def visualize(self, attribution, data, contribution_frac) -> FeatureOutput:
attribution = attribution.squeeze(0)
data = data.squeeze(0)
# L-2 norm
l2_norm = attribution.norm()
normalized_attribution = safe_div(attribution,
l2_norm,
default_value=attribution)
modified = [x * 100 for x in normalized_attribution.tolist()]
base = [
f"{c}: {d:.2f}" for c, d in zip(self.categories, data.tolist())
]
return FeatureOutput(
name=self.name,
base=base,
modified=modified,
type=self.visualization_type(),
contribution=contribution_frac,
)
def visualize(self, attribution, data, contribution_frac) -> FeatureOutput:
if self.visualization_transform:
text = self.visualization_transform(data)
else:
text = data
attribution = attribution.squeeze(0)
data = data.squeeze(0)
if len(attribution.shape) > 1:
attribution = attribution.sum(dim=1)
# L-Infinity norm, if norm is 0, all attr elements are 0
attr_max = attribution.abs().max()
normalized_attribution = safe_div(attribution, attr_max)
modified = [x * 100 for x in normalized_attribution.tolist()]
return FeatureOutput(
name=self.name,
base=text,
modified=modified,
type=self.visualization_type(),
contribution=contribution_frac,
)
def infidelity(
forward_func: Callable,
perturb_func: Callable,
inputs: TensorOrTupleOfTensorsGeneric,
attributions: TensorOrTupleOfTensorsGeneric,
baselines: BaselineType = None,
additional_forward_args: Any = None,
target: TargetType = None,
n_perturb_samples: int = 10,
max_examples_per_batch: int = None,
normalize: bool = False,
) -> Tensor:
r"""
Explanation infidelity represents the expected mean-squared error
between the explanation multiplied by a meaningful input perturbation
and the differences between the predictor function at its input
and perturbed input.
More details about the measure can be found in the following paper:
https://arxiv.org/pdf/1901.09392.pdf
It is derived from the completeness property of well-known attribution
algorithms and is a computationally more efficient and generalized
notion of Sensitivy-n. The latter measures correlations between the sum
of the attributions and the differences of the predictor function at
its input and fixed baseline. More details about the Sensitivity-n can
be found here:
https://arxiv.org/pdf/1711.06104.pdfs
The users can perturb the inputs any desired way by providing any
perturbation function that takes the inputs (and optionally baselines)
and returns perturbed inputs or perturbed inputs and corresponding
perturbations.
This specific implementation is primarily tested for attribution-based
explanation methods but the idea can be expanded to use for non
attribution-based interpretability methods as well.
Args:
forward_func (callable):
The forward function of the model or any modification of it.
perturb_func (callable):
The perturbation function of model inputs. This function takes
model inputs and optionally baselines as input arguments and returns
either a tuple of perturbations and perturbed inputs or just
perturbed inputs. For example:
>>> def my_perturb_func(inputs):
>>> <MY-LOGIC-HERE>
>>> return perturbations, perturbed_inputs
If we want to only return perturbed inputs and compute
perturbations internally then we can wrap perturb_func with
`infidelity_perturb_func_decorator` decorator such as:
>>> from captum.metrics import infidelity_perturb_func_decorator
>>> @infidelity_perturb_func_decorator(<multipy_by_inputs flag>)
>>> def my_perturb_func(inputs):
>>> <MY-LOGIC-HERE>
>>> return perturbed_inputs
In case `multipy_by_inputs` is False we compute perturbations by
`input - perturbed_input` difference and in case `multipy_by_inputs`
flag is True we compute it by dividing
(input - perturbed_input) by (input - baselines).
The user needs to only return perturbed inputs in `perturb_func`
as described above.
`infidelity_perturb_func_decorator` needs to be used with
`multipy_by_inputs` flag set to False in case infidelity
score is being computed for attribution maps that are local aka
that do not factor in inputs in the final attribution score.
Such attribution algorithms include Saliency, GradCam, Guided Backprop,
or Integrated Gradients and DeepLift attribution scores that are already
computed with `multipy_by_inputs=False` flag.
If there are more than one inputs passed to infidelity function those
will be passed to `perturb_func` as tuples in the same order as they
are passed to infidelity function.
If inputs
- is a single tensor, the function needs to return a tuple
of perturbations and perturbed input such as:
perturb, perturbed_input and only perturbed_input in case
`infidelity_perturb_func_decorator` is used.
- is a tuple of tensors, corresponding perturbations and perturbed
inputs must be computed and returned as tuples in the
following format:
(perturb1, perturb2, ... perturbN), (perturbed_input1,
perturbed_input2, ... perturbed_inputN)
Similar to previous case here as well we need to return only
perturbed inputs in case `infidelity_perturb_func_decorator`
decorates out `perturb_func`.
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.
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 values 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 of tensors):
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/pdf/1711.06104.pdf
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/pdf/1901.09392.pdf
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.
`infidelity_perturb_func_decorator` function decorator is a helper
function that computes perturbations under the hood if perturbed
inputs are provided.
For more details about how to use `infidelity_perturb_func_decorator`,
please, read the documentation about `perturb_func`
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.
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. This means that these arguments aren't
being passed to `perturb_func` as an input argument.
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 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
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
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
normalize (bool, optional): Normalize the dot product of the input
perturbation and the attribution so the infidelity value is invariant
to constant scaling of the attribution values. The normalization factor
beta is defined as the ratio of two mean values:
$$ \beta = \frac{
\mathbb{E}_{I \sim \mu_I} [ I^T \Phi(f, x) (f(x) - f(x - I)) ]
}{
\mathbb{E}_{I \sim \mu_I} [ (I^T \Phi(f, x))^2 ]
} $$.
Please refer the original paper for the meaning of the symbols. Same
normalization can be found in the paper's official implementation
https://github.com/chihkuanyeh/saliency_evaluation
Default: False
Returns:
infidelities (tensor): A tensor of scalar infidelity scores per
input example. The first dimension is equal to the
number of examples in the input batch and the second
dimension is one.
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 saliency maps for class 3.
>>> attribution = saliency.attribute(input, target=3)
>>> # define a perturbation function for the input
>>> def perturb_fn(inputs):
>>> noise = torch.tensor(np.random.normal(0, 0.003, inputs.shape)).float()
>>> return noise, inputs - noise
>>> # Computes infidelity score for saliency maps
>>> infid = infidelity(net, perturb_fn, input, attribution)
"""
def _generate_perturbations(
current_n_perturb_samples: int,
) -> Tuple[TensorOrTupleOfTensorsGeneric, TensorOrTupleOfTensorsGeneric]:
r"""
The perturbations are generated for each example
`current_n_perturb_samples` times.
For performance reasons we are not calling `perturb_func` on each example but
on a batch that contains `current_n_perturb_samples`
repeated instances per example.
"""
def call_perturb_func():
r""" """
baselines_pert = None
inputs_pert: Union[Tensor, Tuple[Tensor, ...]]
if len(inputs_expanded) == 1:
inputs_pert = inputs_expanded[0]
if baselines_expanded is not None:
baselines_pert = cast(Tuple, baselines_expanded)[0]
else:
inputs_pert = inputs_expanded
baselines_pert = baselines_expanded
return (
perturb_func(inputs_pert, baselines_pert)
if baselines_pert is not None
else perturb_func(inputs_pert)
)
inputs_expanded = tuple(
torch.repeat_interleave(input, current_n_perturb_samples, dim=0)
for input in inputs
)
baselines_expanded = baselines
if baselines is not None:
baselines_expanded = tuple(
baseline.repeat_interleave(current_n_perturb_samples, dim=0)
if isinstance(baseline, torch.Tensor)
and baseline.shape[0] == input.shape[0]
and baseline.shape[0] > 1
else baseline
for input, baseline in zip(inputs, cast(Tuple, baselines))
)
return call_perturb_func()
def _validate_inputs_and_perturbations(
inputs: Tuple[Tensor, ...],
inputs_perturbed: Tuple[Tensor, ...],
perturbations: Tuple[Tensor, ...],
) -> None:
# asserts the sizes of the perturbations and inputs
assert len(perturbations) == len(inputs), (
"""The number of perturbed
inputs and corresponding perturbations must have the same number of
elements. Found number of inputs is: {} and perturbations:
{}"""
).format(len(perturbations), len(inputs))
# asserts the shapes of the perturbations and perturbed inputs
for perturb, input_perturbed in zip(perturbations, inputs_perturbed):
assert perturb[0].shape == input_perturbed[0].shape, (
"""Perturbed input
and corresponding perturbation must have the same shape and
dimensionality. Found perturbation shape is: {} and the input shape
is: {}"""
).format(perturb[0].shape, input_perturbed[0].shape)
def _next_infidelity_tensors(
current_n_perturb_samples: int,
) -> Union[Tuple[Tensor], Tuple[Tensor, Tensor, Tensor]]:
perturbations, inputs_perturbed = _generate_perturbations(
current_n_perturb_samples
)
perturbations = _format_tensor_into_tuples(perturbations)
inputs_perturbed = _format_tensor_into_tuples(inputs_perturbed)
_validate_inputs_and_perturbations(
cast(Tuple[Tensor, ...], inputs),
cast(Tuple[Tensor, ...], inputs_perturbed),
cast(Tuple[Tensor, ...], perturbations),
)
targets_expanded = _expand_target(
target,
current_n_perturb_samples,
expansion_type=ExpansionTypes.repeat_interleave,
)
additional_forward_args_expanded = _expand_additional_forward_args(
additional_forward_args,
current_n_perturb_samples,
expansion_type=ExpansionTypes.repeat_interleave,
)
inputs_perturbed_fwd = _run_forward(
forward_func,
inputs_perturbed,
targets_expanded,
additional_forward_args_expanded,
)
inputs_fwd = _run_forward(forward_func, inputs, target, additional_forward_args)
inputs_fwd = torch.repeat_interleave(
inputs_fwd, current_n_perturb_samples, dim=0
)
perturbed_fwd_diffs = inputs_fwd - inputs_perturbed_fwd
attributions_expanded = tuple(
torch.repeat_interleave(attribution, current_n_perturb_samples, dim=0)
for attribution in attributions
)
attributions_times_perturb = tuple(
(attribution_expanded * perturbation).view(attribution_expanded.size(0), -1)
for attribution_expanded, perturbation in zip(
attributions_expanded, perturbations
)
)
attr_times_perturb_sums = sum(
torch.sum(attribution_times_perturb, dim=1)
for attribution_times_perturb in attributions_times_perturb
)
attr_times_perturb_sums = cast(Tensor, attr_times_perturb_sums)
# reshape as Tensor(bsz, current_n_perturb_samples)
attr_times_perturb_sums = attr_times_perturb_sums.view(bsz, -1)
perturbed_fwd_diffs = perturbed_fwd_diffs.view(bsz, -1)
if normalize:
# in order to normalize, we have to aggregate the following tensors
# to calculate MSE in its polynomial expansion:
# (a-b)^2 = a^2 - 2ab + b^2
return (
attr_times_perturb_sums.pow(2).sum(-1),
(attr_times_perturb_sums * perturbed_fwd_diffs).sum(-1),
perturbed_fwd_diffs.pow(2).sum(-1),
)
else:
# returns (a-b)^2 if no need to normalize
return ((attr_times_perturb_sums - perturbed_fwd_diffs).pow(2).sum(-1),)
def _sum_infidelity_tensors(agg_tensors, tensors):
return tuple(agg_t + t for agg_t, t in zip(agg_tensors, tensors))
# perform argument formattings
inputs = _format_input(inputs) # type: ignore
if baselines is not None:
baselines = _format_baseline(baselines, cast(Tuple[Tensor, ...], inputs))
additional_forward_args = _format_additional_forward_args(additional_forward_args)
attributions = _format_tensor_into_tuples(attributions) # type: ignore
# Make sure that inputs and corresponding attributions have matching sizes.
assert len(inputs) == len(attributions), (
"""The number of tensors in the inputs and
attributions must match. Found number of tensors in the inputs is: {} and in the
attributions: {}"""
).format(len(inputs), len(attributions))
for inp, attr in zip(inputs, attributions):
assert inp.shape == attr.shape, (
"""Inputs and attributions must have
matching shapes. One of the input tensor's shape is {} and the
attribution tensor's shape is: {}"""
).format(inp.shape, attr.shape)
bsz = inputs[0].size(0)
with torch.no_grad():
# if not normalize, directly return aggrgated MSE ((a-b)^2,)
# else return aggregated MSE's polynomial expansion tensors (a^2, ab, b^2)
agg_tensors = _divide_and_aggregate_metrics(
cast(Tuple[Tensor, ...], inputs),
n_perturb_samples,
_next_infidelity_tensors,
agg_func=_sum_infidelity_tensors,
max_examples_per_batch=max_examples_per_batch,
)
if normalize:
beta_num = agg_tensors[1]
beta_denorm = agg_tensors[0]
beta = safe_div(
beta_num,
beta_denorm,
torch.tensor(1.0, dtype=beta_denorm.dtype, device=beta_denorm.device),
)
infidelity_values = (
beta ** 2 * agg_tensors[0] - 2 * beta * agg_tensors[1] + agg_tensors[2]
)
else:
infidelity_values = agg_tensors[0]
infidelity_values /= n_perturb_samples
return infidelity_values
def test_safe_div_number_denom(self):
num = torch.tensor(4.0)
assert safe_div(num, 2) == 2.0
assert safe_div(num, 0, 2) == 2.0
assert safe_div(num, 2.0) == 2.0
assert safe_div(num, 0.0, 2.0) == 2.0