concrete.ml.search_parameters.p_error_search.md

module concrete.ml.search_parameters.p_error_search

p_error binary search for classification and regression tasks.

Only PyTorch neural networks and Concrete built-in models are supported.

• Concrete built-in models include trees and QNN

• Quantized aware trained model are supported using Brevitas framework

• Torch models can be converted into post-trained quantized models

The p_error represents an essential hyper-parameter in the FHE computation at Zama. As it impacts the speed of the FHE computations and the model's performance.

In this script, we provide an approach to find out an optimal p_error, which would offer an interesting compromise between speed and efficiency.

The p_error represents the probability of a single PBS being incorrect. Know that the FHE scheme allows to perform 2 types of operations

• Linear operations: additions and multiplications

• Non-linear operation: uni-variate activation functions

At Zama, non-linear operations are represented by table lookup (TLU), which are implemented through the Programmable Bootstrapping technology (PBS). A single PBS operation has p_error chances of being incorrect.

It's highly recommended to adjust the p_error as it is linked to the data-set.

The inference is performed via the FHE simulation mode.

The goal is to look for the largest p_error_i, a float ∈ ]0,0.9[, which gives a model_i that has accuracy_i, such that: | accuracy_i - accuracy_0| <= Threshold, where: Threshold ∈ R, given by the user and accuracy_0 refers to original model_0 with p_error_0 ≈ 0.0.

p_error is bounded between 0 and 0.9 p_error ≈ 0.0, refers to the original model in clear, that gives an accuracy that we note as accuracy_0.

We assume that the condition is satisfied when we have a match A match is defined as a uni-variate function, through strategy argument, given by the user, it can be

any = lambda all_matches: any(all_matches) all = lambda all_matches: all(all_matches) mean = lambda all_matches: numpy.mean(all_matches) >= 0.5 median = lambda all_matches: numpy.median(all_matches) == 1

To validate the results of the FHE simulation and get a stable estimation, we do several simulations If match, we update the lower bound to be the current p_error Else, we update the upper bound to be the current p_error Update the current p_error with the mean of the bounds

We stop the search when the maximum number of iterations is reached.

If we don't reach the convergence, a user warning is raised.

---

function compile_and_simulated_fhe_inference

compile_and_simulated_fhe_inference(
    estimator: Module,
    calibration_data: ndarray,
    ground_truth: ndarray,
    p_error: float,
    n_bits: int,
    is_qat: bool,
    metric: Callable,
    predict: str,
    **kwargs: Dict
) → Tuple[ndarray, float]

Get the quantized module of a given model in FHE, simulated or not.

Supported models are:

• Built-in models, including trees and QNN,

• Quantized aware trained model are supported using Brevitas framework,

• Torch models can be converted into post-trained quantized models.

Args:

• estimator (torch.nn.Module): Torch model or a built-in model

• calibration_data (numpy.ndarray): Calibration data required for compilation

• ground_truth (numpy.ndarray): The ground truth

• p_error (float): Concrete ML uses table lookup (TLU) to represent any non-linear

• n_bits (int): Quantization bits

• is_qat (bool): True, if the NN has been trained through QAT. If False it is converted into post-trained quantized model.

• metric (Callable): Classification or regression evaluation metric.

• predict (str): The predict method to use.

• kwargs (Dict): Hyper-parameters to use for the metric.

Returns:

• Tuple[numpy.ndarray, float]: De-quantized or quantized output model depending on is_benchmark_test and the score.

Raises:

• ValueError: If the model is neither a built-in model nor a torch neural network.

---

class BinarySearch

Class for p_error hyper-parameter search for classification and regression tasks.

method __init__

__init__(
    estimator,
    predict: str,
    metric: Callable,
    n_bits: int = 4,
    is_qat: bool = True,
    lower: float = 0.0,
    upper: float = 0.9,
    max_iter: int = 20,
    n_simulation: int = 5,
    strategy: Any = <built-in function all>,
    max_metric_loss: float = 0.01,
    save: bool = False,
    log_file: str = None,
    directory: str = None,
    verbose: bool = False,
    **kwargs: dict
)

p_error binary search algorithm.

Args:

• estimator : Custom model (Brevitas or PyTorch) or built-in models (trees or QNNs).

• predict (str): The prediction method to use for built-in tree models.

• metric (Callable): Evaluation metric for classification or regression tasks.

• n_bits (int): Quantization bits, for PTQ models. Default is 4.

• is_qat (bool): Flag that indicates whether the estimator has been trained through QAT (quantization-aware training). Default is True.

• lower (float): The lower bound of the search space for the p_error. Default is 0.0.

• upper (float): The upper bound of the search space for the p_error. Default is 0.9. Increasing the upper bound beyond this range may result in longer execution times especially when p_error≈1.

• max_iter (int): The maximum number of iterations to run the binary search algorithm. Default is 20.

• n_simulation (int): The number of simulations to validate the results of the FHE simulation. Default is 5.

• strategy (Any): A uni-variate function that defines a "match". It can be built-in functions provided in Python, such as any() or all(), or custom functions, like:

• mean = lambda all_matches: numpy.mean(all_matches) >= 0.5

• median = lambda all_matches: numpy.median(all_matches) == 1 Default is 'all'.

• max_metric_loss (float): The threshold to use to satisfy the condition: | accuracy_i - accuracy_0| <= max_metric_loss. Default is 0.01.

• save (bool): Flag that indicates whether to save some meta data in log file. Default is False.

• log_file (str): The log file name. Default is None.

• directory (str): The directory to save the meta data. Default is None.

• verbose (bool): Flag that indicates whether to print detailed information. Default is False.

• kwargs: Parameter of the evaluation metric.

---

method eval_match

eval_match(strategy: Callable, all_matches: List[bool]) → Union[bool, bool_]

Eval the matches.

Args:

• strategy (Callable): A uni-variate function that defines a "match". It can be built-in functions provided in Python, such as any() or all(), or custom functions, like:

• mean = lambda all_matches: numpy.mean(all_matches) >= 0.5

• median = lambda all_matches: numpy.median(all_matches) == 1

• all_matches (List[bool]): List of matches.

Returns:

• bool: Evaluation of the matches according to the given strategy.

Raises:

• TypeError: If the strategy function is not valid.

---

method reset_history

reset_history() → None

Clean history.

---

method run

run(
    x: ndarray,
    ground_truth: ndarray,
    strategy: Callable = <built-in function all>,
    **kwargs: Dict
) → float

Get an optimal p_error using binary search for classification and regression tasks.

PyTorch models and built-in models are supported.

To find an optimal p_error that offers a balance between speed and efficiency, we use a binary search approach. Where the goal to look for the largest p_error_i, a float ∈ ]0,1[, which gives a model_i that has accuracy_i, such that | accuracy_i - accuracy_0| <= max_metric_loss, where max_metric_loss ∈ R and accuracy_0 refers to original model_0 with p_error ≈ 0.0.

We assume that the condition is satisfied when we have a match. A match is defined as a uni-variate function, specified through strategy argument.

To validate the results of the FHE simulation and get a stable estimation, we perform multiple samplings. If match, we update the lower bound to be the current p_error. Else, we update the upper bound to be the current p_error. Update the current p_error with the mean of the bounds.

We stop the search either when the maximum number of iterations is reached or when the update of the p_error is below at a given threshold.

Args:

• x (numpy.ndarray): Data-set which is used for calibration and evaluation

• ground_truth (numpy.ndarray): The ground truth

• kwargs (Dict): Class parameters

• strategy (Callable): A uni-variate function that defines a "match". It can be: a

• built-in functions provided in Python, like: any or all or a custom function, like:

• mean = lambda all_matches: numpy.mean(all_matches) >= 0.5

• median = lambda all_matches: numpy.median(all_matches) == 1 Default is all.

Returns:

• float: The optimal p_error that aims to speedup computations while maintaining good performance.