Concrete-ML offers some features for advanced users that wish to adjust the cryptographic parameters that are generated by the Concrete stack for a certain machine learning model.
Approximate computations
Probability of errors
Concrete-ML makes use of table lookups (TLUs) to represent any non-linear operation (e.g. sigmoid). TLUs are implemented through the Programmable Bootstrapping (PBS) operation which will apply 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:
setting p_error, the error probability of an individual TLU (see here)
setting global_p_error, the error probability of the full circuit (see here)
not setting p_error nor global_p_error, and using default parameters (see here)
p_error and global_p_error are somehow two concurrent parameters, in the sense they both have an impact on the choice of cryptographic parameters. To avoid a mistake, it is forbidden in Concrete-ML to set both p_error and global_p_errorsimultaneously.
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 one would compute in the clear.
For simplicity, it is best to use default options, irrespective of the type of model. However, especially for deep neural networks, default values may be too pessimistic, reducing computation speed without any improvement in accuracy. For deep neural networks, some TLU errors may not have any impact on accuracy and the p_error can be safely increased (see for example CIFAR classifications in our showcase).
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 the 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. Note, in the graph above, that the decision boundary becomes noisier with higher p_error.
The speedup is dependent on model complexity, but, in an iterative approach, it is possible to search for a good value of p_error to obtain a speedup while maintaining good accuracy. Currently, no heuristic has been proposed to find a good value a priori.
Users have the possibility to change this p_error as they see fit, by passing an argument to the compile function of any of the models. Here is an example:
from concrete.ml.sklearn import XGBClassifierfrom sklearn.datasets import make_classificationfrom sklearn.model_selection import train_test_splitx, y =make_classification(n_samples=100, class_sep=2, n_features=4, random_state=42)# Retrieve train and test setsX_train, _, y_train, _ =train_test_split(x, y, test_size=10, random_state=42)clf =XGBClassifier()clf.fit(X_train, y_train)# Here we set the p_error parameterclf.compile(X_train, p_error =0.1)
If the p_error value is specified and the Virtual Library is enabled, the run will take into account the randomness induced by the p_error, resulting in statistical similarity to the FHE evaluation.
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-Numpy such that the global_p_error is reached.
There might be cases where the user encounters a No cryptography parameter found error message. In such a case, increasing the p_error or the global_p_error might help.
Usage is similar to the p_error parameter:
# Here we set the global_p_error parameterclf.compile(X_train, global_p_error =0.1)
In the above example, XGBoostClassifier in FHE has a 1/10 probability to have a shifted output value compared to the expected value. Note that the shift is relative to the expected value, so even if the result is different, it should be around the expected value.
The global_p_error parameter is only used for FHE evaluation and has no effect on VL simulation (unlike the p_error). Fixing it is in our roadmap.
Using default error probability
If neither p_error or global_p_error are set, Concrete-ML takes a default global_p_error = 0.01.
Seeing compilation information
By using verbose_compilation = True and show_mlir = True during compilation, the user receives a lot of information from the compiler and its inner optimizer. These options are, however, mainly meant for power-users, so they may be hard to understand.
from concrete.ml.sklearn import DecisionTreeClassifierfrom sklearn.datasets import make_classificationfrom sklearn.model_selection import train_test_splitx, y =make_classification(n_samples=100, class_sep=2, n_features=4, random_state=42)# Retrieve train and test setsX_train, _, y_train, _ =train_test_split(x, y, test_size=10, random_state=42)clf =DecisionTreeClassifier(random_state=42)clf.fit(X_train, y_train)clf.compile(X_train, verbose_compilation=True, show_mlir=True, p_error=0.033)
information from the optimizer (including cryptographic parameters):
Optimizer
-------------------------------------------------------------------------------------------------------------------------------
--- Circuit
6 bits integers
7 manp (maxi log2 norm2)
388ms to solve
--- User config
3.300000e-02 error per pbs call
1.000000e+00 error per circuit call
--- Complexity for the full circuit
4.214000e+02 Millions Operations
--- Correctness for each Pbs call
1/30 errors (3.234529e-02)
--- Correctness for the full circuit
1/10 errors (9.390887e-02)
--- Parameters resolution
1x glwe_dimension
2**11 polynomial (2048)
762 lwe dimension
keyswitch l,b=5,3
blindrota l,b=2,15
wopPbs : false
---
In this latter optimization, the following information will be provided:
The bit-width ("6 bits 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 attempt to reduce it as much as possible for fast 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 compiler 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.
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.
and, for cryptographers only, some 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
Once again, this optimizer feedback is a work in progress and will be modified and improved in future releases.
