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. Moreover, the Concrete-ML Python package requires glibc >= 2.28. On Linux, you can check your glibc version by running ldd --version.

Concrete-ML can be installed on Kaggle (see question on community for more details), but not on Google Colab (see question on community for more details).

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 below).

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-Numpy.

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 be used with Docker volumes, see the Docker documentation here.

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

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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 linear models, tree-based models, and neural networks).

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 this introduction or by joining the FHE.org community.

Example usage

Here is a simple example of classification on encrypted data using logistic regression. More examples can be found here.

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, execute_in_fhe=True)

print("In clear  :", y_pred_clear)
print("In FHE    :", y_pred_fhe)
print(f"Similarity: {int((y_pred_fhe == y_pred_clear).mean()*100)}%")

# 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%

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.

• Inference can then be done on encrypted data. The above example shows encrypted inference in the model-development phase. Alternatively, during deployment in a client/server setting, the data is encrypted by the client, processed securely by the server, and then decrypted by the client.

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 are required to 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. 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 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

Concrete-ML is built on top of Zama's Concrete framework. It uses Concrete-Numpy, which itself uses the Concrete-Compiler and the Concrete-Library. To use these libraries directly, refer to the Concrete-Numpy and Concrete-Framework documentations.

Online demos and tutorials

Various tutorials are available for the built-in models and for deep learning. In addition, several standalone demos for use-cases can be found in the Demos and Tutorials section.

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

Additional resources

• Dedicated Concrete-ML community support

• Zama's blog

• FHE.org community

Looking for support? Ask our team!

• Support forum: https://community.zama.ai (we answer in less than 24 hours).

• Live discussion on the FHE.org Discord server: https://discord.fhe.org (inside the #concrete channel).

• Do you have a question about Zama? You can write us on Twitter or send us an email at: hello@zama.ai

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 concepts section, 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 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.

For more information on how to implement this basic secure inference protocol, refer to the Production Deployment section and to the client/server example.

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.

Simpler tutorials that discuss only model usage and compilation are also available for the built-in models and for deep learning.

Example

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 the quantization is done individually on each input feature, the impact of quantization is strongly reduced, and, thus, FHE tree-based models reach similar accuracy as their floating point equivalents. Using 6 bits for quantization makes the Concrete-ML model reach or exceed the floating point accuracy. The number of bits for quantization can be adjusted through the n_bits parameter.

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

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 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.

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 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).

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 receives 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 used by a client.

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 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.

In addition to Concrete-ML models and 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

• Concat

• Constant

• Conv

• Cos

• Cosh

• Div

• Elu

• Equal

• Erf

• Exp

• Flatten

• Floor

• 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

• Sigmoid

• Sign

• Sin

• Sinh

• Softplus

• Sub

• Tan

• Tanh

• ThresholdedRelu

• Transpose

• Unsqueeze

• Where

• onnx.brevitas.Quant

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.

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

and the encrypted inference can be 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, de-quantization 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.

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

Please note that 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

In Concrete-ML, built-in linear models are exact equivalents to their scikit-learn counterparts. Indeed, since 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.

As shown 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 tradeoff.

List of examples

1. Linear and logistic regression

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 classifiers

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.

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

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:

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

The Concrete-ML models are multi-layer, fully-connected networks with customizable activation functions and a number of neurons in each layer. This approach is similar to what is available in scikit-learn using the MLPClassifier/MLPRegressor classes. The built-in 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.

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. 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.

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

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.

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

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

1. tracing the Numpy program and creating a Concrete-Numpy op-graph

2. checking the op-graph for FHE compatability

3. producing machine code for the op-graph (this step automatically determines cryptographic parameters)

Simulation with the Virtual Library

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

• 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

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

Virtual Library

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 about ways it could be modified to compile it to an actual FHE Circuit. As FHE non-linear models work with integers up to 16 bits, with a tradeoff between number of bits and FHE execution speed, the Virtual Lib can help to find the optimal model design.

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.

Compilation debugging

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

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

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:

Input data:

First dense layer and activation function:

Second dense layer and activation function:

Third dense layer:

We can see here that the error is in the second layer because the product has exceeded the 16-bit precision limit. This error is only detected when the PBS operations are actually applied.

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

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 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:

Concrete-ML model

Compiled MLIR model

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:

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

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

The table below summarizes current compatibility:

Example

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, currently 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. Accuracy and R2 scores 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, meaning the FHE predictions are always identical to the quantized clear ones.

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 training with 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 would look as follows:

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 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 the 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 one), 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.

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

For instance, 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.