#!/usr/bin/env python3
# pyre-strict
import typing
from typing import Callable, List, Literal, Optional, Tuple, Union
import torch
from captum._utils.common import (
_expand_additional_forward_args,
_expand_target,
_format_additional_forward_args,
_format_output,
_is_tuple,
)
from captum._utils.typing import BaselineType, TargetType, TensorOrTupleOfTensorsGeneric
from captum.attr._utils.approximation_methods import approximation_parameters
from captum.attr._utils.attribution import GradientAttribution
from captum.attr._utils.batching import _batch_attribution
from captum.attr._utils.common import (
_format_input_baseline,
_reshape_and_sum,
_validate_input,
)
from captum.log import log_usage
from torch import Tensor
[docs]
class IntegratedGradients(GradientAttribution):
r"""
Integrated Gradients is an axiomatic model interpretability algorithm that
assigns an importance score to each input feature by approximating the
integral of gradients of the model's output with respect to the inputs
along the path (straight line) from given baselines / references to inputs.
Baselines can be provided as input arguments to attribute method.
To approximate the integral we can choose to use either a variant of
Riemann sum or Gauss-Legendre quadrature rule.
More details regarding the integrated gradients method can be found in the
original paper:
https://arxiv.org/abs/1703.01365
"""
def __init__(
self,
forward_func: Callable[..., Tensor],
multiply_by_inputs: bool = True,
) -> None:
r"""
Args:
forward_func (Callable): The forward function of the model or any
modification of it
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 integrated gradients, if `multiply_by_inputs`
is set to True, final sensitivity scores are being multiplied by
(inputs - baselines).
"""
GradientAttribution.__init__(self, forward_func)
self._multiply_by_inputs = multiply_by_inputs
# The following overloaded method signatures correspond to the case where
# return_convergence_delta is False, then only attributions are returned,
# and when return_convergence_delta is True, the return type is
# a tuple with both attributions and deltas.
@typing.overload
def attribute(
self,
inputs: TensorOrTupleOfTensorsGeneric,
baselines: BaselineType = None,
target: TargetType = None,
additional_forward_args: Optional[object] = None,
n_steps: int = 50,
method: str = "gausslegendre",
internal_batch_size: Union[None, int] = None,
*,
return_convergence_delta: Literal[True],
) -> Tuple[TensorOrTupleOfTensorsGeneric, Tensor]: ...
@typing.overload
# pyre-fixme[43]: The implementation of `attribute` does not accept all possible
# arguments of overload defined on line `82`.
def attribute(
self,
inputs: TensorOrTupleOfTensorsGeneric,
baselines: BaselineType = None,
target: TargetType = None,
additional_forward_args: Optional[object] = None,
n_steps: int = 50,
method: str = "gausslegendre",
internal_batch_size: Union[None, int] = None,
return_convergence_delta: Literal[False] = False,
) -> TensorOrTupleOfTensorsGeneric: ...
[docs]
@log_usage()
def attribute( # type: ignore
self,
inputs: TensorOrTupleOfTensorsGeneric,
baselines: BaselineType = None,
target: TargetType = None,
additional_forward_args: Optional[object] = None,
n_steps: int = 50,
method: str = "gausslegendre",
internal_batch_size: Union[None, int] = None,
return_convergence_delta: bool = False,
) -> Union[
TensorOrTupleOfTensorsGeneric, Tuple[TensorOrTupleOfTensorsGeneric, Tensor]
]:
r"""
This method attributes the output of the model with given target index
(in case it is provided, otherwise it assumes that output is a
scalar) to the inputs of the model using the approach described above.
In addition to that it also returns, if `return_convergence_delta` is
set to True, integral approximation delta based on the completeness
property of integrated gradients.
Args:
inputs (Tensor or tuple[Tensor, ...]): Input for which integrated
gradients 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, and if multiple input tensors
are provided, the examples must be aligned appropriately.
baselines (scalar, Tensor, tuple of scalar, or Tensor, optional):
Baselines define the starting point from which integral
is computed and 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.
For a tensor, the first dimension of the tensor must
correspond to the number of examples. It will be
repeated for each of `n_steps` along the integrated
path. For all other types, the given argument is used
for all forward evaluations.
Note that attributions are not computed with respect
to these arguments.
Default: None
n_steps (int, optional): The number of steps used by the approximation
method. Default: 50.
method (str, optional): Method for approximating the integral,
one of `riemann_right`, `riemann_left`, `riemann_middle`,
`riemann_trapezoid` or `gausslegendre`.
Default: `gausslegendre` if no method is provided.
internal_batch_size (int, optional): Divides total #steps * #examples
data points into chunks of size at most internal_batch_size,
which are computed (forward / backward passes)
sequentially. internal_batch_size must be at least equal to
#examples.
For DataParallel models, each batch is split among the
available devices, so evaluations on each available
device contain internal_batch_size / num_devices examples.
If internal_batch_size is None, then all evaluations are
processed in one batch.
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
Returns:
**attributions** or 2-element tuple of **attributions**, **delta**:
- **attributions** (*Tensor* or *tuple[Tensor, ...]*):
Integrated gradients 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):
The difference between the total approximated and true
integrated gradients. This is computed using the property
that the total sum of forward_func(inputs) -
forward_func(baselines) must equal the total sum of the
integrated gradient.
Delta is calculated per example, meaning that the number of
elements in returned delta tensor is equal to the number of
examples in inputs.
Examples::
>>> # ImageClassifier takes a single input tensor of images Nx3x32x32,
>>> # and returns an Nx10 tensor of class probabilities.
>>> net = ImageClassifier()
>>> ig = IntegratedGradients(net)
>>> input = torch.randn(2, 3, 32, 32, requires_grad=True)
>>> # Computes integrated gradients for class 3.
>>> attribution = ig.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)
# pyre-fixme[9]: inputs has type `TensorOrTupleOfTensorsGeneric`; used as
# `Tuple[Tensor, ...]`.
formatted_inputs, formatted_baselines = _format_input_baseline(
inputs, baselines
)
# pyre-fixme[6]: For 1st argument expected `Tuple[Tensor, ...]` but got
# `TensorOrTupleOfTensorsGeneric`.
_validate_input(formatted_inputs, formatted_baselines, n_steps, method)
if internal_batch_size is not None:
num_examples = formatted_inputs[0].shape[0]
attributions = _batch_attribution(
self,
num_examples,
internal_batch_size,
n_steps,
inputs=formatted_inputs,
baselines=formatted_baselines,
target=target,
additional_forward_args=additional_forward_args,
method=method,
)
else:
attributions = self._attribute(
inputs=formatted_inputs,
baselines=formatted_baselines,
target=target,
additional_forward_args=additional_forward_args,
n_steps=n_steps,
method=method,
)
if return_convergence_delta:
start_point, end_point = baselines, inputs
# computes approximation error based on the completeness axiom
delta = self.compute_convergence_delta(
attributions,
start_point,
end_point,
additional_forward_args=additional_forward_args,
target=target,
)
# pyre-fixme[7]: Expected `Union[Tuple[Variable[TensorOrTupleOfTensorsGen...
return _format_output(is_inputs_tuple, attributions), delta
# pyre-fixme[7]: Expected
# `Union[Tuple[Variable[TensorOrTupleOfTensorsGeneric <: [Tensor,
# typing.Tuple[Tensor, ...]]], Tensor], Variable[TensorOrTupleOfTensorsGeneric
# <: [Tensor, typing.Tuple[Tensor, ...]]]]` but got `Tuple[Tensor, ...]`.
return _format_output(is_inputs_tuple, attributions)
# pyre-fixme[24] Generic type `Callable` expects 2 type parameters.
[docs]
def attribute_future(self) -> Callable:
r"""
This method is not implemented for IntegratedGradients.
"""
raise NotImplementedError(
"attribute_future is not implemented for IntegratedGradients"
)
def _attribute(
self,
inputs: Tuple[Tensor, ...],
baselines: Tuple[Union[Tensor, int, float], ...],
target: TargetType = None,
additional_forward_args: Optional[object] = None,
n_steps: int = 50,
method: str = "gausslegendre",
step_sizes_and_alphas: Union[None, Tuple[List[float], List[float]]] = None,
) -> Tuple[Tensor, ...]:
if step_sizes_and_alphas is None:
# retrieve step size and scaling factor for specified
# approximation method
step_sizes_func, alphas_func = approximation_parameters(method)
step_sizes, alphas = step_sizes_func(n_steps), alphas_func(n_steps)
else:
step_sizes, alphas = step_sizes_and_alphas
# scale features and compute gradients. (batch size is abbreviated as bsz)
# scaled_features' dim -> (bsz * #steps x inputs[0].shape[1:], ...)
scaled_features_tpl = tuple(
torch.cat(
[baseline + alpha * (input - baseline) for alpha in alphas], dim=0
).requires_grad_()
for input, baseline in zip(inputs, baselines)
)
additional_forward_args = _format_additional_forward_args(
additional_forward_args
)
# apply number of steps to additional forward args
# currently, number of steps is applied only to additional forward arguments
# that are nd-tensors. It is assumed that the first dimension is
# the number of batches.
# dim -> (bsz * #steps x additional_forward_args[0].shape[1:], ...)
input_additional_args = (
_expand_additional_forward_args(additional_forward_args, n_steps)
if additional_forward_args is not None
else None
)
expanded_target = _expand_target(target, n_steps)
# grads: dim -> (bsz * #steps x inputs[0].shape[1:], ...)
grads = self.gradient_func(
forward_fn=self.forward_func,
inputs=scaled_features_tpl,
target_ind=expanded_target,
additional_forward_args=input_additional_args,
)
# flattening grads so that we can multilpy it with step-size
# calling contiguous to avoid `memory whole` problems
scaled_grads = [
grad.contiguous().view(n_steps, -1)
* torch.tensor(step_sizes).float().view(n_steps, 1).to(grad.device)
for grad in grads
]
# aggregates across all steps for each tensor in the input tuple
# total_grads has the same dimensionality as inputs
total_grads = tuple(
_reshape_and_sum(
scaled_grad, n_steps, grad.shape[0] // n_steps, grad.shape[1:]
)
for (scaled_grad, grad) in zip(scaled_grads, grads)
)
# computes attribution for each tensor in input tuple
# attributions has the same dimensionality as inputs
if not self.multiplies_by_inputs:
attributions = total_grads
else:
attributions = tuple(
total_grad * (input - baseline)
for total_grad, input, baseline in zip(total_grads, inputs, baselines)
)
return attributions
[docs]
def has_convergence_delta(self) -> bool:
return True
@property
def multiplies_by_inputs(self) -> bool:
return self._multiply_by_inputs
