In addition to the built-in models, Concrete ML supports generic machine learning models implemented with Torch, or exported as ONNX graphs.
As Quantization Aware Training (QAT) is the most appropriate method of training neural networks that are compatible with FHE constraints, Concrete ML works with Brevitas, a library providing QAT support for PyTorch.
The following example uses a simple QAT PyTorch model that implements a fully connected neural network with two hidden layers. Due to its small size, making this model respect FHE constraints is relatively easy.
Once the model is trained, calling the compile_brevitas_qat_model from Concrete ML will automatically perform conversion and compilation of a QAT network. Here, 3-bit quantization is used for both the weights and activations. The compile_brevitas_qat_model function automatically identifies the number of quantization bits used in the Brevitas model.
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.
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.
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.
FHE simulation allows to measure the impact of the Table Lookup error on the model accuracy. The Table Lookup error can be adjusted using p_error/global_p_error, as described in the approximate computation section.
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.
Suppose that n_bits_qat is the bit-width of activations and weights during the QAT process. To import a PyTorch QAT network, you can use the compile_torch_model library function, passing import_qat=True:
Alternatively, if you want to import an ONNX model directly, please see the ONNX guide. The compile_onnx_model also supports the import_qat parameter.
When importing QAT models using this generic pipeline, a representative calibration set should be given as quantization parameters in the model need to be inferred from the statistics of the values encountered during inference.
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.
Concrete ML supports these operators but also the QAT equivalents from Brevitas.
brevitas.nn.QuantLinear
brevitas.nn.QuantConv2d
brevitas.nn.QuantIdentity
torch.nn.Threshold -- partial support
The equivalent versions from torch.functional are also supported.
| target accumulator bit-width | activation bit-width | weight bit-width | number of active neurons |
|---|---|---|---|
8
3
3
80
10
4
3
90
12
5
5
110
14
6
6
110
16
7
6
120
probability of obtaining the accumulator bit-width
8
10
12
14
16
mnist,fashion
72%
100%
72%
85%
100%
cifar10
88%
88%
75%
75%
88%
cifar100
73%
88%
61%
66%
100%
accuracy for target accumulator bit-width
8
10
12
14
16
cifar10
20%
37%
89%
90%
90%
cifar100
6%
30%
67%
69%
69%