x!FHE.eint<8>>
%cst_6 = arith.constant dense<...> : tensor<34x256xi64>
%cst_7 = arith.constant dense<...]> : tensor<1x50xindex>
%5 = "FHELinalg.apply_mapped_lookup_table"(%4, %cst_6, %cst_7) : (tensor<1x50x!FHE.eint<8>>, tensor<34x256xi64>, tensor<1x50xindex>) -> tensor<1x50x!FHE.eint<8>>

%6 = "FHELinalg.matmul_eint_int"(%5, %cst_0) : (tensor<1x50x!FHE.eint<8>>, tensor<50x50xi9>) -> tensor<1x50x!FHE.eint<8>>
%hack_7_c128_i9_2 = tensor.from_elements %c128_i9_2 : tensor<1xi9>
%7 = "FHELinalg.add_eint_int"(%6, %hack_7_c128_i9_2) : (tensor<1x50x!FHE.eint<8>>, tensor<1xi9>) -> tensor<1x50x!FHE.eint<8>>
%cst_8 = arith.constant dense<...> : tensor<34x256xi64>
%cst_9 = arith.constant dense<...> : tensor<1x50xindex>
%8 = "FHELinalg.apply_mapped_lookup_table"(%7, %cst_8, %cst_9) : (tensor<1x50x!FHE.eint<8>>, tensor<34x256xi64>, tensor<1x50xindex>) -> tensor<1x50x!FHE.eint<8>>

%9 = "FHELinalg.matmul_eint_int"(%8, %cst) : (tensor<1x50x!FHE.eint<8>>, tensor<50x2xi9>) -> tensor<1x2x!FHE.eint<8>>
%hack_10_c128_i9 = tensor.from_elements %c128_i9 : tensor<1xi9>
%10 = "FHELinalg.add_eint_int"(%9, %hack_10_c128_i9) : (tensor<1x2x!FHE.eint<8>>, tensor<1xi9>) -> tensor<1x2x!FHE.eint<8>>
%cst_10 = arith.constant dense<...> : tensor<2x256xi64>
%cst_11 = arith.constant dense<[[0, 1]]> : tensor<1x2xindex>
%11 = "FHELinalg.apply_mapped_lookup_table"(%10, %cst_10, %cst_11) : (tensor<1x2x!FHE.eint<8>>, tensor<2x256xi64>, tensor<1x2xindex>) -> tensor<1x2x!FHE.eint<8>>
return %11 : tensor<1x2x!FHE.eint<8>>

There are several calls to FHELinalg.apply_mapped_lookup_table and FHELinalg.apply_lookup_table. These calls apply PBS to the cells of their input tensors. Their inputs in the listing above are: tensor<1x2x!FHE.eint<8>> for the first and last call and tensor<1x50x!FHE.eint<8>> for the two calls in the middle. Thus, PBS is applied 104 times.

Getting the bit-width of the circuit is then simply:

print(quantized_numpy_module.forward_fhe.graph.maximum_integer_bit_width())

Decreasing the number of bits and the number of PBS induces large reductions in the computation time of the compiled circuit.

In addition to the built-in models, Concrete-ML supports generic machine learning models implemented with Torch, or exported as ONNX graphs.

As Quantization Aware Training (QAT) is the most appropriate method of training neural networks that are compatible with FHE constraints, Concrete-ML works with Brevitas, a library providing QAT support for PyTorch.

The following example uses a simple QAT PyTorch model that implements a fully connected neural network with two hidden layers. Due to its small size, making this model respect FHE constraints is relatively easy.

import brevitas.nn as qnn
import torch.nn as nn
import torch

N_FEAT = 12
n_bits = 3

class QATSimpleNet(nn.Module):
    def __init__(self, n_hidden):
        super().__init__()

        self.quant_inp = qnn.QuantIdentity(bit_width=n_bits, return_quant_tensor=True)
        self.fc1 = qnn.QuantLinear(N_FEAT, n_hidden, True, weight_bit_width=n_bits, bias_quant=None)
        self.quant2 = qnn.QuantIdentity(bit_width=n_bits, return_quant_tensor=True)
        self.fc2 = qnn.QuantLinear(n_hidden, n_hidden, True, weight_bit_width=3, bias_quant=None)
        self.quant3 = qnn.QuantIdentity(bit_width=n_bits, return_quant_tensor=True)
        self.fc3 = qnn.QuantLinear(n_hidden, 2, True, weight_bit_width=n_hidden, bias_quant=None)

    def forward(self, x):
        x = self.quant_inp(x)
        x = self.quant2(torch.relu(self.fc1(x)))
        x = self.quant3(torch.relu(self.fc2(x)))
        x = self.fc3(x)
        return x

Once the model is trained, calling the compile_brevitas_qat_model from Concrete-ML will automatically perform conversion and compilation of a QAT network. Here, 3-bit quantization is used for both the weights and activations.

from concrete.ml.torch.compile import compile_brevitas_qat_model
import numpy

torch_input = torch.randn(100, N_FEAT)
torch_model = QATSimpleNet(30)
quantized_numpy_module = compile_brevitas_qat_model(
    torch_model, # our model
    torch_input, # a representative input-set to be used for both quantization and compilation
    n_bits = n_bits,
)

The model can now be used to perform encrypted inference. Next, the test data is quantized:

x_test = numpy.array([numpy.random.randn(N_FEAT)])
x_test_quantized = quantized_numpy_module.quantize_input(x_test)

and the encrypted inference run using either:

• quantized_numpy_module.forward_and_dequant() to compute predictions in the clear, on quantized data and then de-quantize the result. The return value of this function contains the dequantized (float) output of running the model in the clear. Calling the forward function on the clear data is useful when debugging. The results in FHE will be the same as those on clear quantized data.

• quantized_numpy_module.forward_fhe.encrypt_run_decrypt() to perform the FHE inference. In this case, dequantization is done in a second stage using quantized_numpy_module.dequantize_output().

Generic Quantization Aware Training import

While the example above shows how to import a Brevitas/PyTorch model, Concrete-ML also provides an option to import generic QAT models implemented either in PyTorch or through ONNX. Interestingly, deep learning models made with TensorFlow or Keras should be usable, by preliminary converting them to ONNX.

QAT models contain quantizers in the PyTorch graph. These quantizers ensure that the inputs to the Linear/Dense and Conv layers are quantized.

Suppose that n_bits_qat is the bit-width of activations and weights during the QAT process. To import a PyTorch QAT network, you can use the compile_torch_model library function, passing import_qat=True:

from concrete.ml.torch.compile import compile_torch_model
n_bits_qat = 3

quantized_numpy_module = compile_torch_model(
    torch_model,
    torch_input,
    import_qat=True,
    n_bits=n_bits_qat,
)

Alternatively, if you want to import an ONNX model directly, please see the ONNX guide. The compile_onnx_model also supports the import_qat parameter.

Supported operators and activations

Concrete-ML supports a variety of PyTorch operators that can be used to build fully connected or convolutional neural networks, with normalization and activation layers. Moreover, many element-wise operators are supported.

Operators

univariate operators

• torch.abs

• torch.clip

• torch.exp

• torch.log

• torch.gt

• torch.clamp

• torch.mul, torch.Tensor operator *

• torch.div, torch.Tensor operator /

• torch.nn.identity

shape modifying operators

• torch.reshape

• torch.Tensor.view

• torch.flatten

• torch.transpose

operators that take an encrypted input and unencrypted constants

• torch.conv2d, torch.nn.Conv2D

• torch.matmul

• torch.nn.Linear

Please note that Concrete-ML supports these operators but also the Quantization Aware Training equivalents from Brevitas.

• brevitas.nn.QuantLinear

• brevitas.nn.QuantConv2d

operators that can take both encrypted+unencrypted and encrypted+encrypted inputs

• torch.add, torch.Tensor operator +

• torch.sub, torch.Tensor operator -

Quantizers

• brevitas.nn.QuantIdentity

Activations

• torch.nn.Celu

• torch.nn.Elu

• torch.nn.GELU

• torch.nn.Hardshrink

• torch.nn.HardSigmoid

• torch.nn.Hardswish

• torch.nn.HardTanh

• torch.nn.LeakyRelu

• torch.nn.LogSigmoid

• torch.nn.Mish

• torch.nn.PReLU

• torch.nn.ReLU6

• torch.nn.ReLU

• torch.nn.Selu

• torch.nn.Sigmoid

• torch.nn.SiLU

• torch.nn.Softplus

• torch.nn.Softshrink

• torch.nn.Softsign

• torch.nn.Tanh

• torch.nn.Tanhshrink

• torch.nn.Threshold -- partial support

Concrete-ML provides partial support for Pandas, with most available models (linear and tree-based models) usable on Pandas dataframes the same way they would be used with NumPy arrays.

The table below summarizes the current compatibility:

Example

The following example considers a LogisticRegression model on a simple classification problem. A more advanced example can be found in the Titanic use case notebook, which considers a XGBClassifier.

import numpy as np
import pandas as pd
from concrete.ml.sklearn import LogisticRegression
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split

# Create the data set as a Pandas dataframe
X, y = make_classification(
    n_samples=100,
    n_features=2,
    n_redundant=0,
    random_state=2,
)
X, y = pd.DataFrame(X), pd.DataFrame(y)

# Retrieve train and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=42)

# Instantiate the model
model = LogisticRegression(n_bits=2)

# Fit the model
model.fit(X_train, y_train)

# Evaluate the model on the test set in clear
y_pred_clear = model.predict(X_test)

# Compile the model
model.compile(X_train.to_numpy())

# Perform the inference in FHE
# Warning: this will take a while. It is recommended to run this with a very small batch of
# examples first (e.g. N_TEST_FHE = 1)
# Note that here the encryption and decryption is done behind the scenes.
N_TEST_FHE = 1
y_pred_fhe = model.predict(X_test.head(N_TEST_FHE), execute_in_fhe=True)

# Assert that FHE predictions are the same as the clear predictions
print(f"{(y_pred_fhe == y_pred_clear[:N_TEST_FHE]).sum()} "
      f"examples over {N_TEST_FHE} have a FHE inference equal to the clear inference.")

# Output:
#  1 examples over 1 have a FHE inference equal to the clear inference

This section includes a complete example of converting a neural network to Quantization Aware Training (QAT). This tutorial uses PyTorch and Brevitas to train a simple network on a synthetic data-set. You can find the demo of the final network in the custom-model with quantization aware training demo. To see how to apply these network design principles for a real-world data-set, please see the MNIST use-case example.

For a more formal description of the usage of Brevitas to build FHE-compatible neural networks, please see the Brevitas usage reference.

Summary

1. Building a standard baseline PyTorch model

2. Adding pruning to make learning more robust

3. Converting to Quantization Aware Training with Brevitas

Baseline model

This example shows how to train a fully-connected neural network on a synthetic 2D data-set with a checkerboard grid pattern of 100 x 100 points. The data is split into 9500 training and 500 test samples.

In PyTorch, using standard layers, this network would look as follows:

from torch import nn
import torch

N_FEAT = 2
class SimpleNet(nn.Module):
    """Simple MLP with PyTorch"""

    def __init__(self, n_hidden=30):
        super().__init__()
        self.fc1 = nn.Linear(in_features=N_FEAT, out_features=n_hidden)
        self.fc2 = nn.Linear(in_features=n_hidden, out_features=n_hidden)
        self.fc3 = nn.Linear(in_features=n_hidden, out_features=2)


    def forward(self, x):
        """Forward pass."""
        x = torch.relu(self.fc1(x))
        x = torch.relu(self.fc2(x))
        x = self.fc3(x)
        return x

Once trained, this network can be imported using the compile_torch_model function. This function uses simple Post-Training Quantization.

The network was trained using different numbers of neurons in the hidden layers, and quantized using 3-bits weights and activations. The mean accumulator size shown below was extracted using the Virtual Library.

This shows that the fp32 accuracy and accumulator size increases with the number of hidden neurons, while the 3-bit accuracy remains low irrespective of to the number of neurons. While all the configurations tried here were FHE-compatible (accumulator < 8 bits), it is sometimes preferable to have a lower accumulator size in order for the inference time to be faster.

Pruning using Torch

Considering that FHE only works with limited integer precision, there is a risk of overflowing in the accumulator, resulting in unpredictable results.

This can be leveraged to train a network with more neurons, while not overflowing the accumulator, using a technique called pruning, where the developer can impose a number of zero-valued weights. Torch provides support for pruning out of the box.

The following code shows how to use pruning in the previous example:

import torch.nn.utils.prune as prune

class PrunedSimpleNet(SimpleNet):
    """Simple MLP with PyTorch"""

    def prune(self, max_non_zero, enable):
        # Linear layer weight has dimensions NumOutputs x NumInputs
        for layer in self.named_modules():
            if isinstance(layer, nn.Linear):
                num_zero_weights = (layer.weight.shape[1] - max_non_zero) * layer.weight.shape[0]
                if num_zero_weights <= 0:
                    continue

                if enable:
                    prune.l1_unstructured(layer, "weight", amount=num_zero_weights)
                else:
                    prune.remove(layer, "weight")

Results with PrunedSimpleNet, a pruned version of the SimpleNet with 100 neurons on the hidden layers, are given below:

This shows that the fp32 accuracy has been improved while maintaining constant mean accumulator size.

When pruning a larger neural network during training, it is easier to obtain a low bit-width accumulator while maintaining better final accuracy. Thus, pruning is more robust than training a similar smaller network.

Quantization Aware Training

While pruning helps maintain the post-quantization level of accuracy in low-precision settings, it does not help maintain accuracy when quantizing from floating point models. The best way to guarantee accuracy is to use QAT (read more in the quantization documentation).

In this example, QAT is done using Brevitas, changing Linear layers to QuantLinear and adding quantizers on the inputs of linear layers using QuantIdentity.

import brevitas.nn as qnn


from brevitas.core.bit_width import BitWidthImplType
from brevitas.core.quant import QuantType
from brevitas.core.restrict_val import FloatToIntImplType, RestrictValueType
from brevitas.core.scaling import ScalingImplType
from brevitas.core.zero_point import ZeroZeroPoint
from brevitas.inject import ExtendedInjector
from brevitas.quant.solver import ActQuantSolver, WeightQuantSolver
from dependencies import value

# Configure quantization options
class CommonQuant(ExtendedInjector):
    bit_width_impl_type = BitWidthImplType.CONST
    scaling_impl_type = ScalingImplType.CONST
    restrict_scaling_type = RestrictValueType.FP
    zero_point_impl = ZeroZeroPoint
    float_to_int_impl_type = FloatToIntImplType.ROUND
    scaling_per_output_channel = False
    narrow_range = True
    signed = True

    @value
    def quant_type(bit_width):
        if bit_width is None:
            return QuantType.FP
        elif bit_width == 1:
            return QuantType.BINARY
        else:
            return QuantType.INT

# Quantization options for weights/activations
class CommonWeightQuant(CommonQuant, WeightQuantSolver):
    scaling_const = 1.0
    signed = True


class CommonActQuant(CommonQuant, ActQuantSolver):
    min_val = -1.0
    max_val = 1.0

class QATPrunedSimpleNet(nn.Module):
    def __init__(self, n_hidden):
        super(QATPrunedSimpleNet, self).__init__()

        n_bits = 3
        self.quant_inp = qnn.QuantIdentity(
            act_quant=CommonActQuant,
            bit_width=n_bits,
            return_quant_tensor=True,
        )

        self.fc1 = qnn.QuantLinear(
            N_FEAT,
            n_hidden,
            True,
            weight_quant=CommonWeightQuant,
            weight_bit_width=n_bits,
            bias_quant=None,
        )

        self.q1 = qnn.QuantIdentity(
            act_quant=CommonActQuant, bit_width=n_bits, return_quant_tensor=True
        )

        self.fc2 = qnn.QuantLinear(
            n_hidden,
            n_hidden,
            True,
            weight_quant=CommonWeightQuant,
            weight_bit_width=3,
            bias_quant=None
        )

        self.q2 = qnn.QuantIdentity(
            act_quant=CommonActQuant, bit_width=n_bits, return_quant_tensor=True
        )

        self.fc3 = qnn.QuantLinear(
            n_hidden,
            2,
            True,
            weight_quant=CommonWeightQuant,
            weight_bit_width=n_hidden,
            bias_quant=None,
        )

        for m in self.modules():
            if isinstance(m, qnn.QuantLinear):
                torch.nn.init.uniform_(m.weight.data, -1, 1)

    def forward(self, x):
        x = self.quant_inp(x)
        x = self.q1(torch.relu(self.fc1(x)))
        x = self.q2(torch.relu(self.fc2(x)))
        x = self.fc3(x)
        return x

    def prune(self, max_non_zero, enable):
        # Linear layer weight has dimensions NumOutputs x NumInputs
        for name, layer in self.named_modules():
            if isinstance(layer, nn.Linear):
                num_zero_weights = (layer.weight.shape[1] - max_non_zero) * layer.weight.shape[0]
                if num_zero_weights <= 0:
                    continue

                if enable:
                    print(f"Pruning layer {name} factor {num_zero_weights}")
                    prune.l1_unstructured(layer, "weight", amount=num_zero_weights)
                else:
                    prune.remove(layer, "weight")

Training this network with 30 out of 100 total non-zero neurons gives good accuracy while being FHE-compatible (accumulator size < 8 bits).

The following table summarizes the various examples in this section, along with their accuracies.

A * means that FHE accuracy was calculated on a subset of the validation set.

Concrete-ML models

• LinearRegression.ipynb

• LogisticRegression.ipynb

• PoissonRegression.ipynb

• DecisionTreeClassifier.ipynb

• XGBClassifier.ipynb

• XGBRegressor.ipynb

• GLMComparison.ipynb

Comparison of classifiers

• ClassifierComparison.ipynb

Summary

The following table summarizes the examples in this section:

Examples

• FullyConnectedNeuralNetwork.ipynb

• QuantizationAwareTraining.ipynb

• ConvolutionalNeuralNetwork.ipynb

Quantization is the process of constraining an input from a continuous or otherwise large set of values (such as real numbers) to a discrete set (such as integers).

This means that some accuracy in the representation is lost (e.g. a simple approach is to eliminate least-significant bits). However, in many cases in machine learning, it is possible to adapt the models to give meaningful results while using these smaller data types. This significantly reduces the number of bits necessary for intermediary results during the execution of these machine learning models.

Since FHE is currently limited to 8-bit integers, it is necessary to quantize models to make them compatible. As a general rule, the smaller the precision models, the better the FHE performance.

Overview of quantization in Concrete-ML

Quantization implemented in Concrete-ML is applied in two ways:

1. Built-in models apply quantization internally and the user only needs to configure some quantization parameters. This approach requires little work by the user but may not be a one-size-fits-all solution for all types of models. The final quantized model is FHE friendly and ready to predict over encrypted data. In this setting, Post-Training Quantization (PTQ) is for linear models, data quantization is used for tree-based models and, finally, Quantization Aware Training (QAT) is included in the built-in neural network models.

2. For custom neural networks with more complex topology, obtaining FHE-compatible models with good accuracy requires QAT. Concrete-ML offers the possibility for the user to perform quantization before compiling to FHE. This can be achieved through a third-party library that offers QAT tools, such as Brevitas for PyTorch. In this approach, the user is responsible for implementing a full-integer model, respecting FHE constraints. Please refer to the advanced QAT tutorial for tips on designing FHE neural networks.

Basics of quantization

Let $[\alpha, \beta ]$ be the range of a value to quantize where $\alpha$ is the minimum and $\beta$ is the maximum. To quantize a range of floating point values (in $\mathbb{R}$) to integer values (in $\mathbb{Z}$), the first step is to choose the data type that is going to be used. Concrete, the framework used by Concrete-ML, is currently limited to 8-bit integers, so this will be the value used in this example. Knowing the number of bits that can be used for a value in the range $[\alpha, \beta ]$, the scale $S$ can be computed :

$S = \frac{\beta - \alpha}{2^n - 1}$

where $n$ is the number of bits ($n \leq 8$). For the sake of example, let's take $n = 7$.

In practice, the quantization scale is then $S = \frac{\beta - \alpha}{127}$. This means the gap between consecutive representable values cannot be smaller than $S$, which, in turn, means there can be a substantial loss of precision. Every interval of length $S$ will be represented by a value within the range $[0..127]$.

The other important parameter from this quantization schema is the zero point $Z_p$ value. This essentially brings the 0 floating point value to a specific integer. If the quantization scheme is asymmetric (quantized values are not centered in 0), the resulting integer will be in $\mathbb{Z}$.

When using quantized values in a matrix multiplication or convolution, the equations for computing the result become more complex. The IntelLabs distiller quantization documentation provides a more detailed explanation of the maths used to quantize values and how to keep computations consistent.

Configuring model quantization parameters

Built-in models provide a simple interface for configuring quantization parameters, most notably the number of bits used for inputs, model weights, intermediary and output values.

For linear models, the quantization is done post-training. Thus, the model is trained in floating point, and then, the best integer weight representations are found, depending on the distribution of inputs and weights. For these models, the user can select the value of the n_bits parameter.

For linear models, n_bits is used to quantize both model inputs and weights. Depending on the number of features, you can use a single integer value for the n_bits parameter, e.g. a value between 2 and 7. When the number of features is high, the n_bits parameter should be decreased if you encounter compilation errors. It is also possible to quantize inputs and weights with different number of bits by passing a dictionary to n_bits , containing the op_inputs and op_weights keys.

For tree-based models, the training and test data is quantized. The maximum accumulator bit-width for a model trained with n_bits=n for this type of model is known beforehand: it will need n+1 bits. Thus, as Concrete-ML only supports up to 8-bit integers, n should be less than 8. Through experimentation, it was determined that in many cases a value of 5 or 6 bits gives the same accuracy as training in floating point.

For the built-in neural networks, several linear layers are used. Thus, the outputs of a layer are used as inputs to a new layer. Built-in neural networks use Quantization Aware Training. The parameters controlling the maximum accumulator bit-width are the number of weights and activation bits ( module__n_w_bits, module__n_a_bits ), but also the pruning factor. This factor is determined automatically by specifying a desired accumulator bit-width module__n_accum_bits and, optionally, a multiplier factor, module__n_hidden_neurons_multiplier.

Quantizing model inputs and outputs

The models implemented in Concrete-ML provide features to let the user quantize the input data and de-quantize the output data.

In a client/server setting, the client is responsible for quantizing inputs before sending them, encrypted, to the server. Further, the client must de-quantize the encrypted integer results received from the server. See the Production Deployment section for more details.

Here is a simple example showing how to perform inference, starting from float values and ending up with float values. Note that the FHE engine that is compiled for the ML models does not support data batching.

# Assume quantized_module : QuantizedModule
#        data: numpy.ndarray of float

# Quantization is done in the clear
x_test_q = quantized_module.quantize_input(data)

for i in range(x_test_q.shape[0]):
    # Inputs must have size (1 x N) or (1 x C x H x W), we add the batch dimension with N=1
    x_q = np.expand_dims(x_test_q[i, :], 0)

    # Execute the model in FHE
    out_fhe = quantized_module.forward_fhe.encrypt_run_decrypt(x_q)

    # Dequantization is done in the clear
    output = quantized_module.dequantize_output(out_fhe)

    # For classifiers with multi-class outputs, the arg max is done in the clear
    y_pred = np.argmax(output, 1)

Resources

• IntelLabs distiller explanation of quantization: Distiller documentation

Concrete-ML offers some features for advanced users that wish to adjust the cryptographic parameters that are generated by the Concrete stack for a certain machine learning model.

Approximate computations using the p_error parameter

Concrete-ML makes use of table lookup (TLU) to represent any non-linear operation (e.g. sigmoid). This TLU is implemented through the Programmable Bootstrapping (PBS) operation which will apply a non-linear operation in the cryptographic realm.

In Concrete-ML, the result of the TLU operation is obtained with a specific error probability:

A single PBS operation has 1 - DEFAULT_P_ERROR_PBS = 99.9936657516% chances of being correct. This number plays a role in the cryptographic parameters. As such, the lower the p_error, the more constraining the parameters will become. This has an impact on both key generation and, more importantly, on FHE execution time.

This number is set by default to be relatively low such that any user can build deep circuits without being impacted by this noise as . However, there might be use cases and specific circuits where the Gaussian noise can increase without being too dramatic for the circuit accuracy. In that case, increasing the p_error can be relevant as it will reduce the execution time in FHE.

Here is a visualization of the effect of the p_error over a simple linear regression with a p_error = 0.1 vs the default p_error value:

The execution for the two models are 336 ms per example for the standard p_error and 253 ms per example for a p_error = 0.1 (on a 8 cores Intel CPU machine). Obviously, this speedup is very dependent on model complexity. To obtain a speedup while maintaining good accuracy, it is possible to search for a good value of p_error. Currently no heuristic has been proposed to find a good value a-priori.

Users have the possibility to change this p_error as they choose fit, by passing an argument to the compile function of any of the models. Here is an example:

Pruning is a method to reduce neural network complexity, usually applied in order to reduce the computation cost or memory size. Pruning is used in Concrete-ML to control the size of accumulators in neural networks, thus making them FHE-compatible. See for an explanation of accumulator bit-width constraints.

Overview of pruning in Concrete-ML

Pruning is used in Concrete-ML for two types of neural networks:

1. Built-in include a pruning mechanism that can be parameterized by the user. The pruning type is based on L1-norm. To comply with FHE constraints, Concrete-ML uses unstructured pruning, as the aim is not to eliminate neurons or convolutional filters completely, but to decrease their accumulator bit-width.

2. Custom neural networks, to work well under FHE constraints, should include pruning. When implemented with PyTorch, you can use the (e.g.L1-Unstructured) to good effect.

Basics of pruning

In neural networks, a neuron computes a linear combination of inputs and learned weights, then applies an activation function.

The neuron computes:

When building a full neural network, each layer will contain multiple neurons, which are connected to the neuron outputs of a previous layer or to the inputs.

Fixing some of the weights to 0 makes the network graph look more similar to the following:

Pruning in practice

In the formula above, in the worst-case, the maximum number of the input and weights that can make the result exceed $n$ bits is given by:

Before you start this section, you must install Docker by following official guide.

Building the image

Once you have access to this repository and the dev environment is installed on your host OS (via make setup_env once ), you should be able to launch the commands to build the dev Docker image with make docker_build.

Once you do that, you can get inside the Docker environment using the following command:

After you finish your work, you can leave Docker by using the exit command or by pressing CTRL + D.

Compilation of a model produces machine code that executes the model on encrypted data. In some cases, notably in the client/server setting, the compilation can be done by the server when loading the model for serving.

As FHE execution is much slower than execution on non-encrypted data, Concrete-ML has a simulation mode, using an execution mode named the Virtual Library. Since, by default, the cryptographic parameters are chosen such that the results obtained in FHE are the same as those on clear data, the Virtual Library allows you to benchmark models quickly during development.

Compilation

Concrete-ML implements machine model inference using Concrete-Numpy as a backend. In order to execute in FHE, a numerical program written in Concrete-Numpy needs to be compiled. This functionality is , and Concrete-ML hides away most of the complexity of this step. The entire compilation process is done by Concrete-Numpy.

From the perspective of the Concrete-ML user, the compilation process performed by Concrete-Numpy can be broken up into 3 steps:

1. Numpy program tracing and creation of a Concrete-Numpy op-graph

2. checking that the op-graph is FHE compatible

3. producing machine code for the op-graph. This step automatically determines cryptographic parameters

Additionally, the packages the result of the last step in a way that allows the deployment of the encrypted circuit to a server and key generation, encryption and decryption on the client side.

Simulation with the Virtual Library

The first step in the list above takes a Python function implemented using the Concrete-Numpy and transforms it into an executable operation graph.

The result of this single step of the compilation pipeline allows the:

• execution of the op-graph, which includes TLUs, on clear non-encrypted data. This is, of course, not secure, but it is much faster than executing in FHE. This mode is useful for debugging, i.e. to find the appropriate hyper-parameters. This mode is called the Virtual Library.

• verification of the maximum bit-width of the op-graph, to determine FHE compatibility, without actually compiling the circuit to machine code.

Enabling Virtual Library execution requires the definition of a compilation Configuration. As simulation does not execute in FHE, this can be considered unsafe:

Next, the following code uses the simulation mode for built-in models:

And finally, for custom models, it is possible to enable simulation using the following syntax:

Obtaining the simulated predictions of the models using the Virtual Library has the same syntax as execution in FHE:

Moreover, the maximum accumulator bit-width is determined as follows:

A simple Concrete-Numpy example

Concrete-ML is a constant work-in-progress, and thus may contain bugs or suboptimal APIs.

Before opening an issue or asking for support, please read this documentation to understand common issues and limitations of Concrete-ML. You can also check the .

Furthermore, undefined behavior may occur if the input-set, which is internally used by the compilation core to set bit-widths of some intermediate data, is not sufficiently representative of the future user inputs. With all the inputs in the input-set, it appears that intermediate data can be represented as an n-bit integer. But, for a particular computation, this same intermediate data needs additional bits to be represented. The FHE execution for this computation will result in an incorrect output, as typically occurs in integer overflows in classical programs.

If you didn't find an answer, you can ask a question on the , or in the FHE.org .

Submitting an issue

When submitting an issue (), ideally include as much information as possible. In addition to the Python script, the following information is useful:

• the reproducibility rate you see on your side

• any insight you might have on the bug

• any workaround you have been able to find

If you would like to contribute to project and send pull requests, take a look at the guide.

Concrete-ML is a Python library, so Python should be installed to develop Concrete-ML. v3.8 and v3.9 are the only supported versions. Concrete-ML also uses Poetry and Make.

First of all, you need to git clone the project:

Some tests require files tracked by git-lfs to be downloaded. To do so, please follow the instructions on , then run git lfs pull.

Automatic installation

A simple way to have everything installed is to use the development Docker (see the guide). On Linux and macOS, you have to run the script in ./script/make_utils/setup_os_deps.sh. Specify the --linux-install-python flag if you want to install python3.8 as well on apt-enabled Linux distributions. The script should install everything you need for Docker and bare OS development (you can first review the content of the file to check what it will do).

Manual installation

Python

To manually install Python, you can follow guide (alternatively, you can google how to install Python 3.8 (or 3.9)).

Poetry

Make

The dev tools use make to launch the various commands.

On Linux, you can install make from your distribution's preferred package manager.

On macOS, you can install a more recent version of make via brew:

Cloning the repository

To get the source code of Concrete-ML, clone the code repository using the link for your favourite communication protocol (ssh or https).

Setting up environment on your host OS

We are going to make use of virtual environments. This helps to keep the project isolated from other Python projects in the system. The following commands will create a new virtual environment under the project directory and install dependencies to it.

Activating the environment

Finally, activate the newly created environment using the following command:

macOS or Linux

Windows

Setting up environment on Docker

Docker automatically creates and sources a venv in ~/dev_venv/

The venv persists thanks to volumes. It also creates a volume for ~/.cache to speed up later reinstallations. You can check which Docker volumes exist with:

You can still run all make commands inside Docker (to update the venv, for example). Be mindful of the current venv being used (the name in parentheses at the beginning of your command prompt).

Leaving the environment

After your work is done, you can simply run the following command to leave the environment:

Syncing environment with the latest changes

From time to time, new dependencies will be added to the project or the old ones will be removed. The command below will make sure the project has the proper environment, so run it regularly!

Troubleshooting your environment

in your OS

If you are having issues, consider using the dev Docker exclusively (unless you are working on OS-specific bug fixes or features).

Here are the steps you can take on your OS to try and fix issues:

in Docker

Here are the steps you can take in your Docker to try and fix issues:

If the problem persists at this point, you should ask for help. We're here and ready to assist!

Using GitBook

Documentation with GitBook is done mainly by pushing content on GitHub. GitBook then pulls the docs from the repository and publishes. In most cases, GitBook is just a mirror of what is available in GitHub.

There are, however, some use-cases where documentation can be modified directly in GitBook (and then, push the modifications to GitHub), for example when the documentation is modified by a person outside of Zama. In this case, a GitHub branch is created, and a GitHub space is associated to it: modifications are done in this space and automatically pushed to the branch. Once the modifications are done, one can simply create a pull-request, to finally merge modifications on the main branch.

Using Sphinx

Documentation can alternatively be built using Sphinx:

The documentation contains both files written by hand by developers (the .md files) and files automatically created by parsing the source files.

Then to open it, go to docs/_build/html/index.html or use the follwing command:

To build and open the docs at the same time, use:

There are three ways to contribute to Concrete-ML:

• You can open issues to report bugs and typos and to suggest ideas.

• You can ask to become an official contributor by emailing . Only approved contributors can send pull requests (PR), so please make sure to get in touch before you do.

• You can also provide new tutorials or use-cases, showing what can be done with the library. The more examples we have, the better and clearer it is for the other users.

1. Creating a new branch

Concrete-ML uses a consistent branch naming scheme, and you are expected to follow it as well. Here is the format, along with some examples:

e.g.

2. Before committing

2.1 Conformance

Each commit to Concrete-ML should conform to the standards of the project. You can let the development tools fix some issues automatically with the following command:

Conformance can be checked using the following command:

2.2 Testing

Your code must be well documented, containing tests and not breaking other tests:

You need to make sure you get 100% code coverage. The make pytest command checks that by default and will fail with a coverage report at the end should some lines of your code not be executed during testing.

If your coverage is below 100%, you should write more tests and then create the pull request. If you ignore this warning and create the PR, GitHub actions will fail and your PR will not be merged.

There may be cases where covering your code is not possible (an exception that cannot be triggered in normal execution circumstances). In those cases, you may be allowed to disable coverage for some specific lines. This should be the exception rather than the rule, and reviewers will ask why some lines are not covered. If it appears they can be covered, then the PR won't be accepted in that state.

3. Committing

Concrete-ML uses a consistent commit naming scheme, and you are expected to follow it as well (the CI will make sure you do). The accepted format can be printed to your terminal by running:

e.g.

4. Rebasing

You should rebase on top of the main branch before you create your pull request. Merge commits are not allowed, so rebasing on main before pushing gives you the best chance of avoiding having to rewrite parts of your PR later if conflicts arise with other PRs being merged. After you commit your changes to your new branch, you can use the following commands to rebase:

5. Releases

Concrete-ML provides functionality to deploy FHE machine learning models in a client/server setting. The deployment workflow and model serving pattern is as follows:

Deployment

The training of the model and its compilation to FHE are performed on a development machine. Three different files are created when saving the model:

• client.json contains the secure cryptographic parameters needed for the client to generate private and evaluation keys.

• server.json contains the compiled model. This file is sufficient to run the model on a server.

• serialized_processing.json contains the metadata about pre- and post-processing, such as quantization parameters to quantize the input and de-quantize the output.

The compiled model (server.zip) is deployed to a server and the cryptographic parameters (client.zip) along with the model meta data (serialized_processing.json) are shared with the clients.

Serving

The client obtains the cryptographic parameters (using client.zip) and generates a private encryption/decryption key as well as a set of public evaluation keys. The public evaluation keys are then sent to the server, while the secret key remains on the client.

The private data is then encrypted using serialized_processing.json by the client and sent to the server. Server-side, the FHE model inference is run on the encrypted inputs using the public evaluation keys.

The encrypted result is then returned by the server to the client, which decrypts it using its private key. Finally, the client performs any necessary post-processing of the decrypted result using serialized_processing.json.

Example notebook

For a complete example, see

Quantizing data

Concrete-ML has support for quantized ML models and also provides quantization tools for Quantization Aware Training and Post-Training Quantization. The core of this functionality is the conversion of floating point values to integers and back. This is done using QuantizedArray in concrete.ml.quantization.

The class takes several arguments that determine how float values are quantized:

• n_bits that defines the precision of the quantization

• values are floating point values that will be converted to integers

• is_signed determines if the quantized integer values should allow negative values

• is_symmetric determines if the range of floating point values to be quantized should be taken as symmetric around zero

See also the reference for more information:

It is also possible to use symmetric quantization, where the integer values are centered around 0:

In the following example, showing the de-quantization of model outputs, the QuantizedArray class is used in a different way. Here it uses pre-quantized integer values and has the scale and zero-point set explicitly. Once the QuantizedArray is constructed, calling dequant() will compute the floating point values corresponding to the integer values qvalues, which are the output of the forward_fhe.encrypt_run_decrypt(..) call.

Quantized modules

Machine learning models are implemented with a diverse set of operations, such as convolution, linear transformations, activation functions and element-wise operations. When working with quantized values, these operations cannot be carried out in an equivalent way as for floating point values. With quantization, it is necessary to re-scale the input and output values of each operation to fit in the quantization domain.

In Concrete-ML, the quantized equivalent of a scikit-learn model or a PyTorch nn.Module is the QuantizedModule. Note that only inference is implemented in the QuantizedModule, and it is built through a conversion of the inference function of the corresponding scikit-learn or PyTorch module.

Built-in neural networks expose the quantized_module member, while a QuantizedModule is also the result of the compilation of custom models through compile_torch_model and compile_brevitas_qat_model.

Resources

The section gave an overview of the conversion of a generic ONNX graph to a FHE compatible Concrete-ML op-graph. This section describes the implementation of operations in the Concrete-ML op-graph and the way floating point can be used in some parts of the op-graphs through table lookup operations.

Float vs. quantized operations

Concrete, the underlying implementation of TFHE that powers Concrete-ML, enables two types of operations on integers:

• arithmetic operations: the addition of two encrypted values and multiplication of encrypted values with clear scalars. These are used, for example, in dot-products, matrix multiplication (linear layers) and convolution.

• table lookup operations (TLU): using an encrypted value as an index, return the value of a lookup table at that index. This is implemented using Programmable Bootstrapping. This operation is used to perform any non-linear computation such as activation functions, quantization and normalization.

Since machine learning models use floating point inputs and weights, they first need to be converted to integers using .

Alternatively, it is possible to use a table lookup to avoid the quantization of the entire graph, by converting floating-point ONNX subgraphs into lambdas and computing their corresponding lookup tables to be evaluated directly in FHE. This operator-fusion technique only requires the input and output of the lambdas to be integers.

For example, in the following graph there is a single input, which must be an encrypted integer tensor. The following series of univariate functions is then fed into a matrix multiplication (MatMul) and fused into a single table lookup with integer inputs and outputs.

ONNX operations

Concrete-ML implements ONNX operations using Concrete-Numpy, which can handle floating point operations, as long as they can be fused to an integer lookup table. The ONNX operations implementations are based on the QuantizedOp class.

There are two modes of creation of a single table lookup for a chain of ONNX operations:

• float mode: when the operation can be fused

• mixed float/integer: when the ONNX operation needs to perform arithmetic operations

Thus, QuantizedOp instances may need to quantize their inputs or the result of their computation, depending on their position in the graph.

The QuantizedOp class provides a generic implementation of an ONNX operation, including the quantization of inputs and outputs, with the computation implemented in NumPy in ops_impl.py. It is possible to picture at the architecture of the QuantizedOp as the following structure:

Operations that can fuse to a TLU

Depending on the position of the op in the graph and its inputs, the QuantizedOp can be fully fused to a TLU.

Many ONNX ops are trivially univariate, as they multiply variable inputs with constants or apply univariate functions such as ReLU, Sigmoid, etc. This includes operations between the input and the MatMul in the graph above (subtraction, comparison, multiplication, etc. between inputs and constants).

Operations that work on integers

Operations, such as matrix multiplication of encrypted inputs with a constant matrix or convolution with constant weights, require that the encrypted inputs be integers. In this case, the input quantizer of the QuantizedOp is applied. These types of operations are implemented with a class that derives from QuantizedOp and implements q_impl, such as QuantizedGemm and QuantizedConv.