captum/attr/_core/deep_lift.py

#!/usr/bin/env python3
import typing
import warnings
from typing import Any, Callable, cast, List, Tuple, Union

import torch
import torch.nn as nn
import torch.nn.functional as F
from captum._utils.common import (
    _expand_additional_forward_args,
    _expand_target,
    _format_additional_forward_args,
    _format_baseline,
    _format_output,
    _format_tensor_into_tuples,
    _is_tuple,
    _register_backward_hook,
    _run_forward,
    _select_targets,
    ExpansionTypes,
)
from captum._utils.gradient import (
    apply_gradient_requirements,
    undo_gradient_requirements,
)
from captum._utils.typing import (
    BaselineType,
    Literal,
    TargetType,
    TensorOrTupleOfTensorsGeneric,
)
from captum.attr._utils.attribution import GradientAttribution
from captum.attr._utils.common import (
    _call_custom_attribution_func,
    _compute_conv_delta_and_format_attrs,
    _format_callable_baseline,
    _tensorize_baseline,
    _validate_input,
)
from captum.log import log_usage
from torch import Tensor
from torch.nn import Module
from torch.utils.hooks import RemovableHandle


# Check if module backward hook can safely be used for the module that produced
# this inputs / outputs mapping
def _check_valid_module(inputs_grad_fn, outputs) -> bool:
    def is_output_cloned(output_fn, input_grad_fn) -> bool:
        """
        Checks if the output has been cloned. This happens especially in case of
        layer deeplift.
        """
        return (
            output_fn[0].next_functions is not None
            and output_fn[0].next_functions[0][0] == input_grad_fn
        )

    curr_fn = outputs.grad_fn
    first_next = curr_fn.next_functions[0]
    try:
        # if `inputs` in the input to the network then the grad_fn is None and
        # for that input backward_hook isn't computed. That's the reason why we
        # need to check on `inputs_grad_fns[first_next[1]]` being None.
        return (
            inputs_grad_fn is None
            or first_next[0] == inputs_grad_fn
            or is_output_cloned(first_next, inputs_grad_fn)
        )
    except IndexError:
        return False


class DeepLift(GradientAttribution):
    r"""
    Implements DeepLIFT algorithm based on the following paper:
    Learning Important Features Through Propagating Activation Differences,
    Avanti Shrikumar, et. al.
    https://arxiv.org/abs/1704.02685

    and the gradient formulation proposed in:
    Towards better understanding of gradient-based attribution methods for
    deep neural networks,  Marco Ancona, et.al.
    https://openreview.net/pdf?id=Sy21R9JAW

    This implementation supports only Rescale rule. RevealCancel rule will
    be supported in later releases.
    In addition to that, in order to keep the implementation cleaner, DeepLIFT
    for internal neurons and layers extends current implementation and is
    implemented separately in LayerDeepLift and NeuronDeepLift.
    Although DeepLIFT's(Rescale Rule) attribution quality is comparable with
    Integrated Gradients, it runs significantly faster than Integrated
    Gradients and is preferred for large datasets.

    Currently we only support a limited number of non-linear activations
    but the plan is to expand the list in the future.

    Note: As we know, currently we cannot access the building blocks,
    of PyTorch's built-in LSTM, RNNs and GRUs such as Tanh and Sigmoid.
    Nonetheless, it is possible to build custom LSTMs, RNNS and GRUs
    with performance similar to built-in ones using TorchScript.
    More details on how to build custom RNNs can be found here:
    https://pytorch.org/blog/optimizing-cuda-rnn-with-torchscript/
    """

    def __init__(
        self,
        model: Module,
        multiply_by_inputs: bool = True,
        eps: float = 1e-10,
    ) -> None:
        r"""
        Args:

            model (nn.Module):  The reference to PyTorch model instance. Model cannot
                        contain any in-place nonlinear submodules; these are not
                        supported by the register_full_backward_hook PyTorch API
                        starting from PyTorch v1.9.
            multiply_by_inputs (bool, optional): Indicates whether to factor
                        model inputs' multiplier in the final attribution scores.
                        In the literature this is also known as local vs global
                        attribution. If inputs' multiplier isn't factored in
                        then that type of attribution method is also called local
                        attribution. If it is, then that type of attribution
                        method is called global.
                        More detailed can be found here:
                        https://arxiv.org/abs/1711.06104

                        In case of DeepLift, if `multiply_by_inputs`
                        is set to True, final sensitivity scores
                        are being multiplied by (inputs - baselines).
                        This flag applies only if `custom_attribution_func` is
                        set to None.

            eps (float, optional): A value at which to consider output/input change
                        significant when computing the gradients for non-linear layers.
                        This is useful to adjust, depending on your model's bit depth,
                        to avoid numerical issues during the gradient computation.
                        Default: 1e-10
        """
        GradientAttribution.__init__(self, model)
        self.model = model
        self.eps = eps
        self.forward_handles: List[RemovableHandle] = []
        self.backward_handles: List[RemovableHandle] = []
        self._multiply_by_inputs = multiply_by_inputs

    @typing.overload
    def attribute(
        self,
        inputs: TensorOrTupleOfTensorsGeneric,
        baselines: BaselineType = None,
        target: TargetType = None,
        additional_forward_args: Any = None,
        return_convergence_delta: Literal[False] = False,
        custom_attribution_func: Union[None, Callable[..., Tuple[Tensor, ...]]] = None,
    ) -> TensorOrTupleOfTensorsGeneric:
        ...

    @typing.overload
    def attribute(
        self,
        inputs: TensorOrTupleOfTensorsGeneric,
        baselines: BaselineType = None,
        target: TargetType = None,
        additional_forward_args: Any = None,
        *,
        return_convergence_delta: Literal[True],
        custom_attribution_func: Union[None, Callable[..., Tuple[Tensor, ...]]] = None,
    ) -> Tuple[TensorOrTupleOfTensorsGeneric, Tensor]:
        ...

    @log_usage()
    def attribute(  # type: ignore
        self,
        inputs: TensorOrTupleOfTensorsGeneric,
        baselines: BaselineType = None,
        target: TargetType = None,
        additional_forward_args: Any = None,
        return_convergence_delta: bool = False,
        custom_attribution_func: Union[None, Callable[..., Tuple[Tensor, ...]]] = None,
    ) -> Union[
        TensorOrTupleOfTensorsGeneric, Tuple[TensorOrTupleOfTensorsGeneric, Tensor]
    ]:
        r"""
        Args:

            inputs (tensor or tuple of tensors):  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 scalars or tensors, optional):
                        Baselines define reference samples that are compared with
                        the inputs. In order to assign attribution scores DeepLift
                        computes the differences between the inputs/outputs and
                        corresponding references.
                        Baselines can be provided 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.

                        In the cases when `baselines` is not provided, we internally
                        use zero scalar corresponding to each input tensor.

                        Default: None
            target (int, tuple, tensor or list, optional):  Output indices for
                        which gradients are computed (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 outputs, targets can be either:

                        - a single integer or a tensor containing a single
                          integer, which is applied to all input examples

                        - a list of integers or a 1D tensor, with length matching
                          the number of examples in inputs (dim 0). Each integer
                          is applied as the target 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
            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 attributions are not computed with respect
                        to these arguments.
                        Default: None
            return_convergence_delta (bool, optional): Indicates whether to return
                        convergence delta or not. If `return_convergence_delta`
                        is set to True convergence delta will be returned in
                        a tuple following attributions.
                        Default: False
            custom_attribution_func (callable, optional): A custom function for
                        computing final attribution scores. This function can take
                        at least one and at most three arguments with the
                        following signature:

                        - custom_attribution_func(multipliers)
                        - custom_attribution_func(multipliers, inputs)
                        - custom_attribution_func(multipliers, inputs, baselines)

                        In case this function is not provided, we use the default
                        logic defined as: multipliers * (inputs - baselines)
                        It is assumed that all input arguments, `multipliers`,
                        `inputs` and `baselines` are provided in tuples of same
                        length. `custom_attribution_func` returns a tuple of
                        attribution tensors that have the same length as the
                        `inputs`.

                        Default: None

        Returns:
            **attributions** or 2-element tuple of **attributions**, **delta**:
            - **attributions** (*tensor* or tuple of *tensors*):
                Attribution score computed based on DeepLift rescale rule with respect
                to each input feature. Attributions will always be
                the same size as the provided inputs, with each value
                providing the attribution of the corresponding input index.
                If a single tensor is provided as inputs, a single tensor is
                returned. If a tuple is provided for inputs, a tuple of
                corresponding sized tensors is returned.
            - **delta** (*tensor*, returned if return_convergence_delta=True):
                This is computed using the property that
                the total sum of forward_func(inputs) - forward_func(baselines)
                must equal the total sum of the attributions computed
                based on DeepLift's rescale rule.
                Delta is calculated per example, meaning that the number of
                elements in returned delta tensor is equal to the number of
                of examples in input.
                Note that the logic described for deltas is guaranteed when the
                default logic for attribution computations is used, meaning that the
                `custom_attribution_func=None`, otherwise it is not guaranteed and
                depends on the specifics of the `custom_attribution_func`.

        Examples::

            >>> # ImageClassifier takes a single input tensor of images Nx3x32x32,
            >>> # and returns an Nx10 tensor of class probabilities.
            >>> net = ImageClassifier()
            >>> dl = DeepLift(net)
            >>> input = torch.randn(2, 3, 32, 32, requires_grad=True)
            >>> # Computes deeplift attribution scores for class 3.
            >>> attribution = dl.attribute(input, target=3)
        """

        # Keeps track whether original input is a tuple or not before
        # converting it into a tuple.
        is_inputs_tuple = _is_tuple(inputs)

        inputs = _format_tensor_into_tuples(inputs)
        baselines = _format_baseline(baselines, inputs)

        gradient_mask = apply_gradient_requirements(inputs)

        _validate_input(inputs, baselines)

        # set hooks for baselines
        warnings.warn(
            """Setting forward, backward hooks and attributes on non-linear
               activations. The hooks and attributes will be removed
            after the attribution is finished"""
        )
        baselines = _tensorize_baseline(inputs, baselines)
        main_model_hooks = []
        try:
            main_model_hooks = self._hook_main_model()

            self.model.apply(self._register_hooks)

            additional_forward_args = _format_additional_forward_args(
                additional_forward_args
            )

            expanded_target = _expand_target(
                target, 2, expansion_type=ExpansionTypes.repeat
            )

            wrapped_forward_func = self._construct_forward_func(
                self.model,
                (inputs, baselines),
                expanded_target,
                additional_forward_args,
            )
            gradients = self.gradient_func(wrapped_forward_func, inputs)
            if custom_attribution_func is None:
                if self.multiplies_by_inputs:
                    attributions = tuple(
                        (input - baseline) * gradient
                        for input, baseline, gradient in zip(
                            inputs, baselines, gradients
                        )
                    )
                else:
                    attributions = gradients
            else:
                attributions = _call_custom_attribution_func(
                    custom_attribution_func, gradients, inputs, baselines
                )
        finally:
            # Even if any error is raised, remove all hooks before raising
            self._remove_hooks(main_model_hooks)

        undo_gradient_requirements(inputs, gradient_mask)
        return _compute_conv_delta_and_format_attrs(
            self,
            return_convergence_delta,
            attributions,
            baselines,
            inputs,
            additional_forward_args,
            target,
            is_inputs_tuple,
        )

    def _construct_forward_func(
        self,
        forward_func: Callable,
        inputs: Tuple,
        target: TargetType = None,
        additional_forward_args: Any = None,
    ) -> Callable:
        def forward_fn():
            model_out = _run_forward(
                forward_func, inputs, None, additional_forward_args
            )
            return _select_targets(
                torch.cat((model_out[:, 0], model_out[:, 1])), target
            )

        if hasattr(forward_func, "device_ids"):
            forward_fn.device_ids = forward_func.device_ids  # type: ignore
        return forward_fn

    def _is_non_linear(self, module: Module) -> bool:
        return type(module) in SUPPORTED_NON_LINEAR.keys()

    def _forward_pre_hook_ref(
        self, module: Module, inputs: Union[Tensor, Tuple[Tensor, ...]]
    ) -> None:
        inputs = _format_tensor_into_tuples(inputs)
        module.input_ref = tuple(  # type: ignore
            input.clone().detach() for input in inputs
        )

    def _forward_pre_hook(
        self, module: Module, inputs: Union[Tensor, Tuple[Tensor, ...]]
    ) -> None:
        """
        For the modules that perform in-place operations such as ReLUs, we cannot
        use inputs from forward hooks. This is because in that case inputs
        and outputs are the same. We need access the inputs in pre-hooks and
        set necessary hooks on inputs there.
        """
        inputs = _format_tensor_into_tuples(inputs)
        module.input = inputs[0].clone().detach()
        module.input_grad_fns = inputs[0].grad_fn  # type: ignore

        def tensor_backward_hook(grad):
            if module.saved_grad is None:
                raise RuntimeError(
                    """Module {} was detected as not supporting correctly module
                        backward hook. You should modify your hook to ignore the given
                        grad_inputs (recompute them by hand if needed) and save the
                        newly computed grad_inputs in module.saved_grad. See MaxPool1d
                        as an example.""".format(
                        module
                    )
                )
            return module.saved_grad

        # the hook is set by default but it will be used only for
        # failure cases and will be removed otherwise
        handle = inputs[0].register_hook(tensor_backward_hook)
        module.input_hook = handle

    def _forward_hook(
        self,
        module: Module,
        inputs: Union[Tensor, Tuple[Tensor, ...]],
        outputs: Union[Tensor, Tuple[Tensor, ...]],
    ) -> None:
        r"""
        we need forward hook to access and detach the inputs and
        outputs of a neuron
        """
        outputs = _format_tensor_into_tuples(outputs)
        module.output = outputs[0].clone().detach()
        if not _check_valid_module(module.input_grad_fns, outputs[0]):
            warnings.warn(
                """An invalid module {} is detected. Saved gradients will
                be used as the gradients of the module's input tensor.
                See MaxPool1d as an example.""".format(
                    module
                )
            )
            module.is_invalid = True  # type: ignore
            module.saved_grad = None  # type: ignore
            self.forward_handles.append(cast(RemovableHandle, module.input_hook))
        else:
            module.is_invalid = False  # type: ignore
            # removing the hook if there is no failure case
            cast(RemovableHandle, module.input_hook).remove()
        del module.input_hook
        del module.input_grad_fns

    def _backward_hook(
        self,
        module: Module,
        grad_input: Union[Tensor, Tuple[Tensor, ...]],
        grad_output: Union[Tensor, Tuple[Tensor, ...]],
    ):
        r"""
        `grad_input` is the gradient of the neuron with respect to its input
        `grad_output` is the gradient of the neuron with respect to its output
         we can override `grad_input` according to chain rule with.
        `grad_output` * delta_out / delta_in.

        """
        # before accessing the attributes from the module we want
        # to ensure that the properties exist, if not, then it is
        # likely that the module is being reused.
        attr_criteria = self.satisfies_attribute_criteria(module)
        if not attr_criteria:
            raise RuntimeError(
                "A Module {} was detected that does not contain some of "
                "the input/output attributes that are required for DeepLift "
                "computations. This can occur, for example, if "
                "your module is being used more than once in the network."
                "Please, ensure that module is being used only once in the "
                "network.".format(module)
            )
        multipliers = tuple(
            SUPPORTED_NON_LINEAR[type(module)](
                module,
                module.input,
                module.output,
                grad_input,
                grad_output,
                eps=self.eps,
            )
        )
        # remove all the properies that we set for the inputs and output
        del module.input
        del module.output

        return multipliers

    def satisfies_attribute_criteria(self, module: Module) -> bool:
        return hasattr(module, "input") and hasattr(module, "output")

    def _can_register_hook(self, module: Module) -> bool:
        # TODO find a better way of checking if a module is a container or not
        module_fullname = str(type(module))
        has_already_hooks = len(module._backward_hooks) > 0  # type: ignore
        return not (
            "nn.modules.container" in module_fullname
            or has_already_hooks
            or not self._is_non_linear(module)
        )

    def _register_hooks(
        self, module: Module, attribute_to_layer_input: bool = True
    ) -> None:
        if not self._can_register_hook(module) or (
            not attribute_to_layer_input and module is self.layer  # type: ignore
        ):
            return
        # adds forward hook to leaf nodes that are non-linear
        forward_handle = module.register_forward_hook(self._forward_hook)
        pre_forward_handle = module.register_forward_pre_hook(self._forward_pre_hook)
        backward_handle = _register_backward_hook(module, self._backward_hook, self)
        self.forward_handles.append(forward_handle)
        self.forward_handles.append(pre_forward_handle)
        self.backward_handles.append(backward_handle)

    def _remove_hooks(self, extra_hooks_to_remove: List[RemovableHandle]) -> None:
        for handle in extra_hooks_to_remove:
            handle.remove()
        for forward_handle in self.forward_handles:
            forward_handle.remove()
        for backward_handle in self.backward_handles:
            backward_handle.remove()

    def _hook_main_model(self) -> List[RemovableHandle]:
        def pre_hook(module: Module, baseline_inputs_add_args: Tuple) -> Tuple:
            inputs = baseline_inputs_add_args[0]
            baselines = baseline_inputs_add_args[1]
            additional_args = None
            if len(baseline_inputs_add_args) > 2:
                additional_args = baseline_inputs_add_args[2:]

            baseline_input_tsr = tuple(
                torch.cat([input, baseline])
                for input, baseline in zip(inputs, baselines)
            )
            if additional_args is not None:
                expanded_additional_args = cast(
                    Tuple,
                    _expand_additional_forward_args(
                        additional_args, 2, ExpansionTypes.repeat
                    ),
                )
                return (*baseline_input_tsr, *expanded_additional_args)
            return baseline_input_tsr

        def forward_hook(module: Module, inputs: Tuple, outputs: Tensor):
            return torch.stack(torch.chunk(outputs, 2), dim=1)

        if isinstance(
            self.model, (nn.DataParallel, nn.parallel.DistributedDataParallel)
        ):
            return [
                self.model.module.register_forward_pre_hook(pre_hook),  # type: ignore
                self.model.module.register_forward_hook(forward_hook),
            ]  # type: ignore
        else:
            return [
                self.model.register_forward_pre_hook(pre_hook),  # type: ignore
                self.model.register_forward_hook(forward_hook),
            ]  # type: ignore

    def has_convergence_delta(self) -> bool:
        return True

    @property
    def multiplies_by_inputs(self):
        return self._multiply_by_inputs


class DeepLiftShap(DeepLift):
    r"""
    Extends DeepLift algorithm and approximates SHAP values using Deeplift.
    For each input sample it computes DeepLift attribution with respect to
    each baseline and averages resulting attributions.
    More details about the algorithm can be found here:

    http://papers.nips.cc/paper/7062-a-unified-approach-to-interpreting-model-predictions.pdf

    Note that the explanation model:
        1. Assumes that input features are independent of one another
        2. Is linear, meaning that the explanations are modeled through
            the additive composition of feature effects.
    Although, it assumes a linear model for each explanation, the overall
    model across multiple explanations can be complex and non-linear.
    """

    def __init__(self, model: Module, multiply_by_inputs: bool = True) -> None:
        r"""
        Args:

            model (nn.Module):  The reference to PyTorch model instance. Model cannot
                        contain any in-place nonlinear submodules; these are not
                        supported by the register_full_backward_hook PyTorch API.
            multiply_by_inputs (bool, optional): Indicates whether to factor
                        model inputs' multiplier in the final attribution scores.
                        In the literature this is also known as local vs global
                        attribution. If inputs' multiplier isn't factored in
                        then that type of attribution method is also called local
                        attribution. If it is, then that type of attribution
                        method is called global.
                        More detailed can be found here:
                        https://arxiv.org/abs/1711.06104

                        In case of DeepLiftShap, if `multiply_by_inputs`
                        is set to True, final sensitivity scores
                        are being multiplied by (inputs - baselines).
                        This flag applies only if `custom_attribution_func` is
                        set to None.
        """
        DeepLift.__init__(self, model, multiply_by_inputs=multiply_by_inputs)

    # There's a mismatch between the signatures of DeepLift.attribute and
    # DeepLiftShap.attribute, so we ignore typing here
    @typing.overload  # type: ignore
    def attribute(
        self,
        inputs: TensorOrTupleOfTensorsGeneric,
        baselines: Union[
            TensorOrTupleOfTensorsGeneric, Callable[..., TensorOrTupleOfTensorsGeneric]
        ],
        target: TargetType = None,
        additional_forward_args: Any = None,
        return_convergence_delta: Literal[False] = False,
        custom_attribution_func: Union[None, Callable[..., Tuple[Tensor, ...]]] = None,
    ) -> TensorOrTupleOfTensorsGeneric:
        ...

    @typing.overload
    def attribute(
        self,
        inputs: TensorOrTupleOfTensorsGeneric,
        baselines: Union[
            TensorOrTupleOfTensorsGeneric, Callable[..., TensorOrTupleOfTensorsGeneric]
        ],
        target: TargetType = None,
        additional_forward_args: Any = None,
        *,
        return_convergence_delta: Literal[True],
        custom_attribution_func: Union[None, Callable[..., Tuple[Tensor, ...]]] = None,
    ) -> Tuple[TensorOrTupleOfTensorsGeneric, Tensor]:
        ...

    @log_usage()
    def attribute(  # type: ignore
        self,
        inputs: TensorOrTupleOfTensorsGeneric,
        baselines: Union[
            TensorOrTupleOfTensorsGeneric, Callable[..., TensorOrTupleOfTensorsGeneric]
        ],
        target: TargetType = None,
        additional_forward_args: Any = None,
        return_convergence_delta: bool = False,
        custom_attribution_func: Union[None, Callable[..., Tuple[Tensor, ...]]] = None,
    ) -> Union[
        TensorOrTupleOfTensorsGeneric, Tuple[TensorOrTupleOfTensorsGeneric, Tensor]
    ]:
        r"""
        Args:

            inputs (tensor or tuple of tensors):  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 (tensor, tuple of tensors, callable):
                        Baselines define reference samples that are compared with
                        the inputs. In order to assign attribution scores DeepLift
                        computes the differences between the inputs/outputs and
                        corresponding references. Baselines can be provided as:

                        - a single tensor, if inputs is a single tensor, with
                          the first dimension equal to the number of examples
                          in the baselines' distribution. The remaining dimensions
                          must match with input tensor's dimension starting from
                          the second dimension.

                        - a tuple of tensors, if inputs is a tuple of tensors,
                          with the first dimension of any tensor inside the tuple
                          equal to the number of examples in the baseline's
                          distribution. The remaining dimensions must match
                          the dimensions of the corresponding input tensor
                          starting from the second dimension.

                        - callable function, optionally takes `inputs` as an
                          argument and either returns a single tensor
                          or a tuple of those.

                        It is recommended that the number of samples in the baselines'
                        tensors is larger than one.
            target (int, tuple, tensor or list, optional):  Output indices for
                        which gradients are computed (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 outputs, targets can be either:

                        - a single integer or a tensor containing a single
                          integer, which is applied to all input examples

                        - a list of integers or a 1D tensor, with length matching
                          the number of examples in inputs (dim 0). Each integer
                          is applied as the target 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
            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 attributions are not computed with respect
                        to these arguments.
                        Default: None
            return_convergence_delta (bool, optional): Indicates whether to return
                        convergence delta or not. If `return_convergence_delta`
                        is set to True convergence delta will be returned in
                        a tuple following attributions.
                        Default: False
            custom_attribution_func (callable, optional): A custom function for
                        computing final attribution scores. This function can take
                        at least one and at most three arguments with the
                        following signature:

                        - custom_attribution_func(multipliers)
                        - custom_attribution_func(multipliers, inputs)
                        - custom_attribution_func(multipliers, inputs, baselines)

                        In case this function is not provided we use the default
                        logic defined as: multipliers * (inputs - baselines)
                        It is assumed that all input arguments, `multipliers`,
                        `inputs` and `baselines` are provided in tuples of same
                        length. `custom_attribution_func` returns a tuple of
                        attribution tensors that have the same length as the
                        `inputs`.
                        Default: None

        Returns:
            **attributions** or 2-element tuple of **attributions**, **delta**:
            - **attributions** (*tensor* or tuple of *tensors*):
                        Attribution score computed based on DeepLift rescale rule with
                        respect to each input feature. Attributions will always be
                        the same size as the provided inputs, with each value
                        providing the attribution of the corresponding input index.
                        If a single tensor is provided as inputs, a single tensor is
                        returned. If a tuple is provided for inputs, a tuple of
                        corresponding sized tensors is returned.
            - **delta** (*tensor*, returned if return_convergence_delta=True):
                        This is computed using the property that the
                        total sum of forward_func(inputs) - forward_func(baselines)
                        must be very close to the total sum of attributions
                        computed based on approximated SHAP values using
                        Deeplift's rescale rule.
                        Delta is calculated for each example input and baseline pair,
                        meaning that the number of elements in returned delta tensor
                        is equal to the
                        `number of examples in input` * `number of examples
                        in baseline`. The deltas are ordered in the first place by
                        input example, followed by the baseline.
                        Note that the logic described for deltas is guaranteed
                        when the default logic for attribution computations is used,
                        meaning that the `custom_attribution_func=None`, otherwise
                        it is not guaranteed and depends on the specifics of the
                        `custom_attribution_func`.

        Examples::

            >>> # ImageClassifier takes a single input tensor of images Nx3x32x32,
            >>> # and returns an Nx10 tensor of class probabilities.
            >>> net = ImageClassifier()
            >>> dl = DeepLiftShap(net)
            >>> input = torch.randn(2, 3, 32, 32, requires_grad=True)
            >>> # Computes shap values using deeplift for class 3.
            >>> attribution = dl.attribute(input, target=3)
        """
        baselines = _format_callable_baseline(baselines, inputs)

        assert isinstance(baselines[0], torch.Tensor) and baselines[0].shape[0] > 1, (
            "Baselines distribution has to be provided in form of a torch.Tensor"
            " with more than one example but found: {}."
            " If baselines are provided in shape of scalars or with a single"
            " baseline example, `DeepLift`"
            " approach can be used instead.".format(baselines[0])
        )

        # Keeps track whether original input is a tuple or not before
        # converting it into a tuple.
        is_inputs_tuple = _is_tuple(inputs)

        inputs = _format_tensor_into_tuples(inputs)

        # batch sizes
        inp_bsz = inputs[0].shape[0]
        base_bsz = baselines[0].shape[0]

        (
            exp_inp,
            exp_base,
            exp_tgt,
            exp_addit_args,
        ) = self._expand_inputs_baselines_targets(
            baselines, inputs, target, additional_forward_args
        )
        attributions = super().attribute.__wrapped__(  # type: ignore
            self,
            exp_inp,
            exp_base,
            target=exp_tgt,
            additional_forward_args=exp_addit_args,
            return_convergence_delta=cast(
                Literal[True, False], return_convergence_delta
            ),
            custom_attribution_func=custom_attribution_func,
        )
        if return_convergence_delta:
            attributions, delta = cast(Tuple[Tuple[Tensor, ...], Tensor], attributions)

        attributions = tuple(
            self._compute_mean_across_baselines(
                inp_bsz, base_bsz, cast(Tensor, attribution)
            )
            for attribution in attributions
        )

        if return_convergence_delta:
            return _format_output(is_inputs_tuple, attributions), delta
        else:
            return _format_output(is_inputs_tuple, attributions)

    def _expand_inputs_baselines_targets(
        self,
        baselines: Tuple[Tensor, ...],
        inputs: Tuple[Tensor, ...],
        target: TargetType,
        additional_forward_args: Any,
    ) -> Tuple[Tuple[Tensor, ...], Tuple[Tensor, ...], TargetType, Any]:
        inp_bsz = inputs[0].shape[0]
        base_bsz = baselines[0].shape[0]

        expanded_inputs = tuple(
            [
                input.repeat_interleave(base_bsz, dim=0).requires_grad_()
                for input in inputs
            ]
        )
        expanded_baselines = tuple(
            [
                baseline.repeat(
                    (inp_bsz,) + tuple([1] * (len(baseline.shape) - 1))
                ).requires_grad_()
                for baseline in baselines
            ]
        )
        expanded_target = _expand_target(
            target, base_bsz, expansion_type=ExpansionTypes.repeat_interleave
        )
        input_additional_args = (
            _expand_additional_forward_args(
                additional_forward_args,
                base_bsz,
                expansion_type=ExpansionTypes.repeat_interleave,
            )
            if additional_forward_args is not None
            else None
        )
        return (
            expanded_inputs,
            expanded_baselines,
            expanded_target,
            input_additional_args,
        )

    def _compute_mean_across_baselines(
        self, inp_bsz: int, base_bsz: int, attribution: Tensor
    ) -> Tensor:
        # Average for multiple references
        attr_shape: Tuple = (inp_bsz, base_bsz)
        if len(attribution.shape) > 1:
            attr_shape += attribution.shape[1:]
        return torch.mean(attribution.view(attr_shape), dim=1, keepdim=False)


def nonlinear(
    module: Module,
    inputs: Tensor,
    outputs: Tensor,
    grad_input: Tensor,
    grad_output: Tensor,
    eps: float = 1e-10,
):
    r"""
    grad_input: (dLoss / dprev_layer_out, dLoss / wij, dLoss / bij)
    grad_output: (dLoss / dlayer_out)
    https://github.com/pytorch/pytorch/issues/12331
    """
    delta_in, delta_out = _compute_diffs(inputs, outputs)

    new_grad_inp = list(grad_input)

    # supported non-linear modules take only single tensor as input hence accessing
    # only the first element in `grad_input` and `grad_output`
    new_grad_inp[0] = torch.where(
        abs(delta_in) < eps, new_grad_inp[0], grad_output[0] * delta_out / delta_in
    )

    # If the module is invalid, save the newly computed gradients
    # The original_grad_input will be overridden later in the Tensor hook
    if module.is_invalid:
        module.saved_grad = new_grad_inp[0]
    return new_grad_inp


def softmax(
    module: Module,
    inputs: Tensor,
    outputs: Tensor,
    grad_input: Tensor,
    grad_output: Tensor,
    eps: float = 1e-10,
):
    delta_in, delta_out = _compute_diffs(inputs, outputs)

    new_grad_inp = list(grad_input)
    grad_input_unnorm = torch.where(
        abs(delta_in) < eps, new_grad_inp[0], grad_output[0] * delta_out / delta_in
    )
    # normalizing
    n = grad_input[0].numel()

    # updating only the first half
    new_grad_inp[0] = grad_input_unnorm - grad_input_unnorm.sum() * 1 / n
    return new_grad_inp


def maxpool1d(
    module: Module,
    inputs: Tensor,
    outputs: Tensor,
    grad_input: Tensor,
    grad_output: Tensor,
    eps: float = 1e-10,
):
    return maxpool(
        module,
        F.max_pool1d,
        F.max_unpool1d,
        inputs,
        outputs,
        grad_input,
        grad_output,
        eps=eps,
    )


def maxpool2d(
    module: Module,
    inputs: Tensor,
    outputs: Tensor,
    grad_input: Tensor,
    grad_output: Tensor,
    eps: float = 1e-10,
):
    return maxpool(
        module,
        F.max_pool2d,
        F.max_unpool2d,
        inputs,
        outputs,
        grad_input,
        grad_output,
        eps=eps,
    )


def maxpool3d(
    module: Module, inputs, outputs, grad_input, grad_output, eps: float = 1e-10
):
    return maxpool(
        module,
        F.max_pool3d,
        F.max_unpool3d,
        inputs,
        outputs,
        grad_input,
        grad_output,
        eps=eps,
    )


def maxpool(
    module: Module,
    pool_func: Callable,
    unpool_func: Callable,
    inputs,
    outputs,
    grad_input,
    grad_output,
    eps: float = 1e-10,
):
    with torch.no_grad():
        input, input_ref = inputs.chunk(2)
        output, output_ref = outputs.chunk(2)

        delta_in = input - input_ref
        delta_in = torch.cat(2 * [delta_in])
        # Extracts cross maximum between the outputs of maxpool for the
        # actual inputs and its corresponding references. In case the delta outputs
        # for the references are larger the method relies on the references and
        # corresponding gradients to compute the multiplies and contributions.
        delta_out_xmax = torch.max(output, output_ref)
        delta_out = torch.cat([delta_out_xmax - output_ref, output - delta_out_xmax])

        _, indices = pool_func(
            module.input,
            module.kernel_size,
            module.stride,
            module.padding,
            module.dilation,
            module.ceil_mode,
            True,
        )
        grad_output_updated = grad_output[0]
        unpool_grad_out_delta, unpool_grad_out_ref_delta = torch.chunk(
            unpool_func(
                grad_output_updated * delta_out,
                indices,
                module.kernel_size,
                module.stride,
                module.padding,
                list(cast(torch.Size, module.input.shape)),
            ),
            2,
        )

    unpool_grad_out_delta = unpool_grad_out_delta + unpool_grad_out_ref_delta
    unpool_grad_out_delta = torch.cat(2 * [unpool_grad_out_delta])

    # If the module is invalid, we need to recompute the grad_input
    if module.is_invalid:
        original_grad_input = grad_input
        grad_input = (
            unpool_func(
                grad_output_updated,
                indices,
                module.kernel_size,
                module.stride,
                module.padding,
                list(cast(torch.Size, module.input.shape)),
            ),
        )
    if grad_input[0].shape != inputs.shape:
        raise AssertionError(
            "A problem occurred during maxpool modul's backward pass. "
            "The gradients with respect to inputs include only a "
            "subset of inputs. More details about this issue can "
            "be found here: "
            "https://pytorch.org/docs/stable/"
            "nn.html#torch.nn.Module.register_backward_hook "
            "This can happen for example if you attribute to the outputs of a "
            "MaxPool. As a workaround, please, attribute to the inputs of "
            "the following layer."
        )

    new_grad_inp = torch.where(
        abs(delta_in) < eps, grad_input[0], unpool_grad_out_delta / delta_in
    )
    # If the module is invalid, save the newly computed gradients
    # The original_grad_input will be overridden later in the Tensor hook
    if module.is_invalid:
        module.saved_grad = new_grad_inp
        return original_grad_input
    else:
        return (new_grad_inp,)


def _compute_diffs(inputs: Tensor, outputs: Tensor) -> Tuple[Tensor, Tensor]:
    input, input_ref = inputs.chunk(2)
    # if the model is a single non-linear module and we apply Rescale rule on it
    # we might not be able to perform chunk-ing because the output of the module is
    # usually being replaced by model output.
    output, output_ref = outputs.chunk(2)
    delta_in = input - input_ref
    delta_out = output - output_ref

    return torch.cat(2 * [delta_in]), torch.cat(2 * [delta_out])


SUPPORTED_NON_LINEAR = {
    nn.ReLU: nonlinear,
    nn.ELU: nonlinear,
    nn.LeakyReLU: nonlinear,
    nn.Sigmoid: nonlinear,
    nn.Tanh: nonlinear,
    nn.Softplus: nonlinear,
    nn.MaxPool1d: maxpool1d,
    nn.MaxPool2d: maxpool2d,
    nn.MaxPool3d: maxpool3d,
    nn.Softmax: softmax,
}