Example usage

from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from concrete.ml.sklearn import LogisticRegression

# Lets create a synthetic data-set
x, y = make_classification(n_samples=100, class_sep=2, n_features=30, 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
)

# Now we train in the clear and quantize the weights
model = LogisticRegression(n_bits=8)
model.fit(X_train, y_train)

# We can simulate the predictions in the clear
y_pred_clear = model.predict(X_test)

# We then compile on a representative set
model.compile(X_train)

# Finally we run the inference on encrypted inputs
y_pred_fhe = model.predict(X_test, fhe="execute")

print(f"In clear  : {y_pred_clear}")
print(f"In FHE    : {y_pred_fhe}")
print(f"Similarity: {(y_pred_fhe == y_pred_clear).mean():.1%}")

# Output:
    # In clear  : [0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 0]
    # In FHE    : [0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 0]
    # Similarity: 100.0%

It is also possible to call encryption, model prediction, and decryption functions separately as follows. Executing these steps separately is equivalent to calling predict_proba on the model instance.

# Predict probability for a single example
y_proba_fhe = model.predict_proba(X_test[[0]], fhe="execute")

# Quantize an original float input
q_input = model.quantize_input(X_test[[0]])

# Encrypt the input
q_input_enc = model.fhe_circuit.encrypt(q_input)

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

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

# De-quantize and post-process the result
y0 = model.post_processing(model.dequantize_output(q_y))

print("Probability with `predict_proba`: ", y_proba_fhe)
print("Probability with encrypt/run/decrypt calls: ", y0)

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 an FHE equivalent. Under the hood, the model is first converted to a Concrete Python 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 16-bit integers). Thus, machine learning models must be quantized, which sometimes leads to a loss of accuracy versus the original model, which operates on plaintext.

Additionally, Concrete ML currently only supports FHE inference. Training has to be done on unencrypted data, producing a model which is then converted to an FHE equivalent that can perform encrypted inference (i.e., prediction over encrypted data).

Finally, there is currently no support for pre-processing model inputs and 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.

These issues are currently being addressed, and significant improvements are expected to be released in the coming months.

Concrete stack

Online demos and tutorials

If you have built awesome projects using Concrete ML, feel free to let us know and we'll link to your work!

Additional resources

Support

This section lists several demos that apply Concrete ML to some popular machine learning problems. They show how to build ML models that perform well under FHE constraints, and then how to perform the conversion to FHE.

Concrete ML is built on top of Concrete, 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.

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.

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 set of keys: a private key (to encrypt/decrypt their data and results) and a public evaluation key (for the model's FHE evaluation on the server).

Cryptography concepts

Concrete ML and Concrete 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 receives the decryption key.

3. 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 used by a client.

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

5. public evaluation key: A public evaluation key is used to perform homomorphic operations on encrypted data, typically by a server.

6. guaranteed correctness of encrypted computations: To achieve security, TFHE, the underlying encryption scheme, adds random noise to 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 there is no need to account for noise parametrization. Therefore, the 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 that include non-linear operations over encrypted data must have all inputs, constants, and intermediate values represented with integers of a maximum of 16 bits.

Example

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 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 is done in clear (client machine)
# while the model inference is 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}")

# In the output, the Test accuracy in clear should be > 0.9

# 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], fhe="execute")

# 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 an FHE inference equal to the clear inference.")

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

Quantization parameters

This graph above shows that, when using a sufficiently high bit-width, quantization has little impact on the decision boundaries of the Concrete ML FHE decision tree models. As quantization is done individually on each input feature, the impact of quantization is strongly reduced. This means that FHE tree-based models reach a similar level of accuracy as their floating point equivalents. Using 6 bits for quantization means that the Concrete ML model reaches, or exceeds, the floating point accuracy. The number of bits for quantization can be adjusted through the n_bits parameter.

When n_bits is set to a low value, the quantization process may sometimes create some artifacts that could lead to a decrease in accuracy. At the same time, the execution speed in FHE could improve. In this way, it is possible to adjust the accuracy/speed trade-off, and some accuracy can be recovered by increasing the n_estimators parameter.

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.

FHE Inference time considerations

The inference time in FHE is strongly dependant on the maximum circuit bit-width. For trees, in most cases, the quantization bit-width will be the same as the circuit bit-width. Therefore, reducing the quantization bit-width to 4 or less will result in fast inference times. Adding more bits will increase FHE inference time exponentially.

In some rare cases, the bit-width of the circuit can be higher than the quantization bit-width. This could happen when the quantization bit-width is low but the tree-depth is high. In such cases, the circuit bit-width is upper bounded by ceil(log2(max_depth + 1) + 1).

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

Only some versions of python are supported: In the current release, these are 3.8, 3.9 and 3.10. The Concrete ML Python package requires glibc >= 2.28. On Linux, you can check your glibc version by running ldd --version.

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

Using PyPi

Requirements

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:

pip install -U pip wheel setuptools
pip install concrete-ml

This will automatically install all dependencies, notably Concrete.

Using Docker

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

docker pull zamafhe/concrete-ml:latest
# or
docker pull zamafhe/concrete-ml:v0.4.0

The image can then be used via the following command:

# Without local volume:
docker run --rm -it -p 8888:8888 zamafhe/concrete-ml

# With local volume to save notebooks on host:
docker run --rm -it -p 8888:8888 -v /host/path:/data zamafhe/concrete-ml

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:

docker run --rm -it zamafhe/concrete-ml /bin/bash

Concrete ML fully supports Pandas, allowing built-in models such as linear and tree-based models to use Pandas dataframes and series just as they would be used with NumPy arrays.

The table below summarizes current compatibility:

Example

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=250,
    n_features=30,
    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=8)

# 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)

# Perform the inference in FHE
y_pred_fhe = model.predict(X_test, fhe="execute")

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

# Output:
    # 100 examples over 100 have an FHE inference equal to the clear inference.

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

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:

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 receives 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 simple built-in neural networks models with a scikit-learn interface through the NeuralNetClassifier and NeuralNetRegressor classes.

Concrete ML models are multi-layer, fully-connected, networks with customizable activation functions and have a number of neurons in each layer. This approach is similar to what is available in scikit-learn when using the MLPClassifier/MLPRegressor classes. The built-in models train easily with a single call to .fit(), which will automatically quantize weights and activations. These models use Quantization Aware Training, allowing good performance for low precision (down to 2-3 bits) weights and activations.

Example usage

To create an instance of a Fully Connected Neural Network (FCNN), 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. The parameters related to the model (i.e., the underlying nn.Module), must have the prefix. The parameters related to training options do not require the prefix.

The figure above right shows the Concrete ML neural network, trained with Quantization Aware Training in an 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

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

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_accum_bits parameter influences training accuracy as it controls the number of non-zero neurons that are allowed in each layer. Increasing n_accum_bits improves accuracy, but should take into account precision limitations to avoid an overflow in the accumulator. The default value is a good compromise that avoids an 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.

Furthermore, the number of neurons on intermediate layers is controlled through the n_hidden_neurons_multiplier parameter - a value of 1 will make intermediate layers have the same number of neurons as the number of dimensions of the input data.

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

Quantization parameters

The n_bits parameter controls the bit-width of the inputs and weights of the linear models. When non-linear mapping is applied by the model, such as exp or sigmoid, Concrete ML applies it on the client-side, on clear-text values that are the decrypted output of the linear part of the model. Thus, Linear Models do not use table lookups, and can, therefore, use high precision integers for weight and inputs.

The n_bits parameter can be set to 8 or more bits for models with up to 300 input dimensions. When the input has more dimensions, n_bits must be reduced to 6-7. All performance metrics are preserved down to n_bits=6, compared to the non-quantized float models from scikit-learn.

Example

The overall accuracy scores are identical (93%) between the scikit-learn model (executed in the clear) and the Concrete ML one (executed in FHE). In fact, quantization has little impact on the decision boundaries, as linear models are able to consider large precision numbers when quantizing inputs and weights in Concrete ML. Additionally, as the linear models do not use PBS, the FHE computations are always exact. This means that the FHE predictions are always identical to the quantized clear ones.

Loading a pre-trained model

An alternative to the example above is to train a scikit-learn model in a separate step and then to convert it to Concrete ML.

Concrete ML offers nearest neighbors non-parametric classification models with a scikit-learn interface through the KNeighborsClassifier class.

Example usage

The predict method of the KNeighborsClassifier performs the following steps:

• quantization of the test vectors, performed in the clear

• computation of the top-k class indices of the closest training set vector, on encrypted data

• majority vote of the top-k class labels to find the class for each test vector, performed in the clear

Inference time considerations

The FHE inference latency of this model is heavily influenced by the n_bits, the dimensionality of the data. Furthermore, the size of the data-set has a linear impact on the complexity of the data and the number of nearest neighbors, n_neighbors, also plays a role.

FHE constraints

In Concrete ML, built-in linear models are exact equivalents to their scikit-learn counterparts. As they do not apply any non-linearity during inference, these models are very fast (~1ms FHE inference time) and can use high-precision integers (between 20-25 bits).

Tree-based models apply non-linear functions that enable comparisons of inputs and trained thresholds. Thus, they are limited with respect to the number of bits used to represent the inputs. But as these examples show, in practice 5-6 bits are sufficient to exactly reproduce the behavior of their scikit-learn counterpart models.

In the examples below, built-in neural networks can be configured to work with user-specified accumulator sizes, which allow the user to adjust the speed/accuracy trade-off.

List of examples

1. Linear models

These examples show how to use the built-in linear models on synthetic data, which allows for easy visualization of the decision boundaries or trend lines. Executing these 1D and 2D models in FHE takes around 1 millisecond.

2. Generalized linear models

3. Decision tree

4. XGBoost and Random Forest classifier

5. XGBoost regression

6. Fully connected neural network

7. Comparison of models

Based on three different synthetic data-sets, all the built-in classifiers are demonstrated in this notebook, showing accuracies, inference times, accumulator bit-widths, and decision boundaries.

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.

Quantization Aware Training

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

• Concat

• Constant

• ConstantOfShape

• Conv

• Cos

• Cosh

• Div

• Elu

• Equal

• Erf

• Exp

• Flatten

• Floor

• Gather

• Gemm

• Greater

• GreaterOrEqual

• HardSigmoid

• HardSwish

• Identity

• LeakyRelu

• Less

• LessOrEqual

• Log

• MatMul

• Max

• MaxPool

• Min

• Mul

• Neg

• Not

• Or

• PRelu

• Pad

• Pow

• ReduceSum

• Relu

• Reshape

• Round

• Selu

• Shape

• Sigmoid

• Sign

• Sin

• Sinh

• Slice

• Softplus

• Squeeze

• Sub

• Tan

• Tanh

• ThresholdedRelu

• Transpose

• Unsqueeze

• Where

• onnx.brevitas.Quant

This guide provides a complete example of converting a PyTorch neural network into its FHE-friendly, quantized counterpart. It focuses on Quantization Aware Training a simple network on a synthetic data-set.

In general, quantization can be carried out in two different ways: either during Quantization Aware Training (QAT) or after the training phase with Post-Training Quantization (PTQ).

Baseline PyTorch model

In PyTorch, using standard layers, a fully connected neural network (FCNN) would look like this:

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 is measured as the mean over 10 runs of the experiment. An accumulator of 6.6 means that 4 times out of 10 the accumulator measured was 6 bits while 6 times it was 7 bits.

This shows that the fp32 accuracy and accumulator size increases with the number of hidden neurons, while the 3-bits accuracy remains low irrespective of the number of neurons. While all the configurations tried here were FHE-compatible (accumulator < 16 bits), it is often preferable to have a lower accumulator size in order to speed up inference time.

Quantization Aware Training:

Brevitas provides a quantized version of almost all PyTorch layers (Linear layer becomes QuantLinear, ReLU layer becomes QuantReLU and so on), plus some extra quantization parameters, such as :

• bit_width: precision quantization bits for activations

• act_quant: quantization protocol for the activations

• weight_bit_width: precision quantization bits for weights

• weight_quant: quantization protocol for the weights

In order to use FHE, the network must be quantized from end to end, and thanks to the Brevitas's QuantIdentity layer, it is possible to quantize the input by placing it at the entry point of the network. Moreover, it is also possible to combine PyTorch and Brevitas layers, provided that a QuantIdentity is placed after this PyTorch layer. The following table gives the replacements to be made to convert a PyTorch NN for Concrete ML compatibility.

Some PyTorch operators (from the PyTorch functional API), require a brevitas.quant.QuantIdentity to be applied on their inputs.

With Brevitas, the network above becomes:

Training this network with pruning (see below) with 30 out of 100 total non-zero neurons gives good accuracy while keeping the accumulator size low.

Pruning using Torch

Considering that FHE only works with limited integer precision, there is a risk of overflowing in the accumulator, which will make Concrete ML raise an error.

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

Results with PrunedQuantNet, a pruned version of the QuantSimpleNet with 100 neurons on the hidden layers, are given below, showing a mean accumulator size measured over 10 runs of the experiment:

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.

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.

Configuring quantization parameters

The PyTorch/Brevitas models, created following the example above, require the user to configure quantization parameters such as bit_width (activation bit-width) and weight_bit_width. The quantization parameters, along with the number of neurons on each layer, will determine the accumulator bit-width of the network. Larger accumulator bit-widths result in higher accuracy but slower FHE inference time.

The following configurations were determined through experimentation for convolutional and dense layers.

Using the templates above, the probability of obtaining the target accumulator bit-width, for a single layer, was determined experimentally by training 10 models for each of the following data-sets.

Note that the accuracy on larger data-sets, when the accumulator size is low, is also reduced strongly.

Running encrypted inference

The model can now perform encrypted inference.

In this example, the input values x_test and the predicted values y_pred are floating points. The quantization (resp. de-quantization) step is done in the clear within the forward method, before (resp. after) any FHE computations.

Simulated FHE Inference in the clear

The user can also perform the inference on clear data. Two approaches exist:

• quantized_module.forward(quantized_x, fhe="simulate"): simulates FHE execution taking into account Table Lookup errors. De-quantization must be done in a second step as for actual FHE execution. Simulation takes into account the p_error/global_p_error parameters

• quantized_module.forward(quantized_x, fhe="disable"): computes predictions in the clear on quantized data, and then de-quantize the result. The return value of this function contains the de-quantized (float) output of running the model in the clear. Calling this function on clear data is useful when debugging, but this does not perform actual FHE simulation.

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 in PyTorch or through ONNX. 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.

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

shape modifying operators

operators that take an encrypted input and unencrypted constants

Concrete ML supports these operators but also the QAT equivalents from Brevitas.

• brevitas.nn.QuantLinear

• brevitas.nn.QuantConv2d

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

Quantizers

• brevitas.nn.QuantIdentity

Activations

FHE constraints considerations

Some examples constrain accumulators to 7-8 bits, which can be sufficient for simple data-sets. Up to 16-bit accumulators can be used, but this introduces a slowdown of 4-5x compared to 8-bit accumulators.

List of Examples

1. Step-by-step guide to building a custom NN

This shows how to use Quantization Aware Training and pruning when starting out from a classical PyTorch network. This example uses a simple data-set and a small NN, which achieves good accuracy with low accumulator size.

Concrete ML has APIs that make it easy, during model development and testing, to perform encryption, execution in FHE, and decryption in a single step. For more control, these individual steps can be executed separately. The APIs used to accomplish this are different for:

Built-in models

The following example shows how to create a synthetic data-set and how to use it to train a LogisticRegression model from Concrete ML. Next, we will discuss the dedicated functions for encryption, inference, and decryption.

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)

All Concrete ML built-in models have a monolithic predict method that performs the encryption, FHE execution, and decryption with a single function call. Concrete ML models follow the same API as scikit-learn models, transparently performing the steps related to encryption for convenience.

# 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.

Alternatively, it is possible to execute all main steps (key generation, quantization, encryption, FHE execution, decryption) separately.

# 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 illustrated as:

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.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.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)

Neural networks pose unique challenges with regards to encrypted inference. Each neuron in a network applies an activation function that requires a PBS operation. The latency of a single PBS depends on the bit-width of the input of the PBS.

Several approaches can be used to reduce the overall latency of a neural network.

Circuit bit-width optimization

Structured pruning

Rounded activations and quantizers

TLU error probability adjustment

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 diagram above shows the steps that a developer goes through to prepare a model for encrypted inference in a client/server setting. 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.zip contains client.specs.json which lists the secure cryptographic parameters needed for the client to generate private and evaluation keys. It also contains serialized_processing.json which describes the pre-processing and post-processing required by the machine learning model, such as quantization parameters to quantize the input and de-quantize the output.

• server.zip contains the compiled model. This file is sufficient to run the model on a server. The compiled model is machine-architecture specific (i.e., a model compiled on x86 cannot run on ARM).

The compiled model (server.zip) is deployed to a server and the cryptographic parameters (client.zip) are shared with the clients. In some settings, such as a phone application, the client.zip can be directly deployed on the client device and the server does not need to host it.

Note that for built-in models, the server output + post-processing adheres to the following guidelines: if the model is a regressor, the output follows the format of the scikit-learn .predict() method; if the model is a classifier, the output follows the format of the scikit-learn .predict_proba() method.

Serving

The client-side deployment of a secured inference machine learning model follows the schema above. First, the client obtains the cryptographic parameters (stored in 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 by the client as described in the serialized_processing.json file in client.zip, and it is then sent to the server. Server-side, the FHE model inference is run on 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 as specified in serialized_processing.json (part of client.zip).

The server-side implementation of a Concrete ML model follows the diagram above. The public evaluation keys sent by clients are stored. They are then retrieved for the client that is querying the service and used to evaluate the machine learning model stored in server.zip. Finally, the server sends the encrypted result of the computation back to the client.

Example notebook

AWS

Once this first setup is done you can launch python src/concrete/ml/deployment/deploy_to_aws.py --path-to-model <path_to_your_serialized_model> from the root of the repository to create an instance that runs a FastAPI server serving the model.

Docker

Running Docker with the latest version of Concrete ML will require you to build a Docker image. To do this, run the following command: poetry build && mkdir pkg && cp dist/* pkg/ && make release_docker. You will need to have make, poetry and docker installed on your system. To test locally there is a dedicated script: python src/concrete/ml/deployment/deploy_to_docker.py --path-to-model <path_to_your_serialized_model> whoch should be run from the root of the repository in order to create a Docker that runs a FastAPI server serving the model.

FHE enables cloud applications to process private user data without running the risk of data leaks. Furthermore, deploying ML models in the cloud is advantageous as it eases model updates, allows to scale to large numbers of users by using large amounts of compute power, and protects model IP by keeping the model on a trusted server instead of the client device.

However, not all applications can be easily converted to FHE computation and the computation cost of FHE may make a full conversion exceed latency requirements.

Hybrid models provide a balance between on-device deployment and cloud-based deployment. This approach entails executing parts of the model directly on the client side, while other parts are securely processed with FHE on the server side. Concrete ML facilitates the hybrid deployment of various neural network models, including MLP (multilayer perceptron), CNN (convolutional neural network), and Large Language Models.

Compilation

To use hybrid model deployment, the first step is to define what part of the PyTorch neural network model must be executed in FHE. The model part must be a nn.Module and is identified by its key in the original model's .named_modules().

import numpy as np
import os
import torch

from pathlib import Path
from torch import nn

from concrete.ml.torch.hybrid_model import HybridFHEModel, tuple_to_underscore_str
from concrete.ml.deployment import FHEModelServer


class FCSmall(nn.Module):
    """Torch model for the tests."""

    def __init__(self, dim):
        super().__init__()
        self.seq = nn.Sequential(nn.Linear(dim, dim), nn.ReLU(), nn.Linear(dim, dim))

    def forward(self, x):
        return self.seq(x)

model = FCSmall(10)
model_name = "FCSmall"
submodule_name = "seq.0"

inputs = torch.Tensor(np.random.uniform(size=(10, 10)))
# Prints ['', 'seq', 'seq.0', 'seq.1', 'seq.2']
print([k for (k, _) in model.named_modules()])

# Create a hybrid model
hybrid_model = HybridFHEModel(model, [submodule_name])
hybrid_model.compile_model(
    inputs,
    n_bits=8,
)


models_dir = Path(os.path.abspath('')) / "compiled_models"
models_dir.mkdir(exist_ok=True)
model_dir = models_dir / model_name

hybrid_model.save_and_clear_private_info(model_dir, via_mlir=True)

Server Side Deployment

input_shape_subdir = tuple_to_underscore_str( (1,) + inputs.shape[1:] )
MODULES = { model_name: { submodule_name: {"path":  model_dir / submodule_name / input_shape_subdir }}}
server =  FHEModelServer(str(MODULES[model_name][submodule_name]["path"]))

Client Side

A client application that deploys a model with hybrid deployment can be developed in a very similar manner to on-premise deployment: the model is loaded normally with PyTorch, but an extra step is required to specify the remote endpoint and the model parts that are to be executed remotely.

# Modify model to use remote FHE server instead of local weights
hybrid_model = HybridFHEModel(
    model,
    submodule_name,
    server_remote_address="http://0.0.0.0:8000",
    model_name=f"{model_name}",
    verbose=False,
)

path_to_clients = Path(__file__).parent / "clients"
hybrid_model.init_client(path_to_clients=path_to_clients)

When the client application is ready to make inference requests to the server, it must set the operation mode of the HybridFHEModel instance to HybridFHEMode.REMOTE:

for module in hybrid_model.remote_modules.values():
    module.fhe_local_mode = HybridFHEMode.REMOTE    

When performing inference with the HybridFHEModel instance, hybrid_model, only the regular forward method is called, as if the model was fully deployed locally:

hybrid_model.forward(torch.randn((dim, )))

When calling forward, the HybridFHEModel handles, for each model part that is deployed remotely, all the necessary intermediate steps: quantizing the data, encrypting it, makes the request to the server using requests Python module, decrypting and de-quantizing the result.

This section provides a set of tools and guidelines to help users build optimized FHE-compatible models. It discusses FHE simulation, the key-cache functionality that helps speed-up FHE result debugging, and gives a guide to evaluate circuit complexity.

Simulation

The simulation mode can be useful when developing and iterating on an ML model implementation. As FHE non-linear models work with integers up to 16 bits, with a trade-off between the number of bits and the FHE execution speed, the simulation can help to find the optimal model design.

The following example shows how to use the simulation mode in Concrete ML.

from sklearn.datasets import fetch_openml, make_circles
from concrete.ml.sklearn import RandomForestClassifier

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)

# Running the model using FHE-simulation
y_preds_clear = concrete_clf.predict(X, fhe="simulate")

Caching keys during debugging

It is possible to avoid re-generating the keys of the models you are debugging. This feature is unsafe and should not be used in production. Here is an example that shows how to enable key-caching:

from sklearn.datasets import fetch_openml, make_circles
from concrete.ml.sklearn import RandomForestClassifier
from concrete.fhe 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)

Compilation debugging

The following 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=7,
    )
except RuntimeError as err:
    print(err)

Upon execution, the Compiler will raise the following error within the graph representation:

Function you are trying to compile cannot be converted to MLIR:

%0 = _onnx__Gemm_0                    # EncryptedTensor<int7, shape=(1, 2)>        ∈ [-64, 63]
%1 = [[ 33 -27  ...   22 -29]]        # ClearTensor<int7, shape=(2, 120)>          ∈ [-63, 62]
%2 = matmul(%0, %1)                   # EncryptedTensor<int14, shape=(1, 120)>     ∈ [-4973, 4828]
%3 = subgraph(%2)                     # EncryptedTensor<uint7, shape=(1, 120)>     ∈ [0, 126]
%4 = [[ 16   6  ...   10  54]]        # ClearTensor<int7, shape=(120, 120)>        ∈ [-63, 63]
%5 = matmul(%3, %4)                   # EncryptedTensor<int17, shape=(1, 120)>     ∈ [-45632, 43208]
%6 = subgraph(%5)                     # EncryptedTensor<uint7, shape=(1, 120)>     ∈ [0, 126]
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ table lookups are only supported on circuits with up to 16-bit integers
%7 = [[ -7 -52] ... [-12  62]]        # ClearTensor<int7, shape=(120, 2)>          ∈ [-63, 62]
%8 = matmul(%6, %7)                   # EncryptedTensor<int16, shape=(1, 2)>       ∈ [-26971, 29843]
return %8

quantized_numpy_module = compile_torch_model(
    torch_model,
    torch_input,
    n_bits=7,
    use_virtual_lib=True
)

res = quantized_numpy_module.bitwidth_and_range_report()
print(res)

{
    '/fc1/Gemm': {'range': (-6180, 6840), 'bitwidth': 14}, 
    '/fc2/Gemm': {'range': (-45051, 43090), 'bitwidth': 17}, 
    '/fc3/Gemm': {'range': (-17351, 13868), 'bitwidth': 16}
}

To make this network FHE-compatible one can reduce the bit-width of the second layer named fc2. To do this, a simple solution is to reduce the number of neurons, as it is proportional to the bit-width.

Reducing the number of neurons in this layer resolves the error and makes the network FHE-compatible:

torch_model = SimpleNet(10)

quantized_numpy_module = compile_torch_model(
    torch_model,
    torch_input,
    n_bits=7,
)

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, compared to simpler encrypted operations such as 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:

print(quantized_numpy_module.fhe_circuit.mlir)

MLIR
--------------------------------------------------------------------------------
module {
  func.func @main(%arg0: tensor<1x2x!FHE.eint<15>>) -> tensor<1x2x!FHE.eint<15>> {
    %cst = arith.constant dense<16384> : tensor<1xi16>
    %0 = "FHELinalg.sub_eint_int"(%arg0, %cst) : (tensor<1x2x!FHE.eint<15>>, tensor<1xi16>) -> tensor<1x2x!FHE.eint<15>>
    %cst_0 = arith.constant dense<[[-13, 43], [-31, 63], [1, -44], [-61, 20], [31, 2]]> : tensor<5x2xi16>
    %cst_1 = arith.constant dense<[[-45, 57, 19, 50, -63], [32, 37, 2, 52, -60], [-41, 25, -1, 31, -26], [-51, -40, -53, 0, 4], [20, -25, 56, 54, -23]]> : tensor<5x5xi16>
    %cst_2 = arith.constant dense<[[-56, -50, 57, 37, -22], [14, -1, 57, -63, 3]]> : tensor<2x5xi16>
    %c16384_i16 = arith.constant 16384 : i16
    %1 = "FHELinalg.matmul_eint_int"(%0, %cst_2) : (tensor<1x2x!FHE.eint<15>>, tensor<2x5xi16>) -> tensor<1x5x!FHE.eint<15>>
    %cst_3 = tensor.from_elements %c16384_i16 : tensor<1xi16>
    %cst_4 = tensor.from_elements %c16384_i16 : tensor<1xi16>
    %2 = "FHELinalg.add_eint_int"(%1, %cst_4) : (tensor<1x5x!FHE.eint<15>>, tensor<1xi16>) -> tensor<1x5x!FHE.eint<15>>
    %cst_5 = arith.constant

: tensor<5x32768xi64>
    %cst_6 = arith.constant dense<[[0, 1, 2, 3, 4]]> : tensor<1x5xindex>
    %3 = "FHELinalg.apply_mapped_lookup_table"(%2, %cst_5, %cst_6) : (tensor<1x5x!FHE.eint<15>>, tensor<5x32768xi64>, tensor<1x5xindex>) -> tensor<1x5x!FHE.eint<15>>
    %4 = "FHELinalg.matmul_eint_int"(%3, %cst_1) : (tensor<1x5x!FHE.eint<15>>, tensor<5x5xi16>) -> tensor<1x5x!FHE.eint<15>>
    %5 = "FHELinalg.add_eint_int"(%4, %cst_3) : (tensor<1x5x!FHE.eint<15>>, tensor<1xi16>) -> tensor<1x5x!FHE.eint<15>>
    %cst_7 = arith.constant

: tensor<5x32768xi64>
    %6 = "FHELinalg.apply_mapped_lookup_table"(%5, %cst_7, %cst_6) : (tensor<1x5x!FHE.eint<15>>, tensor<5x32768xi64>, tensor<1x5xindex>) -> tensor<1x5x!FHE.eint<15>>
    %7 = "FHELinalg.matmul_eint_int"(%6, %cst_0) : (tensor<1x5x!FHE.eint<15>>, tensor<5x2xi16>) -> tensor<1x2x!FHE.eint<15>>
    return %7 : tensor<1x2x!FHE.eint<15>>

  }
}
--------------------------------------------------------------------------------

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.

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

print(quantized_numpy_module.fhe_circuit.graph.maximum_integer_bit_width())

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

Concrete ML has support for serializing all available built-in models. Using this feature, one can dump a fitted and compiled model into a JSON string or file. The estimator can then be loaded back using the JSON object.

Saving Models

All built-in models provide the following methods:

• dumps: dumps the model as a string.

• dump: dumps the model into a file.

For example, a logistic regression model can be dumped in a string as below.

Similarly, it can be dumped into a file.

Alternatively, Concrete ML provides two equivalent global functions.

Loading Models

Loading a built-in model is possible through the following functions:

• loads: loads the model from a string.

• load: loads the model from a file.

The above logistic regression model can therefore be loaded as below.

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). 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 16-bit integers, it is necessary to quantize models to make them compatible. As a general rule, the smaller the bit-width of integer values used in models, the better the FHE performance. This trade-off should be taken into account when designing models, especially neural networks.

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 used 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.

Basics of quantization

Quantization special cases

Machine learning acceleration solutions are often based on integer computation of activations. To make quantization computations hardware-friendly, a popular approach is to ensure that scales are powers-of-two, which allows the replacement of the division in the equations above with a shift-right operation. TFHE also has a fast primitive for right bit-shift that enables acceleration in the special case of power-of-two scales.

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 values, and output values.

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 numbers of bits by passing a dictionary to n_bits containing the op_inputs and op_weights keys.

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.

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

Alternatively, the forward method groups the quantization, FHE execution and de-quantization steps all together.

Resources

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:

Automatic installation

Manual installation

Python

Poetry

make

The dev tools use make to launch 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 favorite 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 speedup 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!

Overview of pruning in Concrete ML

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

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 inputs or to the neuron outputs of a previous layer.

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

Pruning in practice

Concrete ML provides features for advanced users to adjust cryptographic parameters generated by the Concrete stack. This allows users to identify the best trade-off between latency and performance for their specific machine learning models.

Approximate computations

Concrete ML makes use of table lookups (TLUs) to represent any non-linear operation (e.g., a sigmoid). TLUs are implemented through the Programmable Bootstrapping (PBS) operation, which applies a non-linear operation in the cryptographic realm.

The result of TLU operations is obtained with a specific error probability. Concrete ML offers the possibility to set this error probability, which influences the cryptographic parameters. The higher the success rate, the more restrictive the parameters become. This can affect both key generation and, more significantly, FHE execution time.

In Concrete ML, there are three different ways to define the error probability:

An error probability for an individual TLU

The first way to set error probabilities in Concrete ML is at the local level, by directly setting the probability of error of each individual TLU. This probability is referred to as p_error. A given PBS operation has a 1 - p_error chance of being successful. The successful evaluation here means that the value decrypted after FHE evaluation is exactly the same as the one that would be computed in the clear.

Here is a visualization of the effect of the p_error on a neural network model with a p_error = 0.1 compared to execution in the clear (i.e., no error):

Varying p_error in the one hidden-layer neural network above produces the following inference times. Increasing p_error to 0.1 halves the inference time with respect to a p_error of 0.001. In the graph above, the decision boundary becomes noisier with a higher p_error.

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

A global error probability for the entire model

A global_p_error is also available and defines the probability of success for the entire model. Here, the p_error for every PBS is computed internally in Concrete such that the global_p_error is reached.

There might be cases where the user encounters a No cryptography parameter found error message. Increasing the p_error or the global_p_error in this case might help.

Usage is similar to the p_error parameter:

In the above example, XGBoostClassifier in FHE has a 1/10 probability to have a shifted output value compared to the expected value. The shift is relative to the expected value, so even if the result is different, it should be around the expected value.

Using default error probability

If neither p_error or global_p_error are set, Concrete ML employs p_error = 2^-40 by default.

Searching for the best error probability

Currently finding a good p_error value a-priori is not possible, as it is difficult to determine the impact of the TLU error on the output of a neural network. Concrete ML provides a tool to find a good p_error value that improves inference speed while maintaining accuracy. The method is based on binary search and evaluates the latency/accuracy trade-off iteratively.

With this optimal p_error, accuracy is maintained while execution time is improved by a factor of 1.51.

Please note that the default setting for the search interval is restricted to a range of 0.0 to 0.9. Increasing the upper bound beyond this range may result in longer execution times, especially when p_error≈1.

Rounded activations and quantizers

The rounding operation is defined as follows:

Then, the rounding operation can be computed as:

In Concrete ML, this feature is currently implemented for custom neural networks through the compile functions, including

• concrete.ml.torch.compile_torch_model,

• concrete.ml.torch.compile_onnx_model and

• concrete.ml.torch.compile_brevitas_qat_model.

The rounding_threshold_bits argument can be set to a specific bit-width. It is important to choose an appropriate bit-width threshold to balance the trade-off between speed and accuracy. By reducing the bit-width of intermediate tensors, it is possible to speed-up computations while maintaining accuracy.

To find the best trade-off between speed and accuracy, it is recommended to experiment with different thresholds and check the accuracy on an evaluation set after compiling the model.

In practice, the process looks like this:

1. Set a rounding_threshold_bits to a relatively high P. Say, 8 bits.

2. Check the accuracy

3. Update P = P - 1

4. repeat steps 2 and 3 until the accuracy loss is above a certain, acceptable threshold.

Seeing compilation information

By using verbose = True and show_mlir = True during compilation, the user receives a lot of information from Concrete. These options are, however, mainly meant for power-users, so they may be hard to understand.

Here, one will see:

• the computation graph (typically):

• the MLIR, produced by Concrete:

• information from the optimizer (including cryptographic parameters):

In this latter optimization, the following information will be provided:

• The bit-width ("6-bit integers") used in the program: for the moment, the compiler only supports a single precision (i.e., that all PBS are promoted to the same bit-width - the largest one). Therefore, this bit-width predominantly drives the speed of the program, and it is essential to reduce it as much as possible for faster execution.

• The maximal norm2 ("7 manp"), which has an impact on the crypto parameters: The larger this norm2, the slower PBS will be. The norm2 is related to the norm of some constants appearing in your program, in a way which will be clarified in the Concrete documentation.

• The probability of error of an individual PBS, which was requested by the user ("3.300000e-02 error per pbs call" in User Config).

• The probability of error of the full circuit, which was requested by the user ("1.000000e+00 error per circuit call" in User Config). Here, the probability 1 stands for "not used", since we had set the individual probability via p_error.

• The probability of error of an individual PBS, which is found by the optimizer ("1/30 errors (3.234529e-02)").

• The probability of error of the full circuit which is found by the optimizer ("1/10 errors (9.390887e-02)").

• An estimation of the cost of the circuit ("4.214000e+02 Millions Operations"): Large values indicate a circuit that will execute more slowly.

Here is some further information about cryptographic parameters:

• 1x glwe_dimension

• 2**11 polynomial (2048)

• 762 lwe dimension

• keyswitch l,b=5,3

• blindrota l,b=2,15

• wopPbs : false

This optimizer feedback is a work in progress and will be modified and improved in future releases.