#!/usr/bin/env python3
# pyre-strict
from copy import deepcopy
from inspect import signature
from typing import Any, Callable, cast, Optional, Tuple, Union
import torch
from captum._utils.common import (
_expand_and_update_additional_forward_args,
_expand_and_update_baselines,
_expand_and_update_target,
_format_baseline,
_format_tensor_into_tuples,
)
from captum._utils.typing import TensorOrTupleOfTensorsGeneric
from captum.log import log_usage
from captum.metrics._utils.batching import _divide_and_aggregate_metrics
from torch import Tensor
def default_perturb_func(
inputs: TensorOrTupleOfTensorsGeneric, perturb_radius: float = 0.02
) -> Tuple[Tensor, ...]:
r"""A default function for generating perturbations of `inputs`
within perturbation radius of `perturb_radius`.
This function samples uniformly random from the L_Infinity ball
with `perturb_radius` radius.
The users can override this function if they prefer to use a
different perturbation function.
Args:
inputs (Tensor or tuple[Tensor, ...]): The input tensors that we'd
like to perturb by adding a random noise sampled uniformly
random from an L_infinity ball with a radius `perturb_radius`.
radius (float): A radius used for sampling from
an L_infinity ball.
Returns:
perturbed_input (tuple[Tensor, ...]): A list of perturbed inputs that
are created by adding noise sampled uniformly random
from L_infiniy ball with a radius `perturb_radius` to the
original inputs.
"""
# pyre-fixme[9]: inputs has type `TensorOrTupleOfTensorsGeneric`; used as
# `Tuple[Tensor, ...]`.
inputs = _format_tensor_into_tuples(inputs)
perturbed_input = tuple(
input
+ torch.FloatTensor(input.size()) # type: ignore
.uniform_(-perturb_radius, perturb_radius)
.to(input.device)
for input in inputs
)
return perturbed_input
[docs]
@log_usage()
def sensitivity_max(
# pyre-fixme[24]: Generic type `Callable` expects 2 type parameters.
explanation_func: Callable,
inputs: TensorOrTupleOfTensorsGeneric,
# pyre-fixme[24]: Generic type `Callable` expects 2 type parameters.
perturb_func: Callable = default_perturb_func,
perturb_radius: float = 0.02,
n_perturb_samples: int = 10,
norm_ord: str = "fro",
max_examples_per_batch: Optional[int] = None,
**kwargs: Any,
) -> Tensor:
r"""
Explanation sensitivity measures the extent of explanation change when
the input is slightly perturbed. It has been shown that the models that
have high explanation sensitivity are prone to adversarial attacks:
`Interpretation of Neural Networks is Fragile`
https://www.aaai.org/ojs/index.php/AAAI/article/view/4252
`sensitivity_max` metric measures maximum sensitivity of an explanation
using Monte Carlo sampling-based approximation. By default in order to
do so it samples multiple data points from a sub-space of an L-Infinity
ball that has a `perturb_radius` radius using `default_perturb_func`
default perturbation function. In a general case users can
use any L_p ball or any other custom sampling technique that they
prefer by providing a custom `perturb_func`.
Note that max sensitivity is similar to Lipschitz Continuity metric
however it is more robust and easier to estimate.
Since the explanation, for instance an attribution function,
may not always be continuous, can lead to unbounded
Lipschitz continuity. Therefore the latter isn't always appropriate.
More about the Lipschitz Continuity Metric can also be found here
`On the Robustness of Interpretability Methods`
https://arxiv.org/abs/1806.08049
and
`Towards Robust Interpretability with Self-Explaining Neural Networks`
https://papers.nips.cc/paper\
8003-towards-robust-interpretability-
with-self-explaining-neural-networks.pdf
More details about sensitivity max can be found here:
`On the (In)fidelity and Sensitivity of Explanations`
https://arxiv.org/abs/1901.09392
Args:
explanation_func (Callable):
This function can be the `attribute` method of an
attribution algorithm or any other explanation method
that returns the explanations.
inputs (Tensor or tuple[Tensor, ...]): Input for which
explanations are computed. If `explanation_func` takes a
single tensor as input, a single input tensor should
be provided.
If `explanation_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.
perturb_func (Callable):
The perturbation function of model inputs. This function takes
model inputs and optionally `perturb_radius` if
the function takes more than one argument and returns
perturbed inputs.
If there are more than one inputs passed to sensitivity function those
will be passed to `perturb_func` as tuples in the same order as they
are passed to sensitivity function.
It is important to note that for performance reasons `perturb_func`
isn't called for each example individually but on a batch of
input examples that are repeated `max_examples_per_batch / batch_size`
times within the batch.
Default: default_perturb_func
perturb_radius (float, optional): The epsilon radius used for sampling.
In the `default_perturb_func` it is used as the radius of
the L-Infinity ball. In a general case it can serve as a radius of
any L_p norm.
This argument is passed to `perturb_func` if it takes more than
one argument.
Default: 0.02
n_perturb_samples (int, optional): The number of times input tensors
are perturbed. Each input example in the inputs tensor is
expanded `n_perturb_samples` times before calling
`perturb_func` function.
Default: 10
norm_ord (int, float, or str, optional): The type of norm that is used to
compute the norm of the sensitivity matrix which is defined as the
difference between the explanation function at its input and perturbed
input. Acceptable values are either a string of 'fro' or 'nuc', or a
number in the range of [-inf, inf] (including float("-inf") &
float("inf")).
Default: 'fro'
max_examples_per_batch (int, optional): The number of maximum input
examples that are processed together. In case the number of
examples (`input batch size * n_perturb_samples`) exceeds
`max_examples_per_batch`, they will be sliced
into batches of `max_examples_per_batch` examples and processed
in a sequential order. If `max_examples_per_batch` is None, all
examples are processed together. `max_examples_per_batch` should
at least be equal `input batch size` and at most
`input batch size * n_perturb_samples`.
Default: None
**kwargs (Any, optional): Contains a list of arguments that are passed
to `explanation_func` explanation function which in some cases
could be the `attribute` function of an attribution algorithm.
Any additional arguments that need be passed to the explanation
function should be included here.
For instance, such arguments include:
`additional_forward_args`, `baselines` and `target`.
Returns:
sensitivities (Tensor): A tensor of scalar sensitivity scores per
input example. The first dimension is equal to the
number of examples in the input batch and the second
dimension is one. Returned sensitivities are normalized by
the magnitudes of the input explanations.
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)
>>> # Computes sensitivity score for saliency maps of class 3
>>> sens = sensitivity_max(saliency.attribute, input, target = 3)
"""
def _generate_perturbations(
current_n_perturb_samples: int,
) -> TensorOrTupleOfTensorsGeneric:
r"""
The perturbations are generated for each example
`current_n_perturb_samples` times.
For perfomance reasons we are not calling `perturb_func` on each example but
on a batch that contains `current_n_perturb_samples` repeated instances
per example.
"""
inputs_expanded: Union[Tensor, Tuple[Tensor, ...]] = tuple(
torch.repeat_interleave(input, current_n_perturb_samples, dim=0)
for input in inputs
)
if len(inputs_expanded) == 1:
inputs_expanded = inputs_expanded[0]
return (
perturb_func(inputs_expanded, perturb_radius)
if len(signature(perturb_func).parameters) > 1
else perturb_func(inputs_expanded)
)
def max_values(input_tnsr: Tensor) -> Tensor:
return torch.max(input_tnsr, dim=1).values # type: ignore
kwarg_expanded_for = None
# pyre-fixme[33]: Given annotation cannot be `Any`.
kwargs_copy: Any = None
# pyre-fixme[53]: Captured variable `bsz` is not annotated.
# pyre-fixme[53]: Captured variable `expl_inputs` is not annotated.
def _next_sensitivity_max(current_n_perturb_samples: int) -> Tensor:
inputs_perturbed = _generate_perturbations(current_n_perturb_samples)
# copy kwargs and update some of the arguments that need to be expanded
nonlocal kwarg_expanded_for
nonlocal kwargs_copy
if (
kwarg_expanded_for is None
or kwarg_expanded_for != current_n_perturb_samples
):
kwarg_expanded_for = current_n_perturb_samples
kwargs_copy = deepcopy(kwargs)
_expand_and_update_additional_forward_args(
current_n_perturb_samples, kwargs_copy
)
_expand_and_update_target(current_n_perturb_samples, kwargs_copy)
if "baselines" in kwargs:
baselines = kwargs["baselines"]
baselines = _format_baseline(
baselines, cast(Tuple[Tensor, ...], inputs)
)
if (
isinstance(baselines[0], Tensor)
# pyre-fixme[16]: Item `float` of `Union[float, int, Tensor]`
# has no attribute `shape`.
and baselines[0].shape == inputs[0].shape
):
_expand_and_update_baselines(
cast(Tuple[Tensor, ...], inputs),
current_n_perturb_samples,
kwargs_copy,
)
expl_perturbed_inputs = explanation_func(inputs_perturbed, **kwargs_copy)
# tuplize `expl_perturbed_inputs` in case it is not
expl_perturbed_inputs = _format_tensor_into_tuples(expl_perturbed_inputs)
expl_inputs_expanded = tuple(
expl_input.repeat_interleave(current_n_perturb_samples, dim=0)
for expl_input in expl_inputs
)
sensitivities = torch.cat(
[
(expl_input - expl_perturbed).view(expl_perturbed.size(0), -1)
for expl_perturbed, expl_input in zip(
# pyre-fixme[6]: For 1st argument expected
# `Iterable[Variable[_T1]]` but got `None`.
expl_perturbed_inputs,
expl_inputs_expanded,
)
],
dim=1,
)
# compute the norm of original input explanations
expl_inputs_norm_expanded = torch.norm(
torch.cat(
[expl_input.view(expl_input.size(0), -1) for expl_input in expl_inputs],
dim=1,
),
p=norm_ord,
dim=1,
keepdim=True,
).repeat_interleave(current_n_perturb_samples, dim=0)
expl_inputs_norm_expanded = torch.where(
expl_inputs_norm_expanded == 0.0,
torch.tensor(
1.0,
device=expl_inputs_norm_expanded.device,
dtype=expl_inputs_norm_expanded.dtype,
),
expl_inputs_norm_expanded,
)
# compute the norm for each input noisy example
sensitivities_norm = (
torch.norm(sensitivities, p=norm_ord, dim=1, keepdim=True)
/ expl_inputs_norm_expanded
)
return max_values(sensitivities_norm.view(bsz, -1))
inputs = _format_tensor_into_tuples(inputs) # type: ignore
bsz = inputs[0].size(0)
with torch.no_grad():
expl_inputs = explanation_func(inputs, **kwargs)
metrics_max = _divide_and_aggregate_metrics(
cast(Tuple[Tensor, ...], inputs),
n_perturb_samples,
_next_sensitivity_max,
max_examples_per_batch=max_examples_per_batch,
agg_func=torch.max,
)
return metrics_max
