def faithfulness_estimate(
    forward_func: Callable,
    inputs: TensorOrTupleOfTensorsGeneric,
    attributions: list[TensorOrTupleOfTensorsGeneric] | TensorOrTupleOfTensorsGeneric,
    baselines: BaselineType = None,
    feature_mask: TensorOrTupleOfTensorsGeneric | None = None,
    additional_forward_args: Any = None,
    target: ExplanationTarget | list[ExplanationTarget] = NoTarget(),
    frozen_features: list[torch.Tensor] | None = None,
    max_features_processed_per_batch: int | None = None,
    percentage_feature_removal_per_step: float = 0.0,
    multi_target: bool = False,
    show_progress: bool = True,
    return_intermediate_results: bool = False,
    return_dict: bool = False,
) -> dict | tuple | torch.Tensor | list[torch.Tensor]:
    """
    Implementation of Faithfulness Estimate by Alvares-Melis at el., 2018a and 2018b. This implementation
    reuses the batch-computation ideas from captum and therefore it is fully compatible with the Captum library.
    In addition, the implementation takes some ideas about the implementation of the metric from the python
    Quantus library.

    Computes the correlations of probability drops and the relevance scores on various points,
    showing the aggregate statistics.

    References:
        1) David Alvarez-Melis and Tommi S. Jaakkola.: "Towards robust interpretability with self-explaining
        neural networks." NeurIPS (2018): 7786-7795.

    Args:
        forward_func (Callable):
                The forward function of the model or any modification of it.

        inputs (Tensor or tuple[Tensor, ...]): Input for which
                attributions are computed. If forward_func takes a single
                tensor as input, a single input tensor should be provided.
                If forward_func takes multiple tensors as input, a tuple
                of the input tensors should be provided. It is assumed
                that for all given input tensors, dimension 0 corresponds
                to the number of examples (aka batch size), and if
                multiple input tensors are provided, the examples must
                be aligned appropriately.

        baselines (scalar, Tensor, tuple of scalar, or Tensor):
                Baselines define reference values against which the completeness is measured which sometimes
                represent ablated values and are used to compare with the actual inputs to compute
                importance scores in attribution algorithms. They can be represented
                as:

                - a single tensor, if inputs is a single tensor, with
                  exactly the same dimensions as inputs or the first
                  dimension is one and the remaining dimensions match
                  with inputs.

                - a single scalar, if inputs is a single tensor, which will
                  be broadcasted for each input value in input tensor.

                - a tuple of tensors or scalars, the baseline corresponding
                  to each tensor in the inputs' tuple can be:

                - either a tensor with matching dimensions to
                  corresponding tensor in the inputs' tuple
                  or the first dimension is one and the remaining
                  dimensions match with the corresponding
                  input tensor.

                - or a scalar, corresponding to a tensor in the
                  inputs' tuple. This scalar value is broadcasted
                  for corresponding input tensor.

                Default: None

        attributions (Tensor or tuple[Tensor, ...]):
                Attribution scores computed based on an attribution algorithm.
                This attribution scores can be computed using the implementations
                provided in the `captum.attr` package. Some of those attribution
                approaches are so called global methods, which means that
                they factor in model inputs' multiplier, as described in:
                https://arxiv.org/abs/1711.06104
                Many global attribution algorithms can be used in local modes,
                meaning that the inputs multiplier isn't factored in the
                attribution scores.
                This can be done duing the definition of the attribution algorithm
                by passing `multipy_by_inputs=False` flag.
                For example in case of Integrated Gradients (IG) we can obtain
                local attribution scores if we define the constructor of IG as:
                ig = IntegratedGradients(multipy_by_inputs=False)

                Some attribution algorithms are inherently local.
                Examples of inherently local attribution methods include:
                Saliency, Guided GradCam, Guided Backprop and Deconvolution.

                For local attributions we can use real-valued perturbations
                whereas for global attributions that perturbation is binary.
                https://arxiv.org/abs/1901.09392

                If we want to compute the infidelity of global attributions we
                can use a binary perturbation matrix that will allow us to select
                a subset of features from `inputs` or `inputs - baselines` space.
                This will allow us to approximate sensitivity-n for a global
                attribution algorithm.

                Attributions have the same shape and dimensionality as the inputs.
                If inputs is a single tensor then the attributions is a single
                tensor as well. If inputs is provided as a tuple of tensors
                then attributions will be tuples of tensors as well.

        feature_mask (Tensor or tuple[Tensor, ...], optional):
                    feature_mask defines a mask for the input, grouping
                    features which should be perturbed together. feature_mask
                    should contain the same number of tensors as inputs.
                    Each tensor should
                    be the same size as the corresponding input or
                    broadcastable to match the input tensor. Each tensor
                    should contain integers in the range 0 to num_features
                    - 1, and indices corresponding to the same feature should
                    have the same value.
                    Note that features within each input tensor are perturbed
                    independently (not across tensors).
                    If the forward function returns a single scalar per batch,
                    we enforce that the first dimension of each mask must be 1,
                    since attributions are returned batch-wise rather than per
                    example, so the attributions must correspond to the
                    same features (indices) in each input example.
                    If None, then a feature mask is constructed which assigns
                    each scalar within a tensor as a separate feature, which
                    is perturbed independently.
                    Default: None

        additional_forward_args (Any, optional): If the forward function
                requires additional arguments other than the inputs for
                which attributions should not be computed, this argument
                can be provided. It must be either a single additional
                argument of a Tensor or arbitrary (non-tuple) type or a tuple
                containing multiple additional arguments including tensors
                or any arbitrary python types. These arguments are provided to
                forward_func in order, following the arguments in inputs.
                Note that the perturbations are not computed with respect
                to these arguments.

                Default: None
        target (int, tuple, Tensor, or list, optional): Indices for selecting
                predictions from output(for classification cases,
                this is usually the target class).
                If the network returns a scalar value per example, no target
                index is necessary.
                For general 2D outputsattributions_sum_perturbedrget for the corresponding example.

                  For outputs with > 2 dimensions, targets can be either:

                - A single tuple, which contains #output_dims - 1
                  elements. This target index is applied to all examples.

                - A list of tuples with length equal to the number of
                  examples in inputs (dim 0), and each tuple containing
                  #output_dims - 1 elements. Each tuple is applied as the
                  target for the corresponding example.

                Default: None
        max_features_processed_per_batch (int, optional): The number of maximum input
                features that are processed together for every example. In case the number of
                features to be perturbed in each example (`total_features_perturbed`) exceeds
                `max_features_processed_per_batch`, they will be sliced
                into batches of `max_features_processed_per_batch` examples and processed
                in a sequential order.
        frozen_features (List[torch.Tensor], optional): A list of frozen features that are not perturbed.
                This can be useful for ignoring the input structure features like padding, etc. Default: None
                In case CLS,PAD,SEP tokens are present in the input, they can be frozen by passing the indices
                of feature masks that correspond to these tokens.
        multi_target (bool, optional): A boolean flag that indicates whether the metric computation is for
                multi-target explanations. if set to true, the targets are required to be a list of integers
                each corresponding to a required target class in the output. The corresponding metric outputs
                are then returned as a list of metric outputs corresponding to each target class.
                Default is False.
        show_progress (bool, optional): Indicates whether to print the progress of the computation.
        return_intermediate_results (bool, optional): Indicates whether to return intermediate results
                of the computation. If set to True, the function will return the sum of attributions for each
                perturbation step and the forward difference between perturbed and unperturbed input for each
                perturbation step. Default is False.
        return_dict (bool, optional): Indicates whether to return the metric outputs as a dictionary
                with keys as the metric names and values as the corresponding metric outputs.
                Default is False.
    Returns:
        Returns:
            A tuple of three tensors:
            Tensor: - The faithfulness estimate scores of the batch. The first dimension is equal to the
                    number of examples in the input batch and the second dimension is 1.
            Tensor: - The sum of attributions for each perturbation step
                    of the batch.
            Tensor: - The forward difference between perturbed and unperturbed input for each perturbation step
                    of the batch.
    Examples::
        >>> # ImageClassifier takes a single input tensor of images Nx3x32x32,
        >>> # and returns an Nx10 tensor of class probabilities.
        >>> net = ImageClassifier()
        >>> saliency = Saliency(net)
        >>> input = torch.randn(2, 3, 32, 32, requires_grad=True)
        >>> baselines = torch.zeros(2, 3, 32, 32)
        >>> # Computes saliency maps for class 3.
        >>> attribution = saliency.attribute(input, target=3)
        >>> # define a perturbation function for the input

        >>> # Computes the faithfulness estimate scores for saliency maps
        >>> faithfulness_estimate, attr_sums, p_fwds = faithfulness_estimate(net, input, attribution, baselines)
    """
    with torch.no_grad():
        if multi_target:
            # faithfulness_estimate computation cannot be batched across targets, this is because it requires the removal
            # of attribution features for each target in an desencding order of their importance. Since for each target
            # the order of importance of features can be different, we cannot batch the computation across targets.
            attributions_list = attributions
            targets_list = target
            assert isinstance(attributions_list, list), (
                "attributions must be a list of tensors or list of tuples of tensors"
            )
            assert isinstance(targets_list, list), "targets must be a list of targets"
            assert len(targets_list) == len(
                attributions_list
            ), f"""The number of targets in the targets_list and
                attributions_list must match. Found number of targets in the targets_list is: {len(targets_list)} and in the
                attributions_list: {len(attributions_list)}"""

            faithfulness_estimate_batch_list = []
            attributions_sum_perturbed_batch_list = []
            inputs_perturbed_fwd_diffs_batch_list = []
            for attributions, target in zip(
                attributions_list, targets_list, strict=True
            ):
                (
                    faithfulness_estimate_batch,
                    attributions_sum_perturbed_batch,
                    inputs_perturbed_fwd_diffs_batch,
                ) = faithfulness_estimate(
                    forward_func=forward_func,
                    inputs=inputs,
                    attributions=attributions,
                    baselines=baselines,
                    feature_mask=feature_mask,
                    additional_forward_args=additional_forward_args,
                    target=target,
                    max_features_processed_per_batch=max_features_processed_per_batch,
                    percentage_feature_removal_per_step=percentage_feature_removal_per_step,
                    frozen_features=frozen_features,
                    show_progress=show_progress,
                    return_dict=False,
                    return_intermediate_results=True,
                )
                faithfulness_estimate_batch_list.append(faithfulness_estimate_batch)
                attributions_sum_perturbed_batch_list.append(
                    attributions_sum_perturbed_batch
                )
                inputs_perturbed_fwd_diffs_batch_list.append(
                    inputs_perturbed_fwd_diffs_batch
                )

            if return_intermediate_results:
                if return_dict:
                    return {
                        "faithfulness_estimate_score": faithfulness_estimate_batch_list,
                        "attributions_sum_perturbed": attributions_sum_perturbed_batch_list,
                        "inputs_perturbed_fwd_diffs": inputs_perturbed_fwd_diffs_batch_list,
                    }
                else:
                    return (
                        faithfulness_estimate_batch_list,
                        attributions_sum_perturbed_batch_list,
                        inputs_perturbed_fwd_diffs_batch_list,
                    )
            else:
                if return_dict:
                    return {
                        "faithfulness_estimate_score": faithfulness_estimate_batch_list
                    }
                return faithfulness_estimate_batch_list
        else:
            assert not isinstance(attributions, list), (
                "attributions must be a single tensor or a tuple of tensors"
            )
            assert isinstance(target, (ExplanationTarget)), (
                "target must be a single target for single-target faithfulness_estimate"
            )
            # perform argument formattings
            inputs = _format_tensor_into_tuples(inputs)  # type: ignore
            if baselines is None:
                baselines = tuple(torch.zeros_like(inp) for inp in inputs)
            else:
                baselines = cast(
                    tuple[Tensor, ...], _format_baseline(baselines, inputs)
                )
            additional_forward_args = _format_additional_forward_args(
                additional_forward_args
            )
            attributions = _format_tensor_into_tuples(attributions)  # type: ignore
            feature_mask = _format_tensor_into_tuples(feature_mask)  # type: ignore

            # Make sure that inputs and corresponding attributions have matching sizes.
            assert len(inputs) == len(
                attributions
            ), f"""The number of tensors in the inputs and
                attributions must match. Found number of tensors in the inputs is: {len(inputs)} and in the
                attributions: {len(attributions)}"""
            if feature_mask is not None:
                assert len(feature_mask) == len(
                    feature_mask
                ), f"""The number of tensors in the inputs and
                    feature_masks must match. Found number of tensors in the inputs is: {len(feature_mask)} and in the
                    attributions: {len(feature_mask)}"""
                for input, attribution, mask in zip(
                    inputs, attributions, feature_mask, strict=True
                ):
                    assert input.shape == mask.shape == attribution.shape, f"""
                        The shape of the input, attribution and feature mask must match. Found shapes are: input {input.shape}
                        attribution {attribution.shape} and feature mask {mask.shape}
                        """

            bsz = inputs[0].size(0)
            faithfulness_estimate_batch = []
            attributions_sum_perturbed_batch = []
            inputs_perturbed_fwd_diffs_batch = []
            for sample_idx in tqdm.tqdm(range(bsz), disable=not show_progress):
                (
                    faithfulness_estimate_score,
                    attributions_sum_perturbed,
                    inputs_perturbed_fwd_diffs,
                ) = eval_faithfulness_estimate_single_sample(
                    forward_func=forward_func,
                    inputs=tuple(input[sample_idx].unsqueeze(0) for input in inputs),
                    attributions=tuple(
                        attr[sample_idx].unsqueeze(0) for attr in attributions
                    ),
                    feature_mask=(
                        tuple(mask[sample_idx].unsqueeze(0) for mask in feature_mask)
                        if feature_mask is not None
                        else None
                    ),
                    baselines=(
                        tuple(
                            baseline[sample_idx].unsqueeze(0) for baseline in baselines
                        )
                    ),
                    additional_forward_args=(
                        tuple(
                            (
                                arg[sample_idx].unsqueeze(0)
                                if isinstance(arg, torch.Tensor)
                                else arg
                            )
                            for arg in additional_forward_args
                        )
                        if additional_forward_args is not None
                        else None
                    ),
                    target=(
                        target.value[sample_idx]
                        if isinstance(target.value, (list, torch.Tensor))
                        else target.value
                    ),
                    max_features_processed_per_batch=max_features_processed_per_batch,
                    percentage_feature_removal_per_step=percentage_feature_removal_per_step,
                    frozen_features=(
                        frozen_features[sample_idx]
                        if frozen_features is not None
                        else frozen_features
                    ),
                    show_progress=show_progress,
                )
                faithfulness_estimate_batch.append(faithfulness_estimate_score)
                attributions_sum_perturbed_batch.append(attributions_sum_perturbed)
                inputs_perturbed_fwd_diffs_batch.append(inputs_perturbed_fwd_diffs)
            faithfulness_estimate_batch = torch.tensor(faithfulness_estimate_batch)

            if return_intermediate_results:
                if return_dict:
                    return {
                        "faithfulness_estimate_score": faithfulness_estimate_batch,
                        "attributions_sum_perturbed": attributions_sum_perturbed_batch,
                        "inputs_perturbed_fwd_diffs": inputs_perturbed_fwd_diffs_batch,
                    }
                else:
                    return (
                        faithfulness_estimate_batch,
                        attributions_sum_perturbed_batch,
                        inputs_perturbed_fwd_diffs_batch,
                    )
            else:
                if return_dict:
                    return {"faithfulness_estimate_score": faithfulness_estimate_batch}
                return faithfulness_estimate_batch