def attribute( # type: ignore
self,
inputs: TensorOrTupleOfTensorsGeneric,
baselines: BaselineType = None,
target: TargetType = None,
additional_forward_args: Any = None,
return_convergence_delta: bool = False,
) -> Union[TensorOrTupleOfTensorsGeneric, Tuple[
TensorOrTupleOfTensorsGeneric, Tensor]]:
# Keeps track whether original input is a tuple or not before
# converting it into a tuple.
is_inputs_tuple = _is_tuple(inputs)
inputs, baselines = _format_input_baseline(inputs, baselines)
rand_coefficient = torch.tensor(
np.random.uniform(0.0, 1.0, inputs[0].shape[0]),
device=inputs[0].device,
dtype=inputs[0].dtype,
)
input_baseline_scaled = tuple(
_scale_input(input, baseline, rand_coefficient)
for input, baseline in zip(inputs, baselines))
grads = self.gradient_func(self.forward_func, input_baseline_scaled,
target, additional_forward_args)
if self.multiplies_by_inputs:
input_baseline_diffs = tuple(
input - baseline for input, baseline in zip(inputs, baselines))
attributions = tuple(input_baseline_diff * grad
for input_baseline_diff, grad in zip(
input_baseline_diffs, grads))
else:
attributions = grads
return _compute_conv_delta_and_format_attrs(
self,
return_convergence_delta,
attributions,
baselines,
inputs,
additional_forward_args,
target,
is_inputs_tuple,
)
def _lime_test_assert(
self,
model: Callable,
test_input: TensorOrTupleOfTensorsGeneric,
expected_attr,
expected_coefs_only=None,
feature_mask: Union[None, TensorOrTupleOfTensorsGeneric] = None,
additional_input: Any = None,
perturbations_per_eval: Tuple[int, ...] = (1, ),
baselines: BaselineType = None,
target: Union[None, int] = 0,
n_perturb_samples: int = 100,
alpha: float = 1.0,
delta: float = 1.0,
batch_attr: bool = False,
) -> None:
for batch_size in perturbations_per_eval:
lime = Lime(
model,
similarity_func=get_exp_kernel_similarity_function(
"cosine", 10.0),
)
attributions = lime.attribute(
test_input,
target=target,
feature_mask=feature_mask,
additional_forward_args=additional_input,
baselines=baselines,
perturbations_per_eval=batch_size,
n_perturb_samples=n_perturb_samples,
alpha=alpha,
)
assertTensorTuplesAlmostEqual(self,
attributions,
expected_attr,
delta=delta,
mode="max")
if expected_coefs_only is not None:
# Test with return_input_shape = False
attributions = lime.attribute(
test_input,
target=target,
feature_mask=feature_mask,
additional_forward_args=additional_input,
baselines=baselines,
perturbations_per_eval=batch_size,
n_perturb_samples=n_perturb_samples,
alpha=alpha,
return_input_shape=False,
)
assertTensorAlmostEqual(self,
attributions,
expected_coefs_only,
delta=delta,
mode="max")
lime_alt = LimeBase(
model,
lasso_interpretable_model_trainer,
get_exp_kernel_similarity_function("euclidean", 1000.0),
alt_perturb_func,
False,
None,
alt_to_interp_rep,
)
# Test with equivalent sampling in original input space
formatted_inputs, baselines = _format_input_baseline(
test_input, baselines)
if feature_mask is None:
(
formatted_feature_mask,
num_interp_features,
) = _construct_default_feature_mask(formatted_inputs)
else:
formatted_feature_mask = _format_input(feature_mask)
num_interp_features = int(
max(
torch.max(single_inp).item()
for single_inp in feature_mask) + 1)
if batch_attr:
attributions = lime_alt.attribute(
test_input,
target=target,
feature_mask=formatted_feature_mask if isinstance(
test_input, tuple) else formatted_feature_mask[0],
additional_forward_args=additional_input,
baselines=baselines,
perturbations_per_eval=batch_size,
n_perturb_samples=n_perturb_samples,
alpha=alpha,
num_interp_features=num_interp_features,
)
assertTensorAlmostEqual(self,
attributions,
expected_coefs_only,
delta=delta,
mode="max")
return
bsz = formatted_inputs[0].shape[0]
for (
curr_inps,
curr_target,
curr_additional_args,
curr_baselines,
curr_feature_mask,
expected_coef_single,
) in _batch_example_iterator(
bsz,
test_input,
target,
additional_input,
baselines
if isinstance(test_input, tuple) else baselines[0],
formatted_feature_mask if isinstance(
test_input, tuple) else formatted_feature_mask[0],
expected_coefs_only,
):
attributions = lime_alt.attribute(
curr_inps,
target=curr_target,
feature_mask=curr_feature_mask,
additional_forward_args=curr_additional_args,
baselines=curr_baselines,
perturbations_per_eval=batch_size,
n_perturb_samples=n_perturb_samples,
alpha=alpha,
num_interp_features=num_interp_features,
)
assertTensorAlmostEqual(
self,
attributions,
expected_coef_single,
delta=delta,
mode="max",
)
def attribute( # type: ignore
self,
inputs: TensorOrTupleOfTensorsGeneric,
baselines: BaselineType = None,
target: TargetType = None,
additional_forward_args: Any = None,
feature_mask: Union[None, Tensor, Tuple[Tensor, ...]] = None,
n_samples: int = 25,
perturbations_per_eval: int = 1,
return_input_shape: bool = True,
) -> TensorOrTupleOfTensorsGeneric:
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,
training an interpretable model based on KernelSHAP and returning a
representation of the interpretable model.
It is recommended to only provide a single example as input (tensors
with first dimension or batch size = 1). This is because LIME / KernelShap
is generally used for sample-based interpretability, training a separate
interpretable model to explain a model's prediction on each individual example.
A batch of inputs can also be provided as inputs, similar to
other perturbation-based attribution methods. In this case, if forward_fn
returns a scalar per example, attributions will be computed for each
example independently, with a separate interpretable model trained for each
example. Note that provided similarity and perturbation functions will be
provided each example separately (first dimension = 1) in this case.
If forward_fn returns a scalar per batch (e.g. loss), attributions will
still be computed using a single interpretable model for the full batch.
In this case, similarity and perturbation functions will be provided the
same original input containing the full batch.
The number of interpretable features is determined from the provided
feature mask, or if none is provided, from the default feature mask,
which considers each scalar input as a separate feature. It is
generally recommended to provide a feature mask which groups features
into a small number of interpretable features / components (e.g.
superpixels in images).
Args:
inputs (tensor or tuple of tensors): Input for which KernelShap
is 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 scalars or tensors, optional):
Baselines define the reference value which replaces each
feature when the corresponding interpretable feature
is set to 0.
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 surrogate model is trained
(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
feature_mask (tensor or tuple of tensors, optional):
feature_mask defines a mask for the input, grouping
features which correspond to the same
interpretable feature. feature_mask
should contain the same number of tensors as inputs.
Each tensor should
be the same size as the corresponding input or
broadcastable to match the input tensor. Values across
all tensors should be integers in the range 0 to
num_interp_features - 1, and indices corresponding to the
same feature should have the same value.
Note that features are grouped across tensors
(unlike feature ablation and occlusion), so
if the same index is used in different tensors, those
features are still grouped and added simultaneously.
If None, then a feature mask is constructed which assigns
each scalar within a tensor as a separate feature.
Default: None
n_samples (int, optional): The number of samples of the original
model used to train the surrogate interpretable model.
Default: `50` if `n_samples` is not provided.
perturbations_per_eval (int, optional): Allows multiple samples
to be processed simultaneously in one call to forward_fn.
Each forward pass will contain a maximum of
perturbations_per_eval * #examples samples.
For DataParallel models, each batch is split among the
available devices, so evaluations on each available
device contain at most
(perturbations_per_eval * #examples) / num_devices
samples.
If the forward function returns a single scalar per batch,
perturbations_per_eval must be set to 1.
Default: 1
return_input_shape (bool, optional): Determines whether the returned
tensor(s) only contain the coefficients for each interp-
retable feature from the trained surrogate model, or
whether the returned attributions match the input shape.
When return_input_shape is True, the return type of attribute
matches the input shape, with each element containing the
coefficient of the corresponding interpretable feature.
All elements with the same value in the feature mask
will contain the same coefficient in the returned
attributions. If return_input_shape is False, a 1D
tensor is returned, containing only the coefficients
of the trained interpretable model, with length
num_interp_features.
Returns:
*tensor* or tuple of *tensors* of **attributions**:
- **attributions** (*tensor* or tuple of *tensors*):
The attributions with respect to each input feature.
If return_input_shape = True, attributions will be
the same size as the provided inputs, with each value
providing the coefficient of the corresponding
interpretale feature.
If return_input_shape is False, a 1D
tensor is returned, containing only the coefficients
of the trained interpreatable models, with length
num_interp_features.
Examples::
>>> # SimpleClassifier takes a single input tensor of size Nx4x4,
>>> # and returns an Nx3 tensor of class probabilities.
>>> net = SimpleClassifier()
>>> # Generating random input with size 1 x 4 x 4
>>> input = torch.randn(1, 4, 4)
>>> # Defining KernelShap interpreter
>>> ks = KernelShap(net)
>>> # Computes attribution, with each of the 4 x 4 = 16
>>> # features as a separate interpretable feature
>>> attr = ks.attribute(input, target=1, n_samples=200)
>>> # Alternatively, we can group each 2x2 square of the inputs
>>> # as one 'interpretable' feature and perturb them together.
>>> # This can be done by creating a feature mask as follows, which
>>> # defines the feature groups, e.g.:
>>> # +---+---+---+---+
>>> # | 0 | 0 | 1 | 1 |
>>> # +---+---+---+---+
>>> # | 0 | 0 | 1 | 1 |
>>> # +---+---+---+---+
>>> # | 2 | 2 | 3 | 3 |
>>> # +---+---+---+---+
>>> # | 2 | 2 | 3 | 3 |
>>> # +---+---+---+---+
>>> # With this mask, all inputs with the same value are set to their
>>> # baseline value, when the corresponding binary interpretable
>>> # feature is set to 0.
>>> # The attributions can be calculated as follows:
>>> # feature mask has dimensions 1 x 4 x 4
>>> feature_mask = torch.tensor([[[0,0,1,1],[0,0,1,1],
>>> [2,2,3,3],[2,2,3,3]]])
>>> # Computes KernelSHAP attributions with feature mask.
>>> attr = ks.attribute(input, target=1, feature_mask=feature_mask)
"""
formatted_inputs, baselines = _format_input_baseline(inputs, baselines)
feature_mask, num_interp_features = construct_feature_mask(
feature_mask, formatted_inputs)
num_features_list = torch.arange(num_interp_features,
dtype=torch.float)
denom = num_features_list * (num_interp_features - num_features_list)
probs = (num_interp_features - 1) / denom
probs[0] = 0.0
return self._attribute_kwargs(
inputs=inputs,
baselines=baselines,
target=target,
additional_forward_args=additional_forward_args,
feature_mask=feature_mask,
n_samples=n_samples,
perturbations_per_eval=perturbations_per_eval,
return_input_shape=return_input_shape,
num_select_distribution=Categorical(probs),
)
def attribute(
self,
inputs: Union[Tensor, Tuple[Tensor, ...]],
baselines: Optional[
Union[Tensor, int, float, Tuple[Union[Tensor, int, float], ...]]
] = None,
target: Optional[
Union[int, Tuple[int, ...], Tensor, List[Tuple[int, ...]]]
] = None,
additional_forward_args: Any = None,
n_steps: int = 50,
method: str = "gausslegendre",
internal_batch_size: Optional[int] = None,
return_convergence_delta: bool = False,
attribute_to_layer_input: bool = False,
) -> Union[
Tensor, Tuple[Tensor, ...], Tuple[Union[Tensor, Tuple[Tensor, ...]], 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 layer inputs or outputs of the model, depending on whether
`attribute_to_layer_input` is set to True or False, 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 of tensors): Input for which layer 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 scalars or tensors, 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 (string, 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 internal_batch_size,
which are computed (forward / backward passes)
sequentially.
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
attribute_to_layer_input (bool, optional): Indicates whether to
compute the attribution with respect to the layer input
or output. If `attribute_to_layer_input` is set to True
then the attributions will be computed with respect to
layer input, otherwise it will be computed with respect
to layer output.
Note that currently it is assumed that either the input
or the output of internal layer, depending on whether we
attribute to the input or output, is a single tensor.
Support for multiple tensors will be added later.
Default: False
Returns:
**attributions** or 2-element tuple of **attributions**, **delta**:
- **attributions** (*tensor* or tuple of *tensors*):
Integrated gradients with respect to `layer`'s inputs or
outputs. Attributions will always be the same size and
dimensionality as the input or output of the given layer,
depending on whether we attribute to the inputs or outputs
of the layer which is decided by the input flag
`attribute_to_layer_input`.
- **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
of examples in inputs.
Examples::
>>> # ImageClassifier takes a single input tensor of images Nx3x32x32,
>>> # and returns an Nx10 tensor of class probabilities.
>>> # It contains an attribute conv1, which is an instance of nn.conv2d,
>>> # and the output of this layer has dimensions Nx12x32x32.
>>> net = ImageClassifier()
>>> lig = LayerIntegratedGradients(net, net.conv1)
>>> input = torch.randn(2, 3, 32, 32, requires_grad=True)
>>> # Computes layer integrated gradients for class 3.
>>> # attribution size matches layer output, Nx12x32x32
>>> attribution = lig.attribute(input, target=3)
"""
inps, baselines = _format_input_baseline(inputs, baselines)
_validate_input(inps, baselines, n_steps, method)
baselines = _tensorize_baseline(inps, baselines)
additional_forward_args = _format_additional_forward_args(
additional_forward_args
)
if self.device_ids is None:
self.device_ids = getattr(self.forward_func, "device_ids", None)
inputs_layer, is_layer_tuple = _forward_layer_eval(
self.forward_func,
inps,
self.layer,
device_ids=self.device_ids,
additional_forward_args=additional_forward_args,
attribute_to_layer_input=attribute_to_layer_input,
)
baselines_layer, _ = _forward_layer_eval(
self.forward_func,
baselines,
self.layer,
device_ids=self.device_ids,
additional_forward_args=additional_forward_args,
attribute_to_layer_input=attribute_to_layer_input,
)
# inputs -> these inputs are scaled
def gradient_func(
forward_fn: Callable,
inputs: Union[Tensor, Tuple[Tensor, ...]],
target_ind: Optional[
Union[int, Tuple[int, ...], Tensor, List[Tuple[int, ...]]]
] = None,
additional_forward_args: Any = None,
) -> Tuple[Tensor, ...]:
if self.device_ids is None:
scattered_inputs = (inputs,)
else:
# scatter method does not have a precise enough return type in its
# stub, so suppress the type warning.
scattered_inputs = scatter( # type:ignore
inputs, target_gpus=self.device_ids
)
scattered_inputs_dict = {
scattered_input[0].device: scattered_input
for scattered_input in scattered_inputs
}
with torch.autograd.set_grad_enabled(True):
def layer_forward_hook(module, hook_inputs, hook_outputs=None):
device = _extract_device(module, hook_inputs, hook_outputs)
if is_layer_tuple:
return scattered_inputs_dict[device]
return scattered_inputs_dict[device][0]
if attribute_to_layer_input:
hook = self.layer.register_forward_pre_hook(layer_forward_hook)
else:
hook = self.layer.register_forward_hook(layer_forward_hook)
output = _run_forward(
self.forward_func, additional_forward_args, target_ind,
)
hook.remove()
assert output[0].numel() == 1, (
"Target not provided when necessary, cannot"
" take gradient with respect to multiple outputs."
)
# torch.unbind(forward_out) is a list of scalar tensor tuples and
# contains batch_size * #steps elements
grads = torch.autograd.grad(torch.unbind(output), inputs)
return grads
self.ig.gradient_func = gradient_func
all_inputs = (
(inps + additional_forward_args)
if additional_forward_args is not None
else inps
)
attributions = self.ig.attribute(
inputs_layer,
baselines=baselines_layer,
target=target,
additional_forward_args=all_inputs,
n_steps=n_steps,
method=method,
internal_batch_size=internal_batch_size,
return_convergence_delta=False,
)
if return_convergence_delta:
start_point, end_point = baselines, inps
# 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,
)
return _format_attributions(is_layer_tuple, attributions), delta
return _format_attributions(is_layer_tuple, attributions)
def attribute( # type: ignore
self,
inputs: Union[Tensor, Tuple[Tensor, ...]],
baselines: Union[Tensor, Tuple[Tensor, ...]],
target: TargetType = None,
additional_forward_args: Any = None,
return_convergence_delta: bool = False,
attribute_to_layer_input: bool = False,
) -> Union[Tensor, Tuple[Tensor, ...], Tuple[Union[Tensor, Tuple[
Tensor, ...]], Tensor]]:
inputs, baselines = _format_input_baseline(inputs, baselines)
rand_coefficient = torch.tensor(
np.random.uniform(0.0, 1.0, inputs[0].shape[0]),
device=inputs[0].device,
dtype=inputs[0].dtype,
)
input_baseline_scaled = tuple(
_scale_input(input, baseline, rand_coefficient)
for input, baseline in zip(inputs, baselines))
grads, _ = compute_layer_gradients_and_eval(
self.forward_func,
self.layer,
input_baseline_scaled,
target,
additional_forward_args,
device_ids=self.device_ids,
attribute_to_layer_input=attribute_to_layer_input,
)
attr_baselines = _forward_layer_eval(
self.forward_func,
baselines,
self.layer,
additional_forward_args=additional_forward_args,
device_ids=self.device_ids,
attribute_to_layer_input=attribute_to_layer_input,
)
attr_inputs = _forward_layer_eval(
self.forward_func,
inputs,
self.layer,
additional_forward_args=additional_forward_args,
device_ids=self.device_ids,
attribute_to_layer_input=attribute_to_layer_input,
)
if self.multiplies_by_inputs:
input_baseline_diffs = tuple(
input - baseline
for input, baseline in zip(attr_inputs, attr_baselines))
attributions = tuple(input_baseline_diff * grad
for input_baseline_diff, grad in zip(
input_baseline_diffs, grads))
else:
attributions = grads
return _compute_conv_delta_and_format_attrs(
self,
return_convergence_delta,
attributions,
baselines,
inputs,
additional_forward_args,
target,
cast(Union[Literal[True], Literal[False]],
len(attributions) > 1),
)
def attribute(
self,
inputs: TensorOrTupleOfTensorsGeneric,
neuron_selector: Union[int, Tuple[int, ...], Callable],
baselines: BaselineType = None,
target: TargetType = None,
additional_forward_args: Any = None,
n_steps: int = 50,
method: str = "riemann_trapezoid",
internal_batch_size: Union[None, int] = None,
attribute_to_neuron_input: bool = False,
) -> TensorOrTupleOfTensorsGeneric:
r"""
Args:
inputs (tensor or tuple of tensors): Input for which neuron
conductance is 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.
neuron_selector (int, callable, or tuple of ints or slices):
Selector for neuron
in given layer for which attribution is desired.
Neuron selector can be provided as:
- a single integer, if the layer output is 2D. This integer
selects the appropriate neuron column in the layer input
or output
- a tuple of integers. Length of this
tuple must be one less than the number of dimensions
in the input / output of the given layer (since
dimension 0 corresponds to number of examples).
This can be used as long as the layer input / output
is a single tensor.
- a callable, which should
take the target layer as input (single tensor or tuple
if multiple tensors are in layer) and return a selected
neuron - output shape should be 1D with length equal to
batch_size (one scalar per input example)
NOTE: Callables applicable for neuron conductance are
less general than those of other methods and should
NOT aggregate values of the layer, only return a specific
output. This option should only be used in cases where the
layer input / output is a tuple of tensors, where the other
options would not suffice. This limitation is necessary since
neuron conductance, unlike other neuron methods, also utilizes
the gradient of output with respect to the intermedite neuron,
which cannot be computed for aggregations of multiple
intemediate neurons.
baselines (scalar, tensor, tuple of scalars or tensors, 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 (string, 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
attribute_to_neuron_input (bool, optional): Indicates whether to
compute the attributions with respect to the neuron input
or output. If `attribute_to_neuron_input` is set to True
then the attributions will be computed with respect to
neuron's inputs, otherwise it will be computed with respect
to neuron's outputs.
Note that currently it is assumed that either the input
or the output of internal neuron, depending on whether we
attribute to the input or output, is a single tensor.
Support for multiple tensors will be added later.
Default: False
Returns:
*tensor* or tuple of *tensors* of **attributions**:
- **attributions** (*tensor* or tuple of *tensors*):
Conductance for
particular neuron 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.
Examples::
>>> # ImageClassifier takes a single input tensor of images Nx3x32x32,
>>> # and returns an Nx10 tensor of class probabilities.
>>> # It contains an attribute conv1, which is an instance of nn.conv2d,
>>> # and the output of this layer has dimensions Nx12x32x32.
>>> net = ImageClassifier()
>>> neuron_cond = NeuronConductance(net, net.conv1)
>>> input = torch.randn(2, 3, 32, 32, requires_grad=True)
>>> # To compute neuron attribution, we need to provide the neuron
>>> # index for which attribution is desired. Since the layer output
>>> # is Nx12x32x32, we need a tuple in the form (0..11,0..31,0..31)
>>> # which indexes a particular neuron in the layer output.
>>> # Computes neuron conductance for neuron with
>>> # index (4,1,2).
>>> attribution = neuron_cond.attribute(input, (4,1,2))
"""
if callable(neuron_selector):
warnings.warn(
"The neuron_selector provided is a callable. Please ensure that this"
" function only selects neurons from the given layer; aggregating"
" or performing other operations on the tensor may lead to inaccurate"
" results.")
is_inputs_tuple = _is_tuple(inputs)
inputs, baselines = _format_input_baseline(inputs, baselines)
_validate_input(inputs, baselines, n_steps, method)
num_examples = inputs[0].shape[0]
if internal_batch_size is not None:
num_examples = inputs[0].shape[0]
attrs = _batch_attribution(
self,
num_examples,
internal_batch_size,
n_steps,
inputs=inputs,
baselines=baselines,
neuron_selector=neuron_selector,
target=target,
additional_forward_args=additional_forward_args,
method=method,
attribute_to_neuron_input=attribute_to_neuron_input,
)
else:
attrs = self._attribute(
inputs=inputs,
neuron_selector=neuron_selector,
baselines=baselines,
target=target,
additional_forward_args=additional_forward_args,
n_steps=n_steps,
method=method,
attribute_to_neuron_input=attribute_to_neuron_input,
)
return _format_output(is_inputs_tuple, attrs)
def attribute(
self,
inputs: Union[Tensor, Tuple[Tensor, ...]],
baselines: BaselineType = None,
target: TargetType = None,
additional_forward_args: Any = None,
n_steps: int = 50,
method: str = "gausslegendre",
internal_batch_size: Union[None, int] = None,
attribute_to_layer_input: bool = False,
) -> Union[Tensor, Tuple[Tensor, ...]]:
r"""
Args:
inputs (tensor or tuple of tensors): Input for which internal
influence is 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 scalars or tensors, optional):
Baselines define a 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 (string, 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
attribute_to_layer_input (bool, optional): Indicates whether to
compute the attribution with respect to the layer input
or output. If `attribute_to_layer_input` is set to True
then the attributions will be computed with respect to
layer inputs, otherwise it will be computed with respect
to layer outputs.
Note that currently it is assumed that either the input
or the output of internal layer, depending on whether we
attribute to the input or output, is a single tensor.
Support for multiple tensors will be added later.
Default: False
Returns:
*tensor* or tuple of *tensors* of **attributions**:
- **attributions** (*tensor* or tuple of *tensors*):
Internal influence of each neuron in given
layer output. Attributions will always be the same size
as the output or input of the given layer depending on
whether `attribute_to_layer_input` is set to `False` or
`True`respectively.
Attributions are returned in a tuple if
the layer inputs / outputs contain multiple tensors,
otherwise a single tensor is returned.
Examples::
>>> # ImageClassifier takes a single input tensor of images Nx3x32x32,
>>> # and returns an Nx10 tensor of class probabilities.
>>> # It contains an attribute conv1, which is an instance of nn.conv2d,
>>> # and the output of this layer has dimensions Nx12x32x32.
>>> net = ImageClassifier()
>>> layer_int_inf = InternalInfluence(net, net.conv1)
>>> input = torch.randn(2, 3, 32, 32, requires_grad=True)
>>> # Computes layer internal influence.
>>> # attribution size matches layer output, Nx12x32x32
>>> attribution = layer_int_inf.attribute(input)
"""
inputs, baselines = _format_input_baseline(inputs, baselines)
_validate_input(inputs, baselines, n_steps, method)
if internal_batch_size is not None:
num_examples = inputs[0].shape[0]
attrs = _batch_attribution(
self,
num_examples,
internal_batch_size,
n_steps,
inputs=inputs,
baselines=baselines,
target=target,
additional_forward_args=additional_forward_args,
method=method,
attribute_to_layer_input=attribute_to_layer_input,
)
else:
attrs = self._attribute(
inputs=inputs,
baselines=baselines,
target=target,
additional_forward_args=additional_forward_args,
n_steps=n_steps,
method=method,
attribute_to_layer_input=attribute_to_layer_input,
)
return attrs
def attribute(
self,
inputs: TensorOrTupleOfTensorsGeneric,
baselines: BaselineType = None,
target: TargetType = None,
additional_forward_args: Any = None,
feature_mask: Union[None, Tensor, Tuple[Tensor, ...]] = None,
perturbations_per_eval: int = 1,
**kwargs: Any
) -> TensorOrTupleOfTensorsGeneric:
r"""
Args:
inputs (tensor or tuple of tensors): Input for which ablation
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 value which replaces each
feature when ablated.
Baselines can be provided as:
- a single tensor, if inputs is a single tensor, with
exactly the same dimensions as inputs or
broadcastable to match the dimensions of 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. 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
feature_mask (tensor or tuple of tensors, optional):
feature_mask defines a mask for the input, grouping
features which should be ablated together. feature_mask
should contain the same number of tensors as inputs.
Each tensor should
be the same size as the corresponding input or
broadcastable to match the input tensor. Each tensor
should contain integers in the range 0 to num_features
- 1, and indices corresponding to the same feature should
have the same value.
Note that features within each input tensor are ablated
independently (not across tensors).
If the forward function returns a single scalar per batch,
we enforce that the first dimension of each mask must be 1,
since attributions are returned batch-wise rather than per
example, so the attributions must correspond to the
same features (indices) in each input example.
If None, then a feature mask is constructed which assigns
each scalar within a tensor as a separate feature, which
is ablated independently.
Default: None
perturbations_per_eval (int, optional): Allows ablation of multiple
features to be processed simultaneously in one call to
forward_fn.
Each forward pass will contain a maximum of
perturbations_per_eval * #examples samples.
For DataParallel models, each batch is split among the
available devices, so evaluations on each available
device contain at most
(perturbations_per_eval * #examples) / num_devices
samples.
If the forward function's number of outputs does not
change as the batch size grows (e.g. if it outputs a
scalar value), you must set perturbations_per_eval to 1
and use a single feature mask to describe the features
for all examples in the batch.
Default: 1
**kwargs (Any, optional): Any additional arguments used by child
classes of FeatureAblation (such as Occlusion) to construct
ablations. These arguments are ignored when using
FeatureAblation directly.
Default: None
Returns:
*tensor* or tuple of *tensors* of **attributions**:
- **attributions** (*tensor* or tuple of *tensors*):
The attributions with respect to each input feature.
If the forward function returns
a scalar value per example, attributions will be
the same size as the provided inputs, with each value
providing the attribution of the corresponding input index.
If the forward function returns a scalar per batch, then
attribution tensor(s) will have first dimension 1 and
the remaining dimensions will match the input.
If a single tensor is provided as inputs, a single tensor is
returned. If a tuple of tensors is provided for inputs, a
tuple of corresponding sized tensors is returned.
Examples::
>>> # SimpleClassifier takes a single input tensor of size Nx4x4,
>>> # and returns an Nx3 tensor of class probabilities.
>>> net = SimpleClassifier()
>>> # Generating random input with size 2 x 4 x 4
>>> input = torch.randn(2, 4, 4)
>>> # Defining FeatureAblation interpreter
>>> ablator = FeatureAblation(net)
>>> # Computes ablation attribution, ablating each of the 16
>>> # scalar input independently.
>>> attr = ablator.attribute(input, target=1)
>>> # Alternatively, we may want to ablate features in groups, e.g.
>>> # grouping each 2x2 square of the inputs and ablating them together.
>>> # This can be done by creating a feature mask as follows, which
>>> # defines the feature groups, e.g.:
>>> # +---+---+---+---+
>>> # | 0 | 0 | 1 | 1 |
>>> # +---+---+---+---+
>>> # | 0 | 0 | 1 | 1 |
>>> # +---+---+---+---+
>>> # | 2 | 2 | 3 | 3 |
>>> # +---+---+---+---+
>>> # | 2 | 2 | 3 | 3 |
>>> # +---+---+---+---+
>>> # With this mask, all inputs with the same value are ablated
>>> # simultaneously, and the attribution for each input in the same
>>> # group (0, 1, 2, and 3) per example are the same.
>>> # The attributions can be calculated as follows:
>>> # feature mask has dimensions 1 x 4 x 4
>>> feature_mask = torch.tensor([[[0,0,1,1],[0,0,1,1],
>>> [2,2,3,3],[2,2,3,3]]])
>>> attr = ablator.attribute(input, target=1, feature_mask=feature_mask)
"""
# Keeps track whether original input is a tuple or not before
# converting it into a tuple.
is_inputs_tuple = _is_tuple(inputs)
inputs, baselines = _format_input_baseline(inputs, baselines)
additional_forward_args = _format_additional_forward_args(
additional_forward_args
)
num_examples = inputs[0].shape[0]
feature_mask = _format_input(feature_mask) if feature_mask is not None else None
assert (
isinstance(perturbations_per_eval, int) and perturbations_per_eval >= 1
), "Perturbations per evaluation must be an integer and at least 1."
with torch.no_grad():
# Computes initial evaluation with all features, which is compared
# to each ablated result.
initial_eval = _run_forward(
self.forward_func, inputs, target, additional_forward_args
)
agg_output_mode = FeatureAblation._find_output_mode(
perturbations_per_eval, feature_mask
)
# get as a 2D tensor (if it is not a scalar)
if isinstance(initial_eval, torch.Tensor):
initial_eval = initial_eval.reshape(1, -1)
num_outputs = initial_eval.shape[1]
else:
num_outputs = 1
if not agg_output_mode:
assert (
isinstance(initial_eval, torch.Tensor)
and num_outputs == num_examples
), (
"expected output of `forward_func` to have "
+ "`batch_size` elements for perturbations_per_eval > 1 "
+ "and all feature_mask.shape[0] > 1"
)
# Initialize attribution totals and counts
attrib_type = cast(
dtype,
initial_eval.dtype
if isinstance(initial_eval, Tensor)
else type(initial_eval),
)
total_attrib = [
torch.zeros(
(num_outputs,) + input.shape[1:],
dtype=attrib_type,
device=input.device,
)
for input in inputs
]
# Weights are used in cases where ablations may be overlapping.
if self.use_weights:
weights = [
torch.zeros(
(num_outputs,) + input.shape[1:], device=input.device
).float()
for input in inputs
]
# Iterate through each feature tensor for ablation
for i in range(len(inputs)):
# Skip any empty input tensors
if torch.numel(inputs[i]) == 0:
continue
for (
current_inputs,
current_add_args,
current_target,
current_mask,
) in self._ablation_generator(
i,
inputs,
additional_forward_args,
target,
baselines,
feature_mask,
perturbations_per_eval,
**kwargs
):
# modified_eval dimensions: 1D tensor with length
# equal to #num_examples * #features in batch
modified_eval = _run_forward(
self.forward_func,
current_inputs,
current_target,
current_add_args,
)
# (contains 1 more dimension than inputs). This adds extra
# dimensions of 1 to make the tensor broadcastable with the inputs
# tensor.
if not isinstance(modified_eval, torch.Tensor):
eval_diff = initial_eval - modified_eval
else:
if not agg_output_mode:
assert (
modified_eval.numel() == current_inputs[0].shape[0]
), """expected output of forward_func to grow with
batch_size. If this is not the case for your model
please set perturbations_per_eval = 1"""
eval_diff = (
initial_eval - modified_eval.reshape((-1, num_outputs))
).reshape((-1, num_outputs) + (len(inputs[i].shape) - 1) * (1,))
if self.use_weights:
weights[i] += current_mask.float().sum(dim=0)
total_attrib[i] += (eval_diff * current_mask.to(attrib_type)).sum(
dim=0
)
# Divide total attributions by counts and return formatted attributions
if self.use_weights:
attrib = tuple(
single_attrib.float() / weight
for single_attrib, weight in zip(total_attrib, weights)
)
else:
attrib = tuple(total_attrib)
_result = _format_output(is_inputs_tuple, attrib)
return _result
def compute_convergence_delta(
self,
attributions: Union[Tensor, Tuple[Tensor, ...]],
start_point: Union[None, int, float, Tensor,
Tuple[Union[int, float, Tensor], ...]],
end_point: Union[Tensor, Tuple[Tensor, ...]],
target: TargetType = None,
additional_forward_args: Any = None,
) -> Tensor:
r"""
Here we provide a specific implementation for `compute_convergence_delta`
which is based on a common property among gradient-based attribution algorithms.
In the literature sometimes it is also called completeness axiom. Completeness
axiom states that the sum of the attribution must be equal to the differences of
NN Models's function at its end and start points. In other words:
sum(attributions) - (F(end_point) - F(start_point)) is close to zero.
Returned delta of this method is defined as above stated difference.
This implementation assumes that both the `start_point` and `end_point` have
the same shape and dimensionality. It also assumes that the target must have
the same number of examples as the `start_point` and the `end_point` in case
it is provided in form of a list or a non-singleton tensor.
Args:
attributions (tensor or tuple of tensors): Precomputed attribution
scores. The user can compute those using any attribution
algorithm. It is assumed the the shape and the
dimensionality of attributions must match the shape and
the dimensionality of `start_point` and `end_point`.
It also assumes that the attribution tensor's
dimension 0 corresponds to the number of
examples, and if multiple input tensors are provided,
the examples must be aligned appropriately.
start_point (tensor or tuple of tensors, optional): `start_point`
is passed as an input to model's forward function. It
is the starting point of attributions' approximation.
It is assumed that both `start_point` and `end_point`
have the same shape and dimensionality.
end_point (tensor or tuple of tensors): `end_point`
is passed as an input to model's forward function. It
is the end point of attributions' approximation.
It is assumed that both `start_point` and `end_point`
have the same shape and dimensionality.
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.
`additional_forward_args` is used both for `start_point`
and `end_point` when computing the forward pass.
Default: None
Returns:
*tensor* of **deltas**:
- **deltas** (*tensor*):
This implementation returns convergence delta per
sample. Deriving sub-classes may do any type of aggregation
of those values, if necessary.
"""
end_point, start_point = _format_input_baseline(end_point, start_point)
additional_forward_args = _format_additional_forward_args(
additional_forward_args)
# tensorizing start_point in case it is a scalar or one example baseline
# If the batch size is large we could potentially also tensorize only one
# sample and expand the output to the rest of the elements in the batch
start_point = _tensorize_baseline(end_point, start_point)
attributions = _format_tensor_into_tuples(attributions)
# verify that the attributions and end_point match on 1st dimension
for attribution, end_point_tnsr in zip(attributions, end_point):
assert end_point_tnsr.shape[0] == attribution.shape[0], (
"Attributions tensor and the end_point must match on the first"
" dimension but found attribution: {} and end_point: {}".
format(attribution.shape[0], end_point_tnsr.shape[0]))
num_samples = end_point[0].shape[0]
_validate_input(end_point, start_point)
_validate_target(num_samples, target)
with torch.no_grad():
start_out_sum = _sum_rows(
_run_forward(self.forward_func, start_point, target,
additional_forward_args))
end_out_sum = _sum_rows(
_run_forward(self.forward_func, end_point, target,
additional_forward_args))
row_sums = [_sum_rows(attribution) for attribution in attributions]
attr_sum = torch.stack(
[cast(Tensor, sum(row_sum)) for row_sum in zip(*row_sums)])
_delta = attr_sum - (end_out_sum - start_out_sum)
return _delta
def attribute( # type: ignore
self,
inputs: TensorOrTupleOfTensorsGeneric,
baselines: BaselineType = None,
target: TargetType = None,
additional_forward_args: Any = 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 of tensors): 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 scalars or tensors, 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 (string, 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 of *tensors*):
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
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)
inputs, baselines = _format_input_baseline(inputs, baselines)
_validate_input(inputs, baselines, n_steps, method)
if internal_batch_size is not None:
num_examples = inputs[0].shape[0]
attributions = _batch_attribution(
self,
num_examples,
internal_batch_size,
n_steps,
inputs=inputs,
baselines=baselines,
target=target,
additional_forward_args=additional_forward_args,
method=method,
)
else:
attributions = self._attribute(
inputs=inputs,
baselines=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,
)
return _format_output(is_inputs_tuple, attributions), delta
return _format_output(is_inputs_tuple, attributions)
def attribute(
self,
inputs: TensorOrTupleOfTensorsGeneric,
baselines: BaselineType = None,
target: TargetType = None,
additional_forward_args: Any = None,
feature_mask: Union[None, TensorOrTupleOfTensorsGeneric] = None,
n_samples: int = 25,
perturbations_per_eval: int = 1,
show_progress: bool = False,
) -> TensorOrTupleOfTensorsGeneric:
r"""
NOTE: The feature_mask argument differs from other perturbation based
methods, since feature indices can overlap across tensors. See the
description of the feature_mask argument below for more details.
Args:
inputs (tensor or tuple of tensors): Input for which Shapley value
sampling 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 value which replaces each
feature when ablated.
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 difference is 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. 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
feature_mask (tensor or tuple of tensors, optional):
feature_mask defines a mask for the input, grouping
features which should be added together. feature_mask
should contain the same number of tensors as inputs.
Each tensor should
be the same size as the corresponding input or
broadcastable to match the input tensor. Values across
all tensors should be integers in the range 0 to
num_features - 1, and indices corresponding to the same
feature should have the same value.
Note that features are grouped across tensors
(unlike feature ablation and occlusion), so
if the same index is used in different tensors, those
features are still grouped and added simultaneously.
If the forward function returns a single scalar per batch,
we enforce that the first dimension of each mask must be 1,
since attributions are returned batch-wise rather than per
example, so the attributions must correspond to the
same features (indices) in each input example.
If None, then a feature mask is constructed which assigns
each scalar within a tensor as a separate feature
Default: None
n_samples (int, optional): The number of feature permutations
tested.
Default: `25` if `n_samples` is not provided.
perturbations_per_eval (int, optional): Allows multiple ablations
to be processed simultaneously in one call to forward_fn.
Each forward pass will contain a maximum of
perturbations_per_eval * #examples samples.
For DataParallel models, each batch is split among the
available devices, so evaluations on each available
device contain at most
(perturbations_per_eval * #examples) / num_devices
samples.
If the forward function returns a single scalar per batch,
perturbations_per_eval must be set to 1.
Default: 1
show_progress (bool, optional): Displays the progress of computation.
It will try to use tqdm if available for advanced features
(e.g. time estimation). Otherwise, it will fallback to
a simple output of progress.
Default: False
Returns:
*tensor* or tuple of *tensors* of **attributions**:
- **attributions** (*tensor* or tuple of *tensors*):
The attributions with respect to each input feature.
If the forward function returns
a scalar value per example, attributions will be
the same size as the provided inputs, with each value
providing the attribution of the corresponding input index.
If the forward function returns a scalar per batch, then
attribution tensor(s) will have first dimension 1 and
the remaining dimensions will match the input.
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.
Examples::
>>> # SimpleClassifier takes a single input tensor of size Nx4x4,
>>> # and returns an Nx3 tensor of class probabilities.
>>> net = SimpleClassifier()
>>> # Generating random input with size 2 x 4 x 4
>>> input = torch.randn(2, 4, 4)
>>> # Defining ShapleyValueSampling interpreter
>>> svs = ShapleyValueSampling(net)
>>> # Computes attribution, taking random orderings
>>> # of the 16 features and computing the output change when adding
>>> # each feature. We average over 200 trials (random permutations).
>>> attr = svs.attribute(input, target=1, n_samples=200)
>>> # Alternatively, we may want to add features in groups, e.g.
>>> # grouping each 2x2 square of the inputs and adding them together.
>>> # This can be done by creating a feature mask as follows, which
>>> # defines the feature groups, e.g.:
>>> # +---+---+---+---+
>>> # | 0 | 0 | 1 | 1 |
>>> # +---+---+---+---+
>>> # | 0 | 0 | 1 | 1 |
>>> # +---+---+---+---+
>>> # | 2 | 2 | 3 | 3 |
>>> # +---+---+---+---+
>>> # | 2 | 2 | 3 | 3 |
>>> # +---+---+---+---+
>>> # With this mask, all inputs with the same value are added
>>> # together, and the attribution for each input in the same
>>> # group (0, 1, 2, and 3) per example are the same.
>>> # The attributions can be calculated as follows:
>>> # feature mask has dimensions 1 x 4 x 4
>>> feature_mask = torch.tensor([[[0,0,1,1],[0,0,1,1],
>>> [2,2,3,3],[2,2,3,3]]])
>>> attr = svs.attribute(input, target=1, feature_mask=feature_mask)
"""
# Keeps track whether original input is a tuple or not before
# converting it into a tuple.
is_inputs_tuple = _is_tuple(inputs)
inputs, baselines = _format_input_baseline(inputs, baselines)
additional_forward_args = _format_additional_forward_args(
additional_forward_args
)
feature_mask = (
_format_tensor_into_tuples(feature_mask)
if feature_mask is not None
else None
)
assert (
isinstance(perturbations_per_eval, int) and perturbations_per_eval >= 1
), "Ablations per evaluation must be at least 1."
with torch.no_grad():
baselines = _tensorize_baseline(inputs, baselines)
num_examples = inputs[0].shape[0]
if feature_mask is None:
feature_mask, total_features = _construct_default_feature_mask(inputs)
else:
total_features = int(
max(torch.max(single_mask).item() for single_mask in feature_mask)
+ 1
)
if show_progress:
attr_progress = progress(
desc=f"{self.get_name()} attribution",
total=self._get_n_evaluations(
total_features, n_samples, perturbations_per_eval
)
+ 1, # add 1 for the initial eval
)
attr_progress.update(0)
initial_eval = _run_forward(
self.forward_func, baselines, target, additional_forward_args
)
if show_progress:
attr_progress.update()
agg_output_mode = _find_output_mode_and_verify(
initial_eval, num_examples, perturbations_per_eval, feature_mask
)
# Initialize attribution totals and counts
total_attrib = [
torch.zeros_like(
input[0:1] if agg_output_mode else input, dtype=torch.float
)
for input in inputs
]
iter_count = 0
# Iterate for number of samples, generate a permutation of the features
# and evalute the incremental increase for each feature.
for feature_permutation in self.permutation_generator(
total_features, n_samples
):
iter_count += 1
prev_results = initial_eval
for (
current_inputs,
current_add_args,
current_target,
current_masks,
) in self._perturbation_generator(
inputs,
additional_forward_args,
target,
baselines,
feature_mask,
feature_permutation,
perturbations_per_eval,
):
if sum(torch.sum(mask).item() for mask in current_masks) == 0:
warnings.warn(
"Feature mask is missing some integers between 0 and "
"num_features, for optimal performance, make sure each"
" consecutive integer corresponds to a feature."
)
# modified_eval dimensions: 1D tensor with length
# equal to #num_examples * #features in batch
modified_eval = _run_forward(
self.forward_func,
current_inputs,
current_target,
current_add_args,
)
if show_progress:
attr_progress.update()
if agg_output_mode:
eval_diff = modified_eval - prev_results
prev_results = modified_eval
else:
all_eval = torch.cat((prev_results, modified_eval), dim=0)
eval_diff = all_eval[num_examples:] - all_eval[:-num_examples]
prev_results = all_eval[-num_examples:]
for j in range(len(total_attrib)):
current_eval_diff = eval_diff
if not agg_output_mode:
# current_eval_diff dimensions:
# (#features in batch, #num_examples, 1,.. 1)
# (contains 1 more dimension than inputs). This adds extra
# dimensions of 1 to make the tensor broadcastable with the
# inputs tensor.
current_eval_diff = current_eval_diff.reshape(
(-1, num_examples) + (len(inputs[j].shape) - 1) * (1,)
)
total_attrib[j] += (
current_eval_diff * current_masks[j].float()
).sum(dim=0)
if show_progress:
attr_progress.close()
# Divide total attributions by number of random permutations and return
# formatted attributions.
attrib = tuple(
tensor_attrib_total / iter_count for tensor_attrib_total in total_attrib
)
formatted_attr = _format_output(is_inputs_tuple, attrib)
return formatted_attr
