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boundary_attack.py
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boundary_attack.py
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from typing import Union, Tuple, Optional, Any
from typing_extensions import Literal
import numpy as np
import eagerpy as ep
import logging
from ..devutils import flatten
from ..devutils import atleast_kd
from ..types import Bounds
from ..models import Model
from ..criteria import Criterion
from ..distances import l2
from ..tensorboard import TensorBoard
from .blended_noise import LinearSearchBlendedUniformNoiseAttack
from .base import MinimizationAttack
from .base import T
from .base import get_criterion
from .base import get_is_adversarial
from .base import raise_if_kwargs
from .base import verify_input_bounds
class BoundaryAttack(MinimizationAttack):
"""A powerful adversarial attack that requires neither gradients
nor probabilities.
This is the reference implementation for the attack. [#Bren18]_
Notes:
Differences to the original reference implementation:
* We do not perform internal operations with float64
* The samples within a batch can currently influence each other a bit
* We don't perform the additional convergence confirmation
* The success rate tracking changed a bit
* Some other changes due to batching and merged loops
Args:
init_attack : Attack to use to find a starting points. Defaults to
LinearSearchBlendedUniformNoiseAttack. Only used if starting_points is None.
steps : Maximum number of steps to run. Might converge and stop before that.
spherical_step : Initial step size for the orthogonal (spherical) step.
source_step : Initial step size for the step towards the target.
source_step_convergance : Sets the threshold of the stop criterion:
if source_step becomes smaller than this value during the attack,
the attack has converged and will stop.
step_adaptation : Factor by which the step sizes are multiplied or divided.
tensorboard : The log directory for TensorBoard summaries. If False, TensorBoard
summaries will be disabled (default). If None, the logdir will be
runs/CURRENT_DATETIME_HOSTNAME.
update_stats_every_k :
References:
.. [#Bren18] Wieland Brendel (*), Jonas Rauber (*), Matthias Bethge,
"Decision-Based Adversarial Attacks: Reliable Attacks
Against Black-Box Machine Learning Models",
https://arxiv.org/abs/1712.04248
"""
distance = l2
def __init__(
self,
init_attack: Optional[MinimizationAttack] = None,
steps: int = 25000,
spherical_step: float = 1e-2,
source_step: float = 1e-2,
source_step_convergance: float = 1e-7,
step_adaptation: float = 1.5,
tensorboard: Union[Literal[False], None, str] = False,
update_stats_every_k: int = 10,
):
if init_attack is not None and not isinstance(init_attack, MinimizationAttack):
raise NotImplementedError
self.init_attack = init_attack
self.steps = steps
self.spherical_step = spherical_step
self.source_step = source_step
self.source_step_convergance = source_step_convergance
self.step_adaptation = step_adaptation
self.tensorboard = tensorboard
self.update_stats_every_k = update_stats_every_k
def run(
self,
model: Model,
inputs: T,
criterion: Union[Criterion, T],
*,
early_stop: Optional[float] = None,
starting_points: Optional[T] = None,
**kwargs: Any,
) -> T:
raise_if_kwargs(kwargs)
originals, restore_type = ep.astensor_(inputs)
del inputs, kwargs
verify_input_bounds(originals, model)
criterion = get_criterion(criterion)
is_adversarial = get_is_adversarial(criterion, model)
if starting_points is None:
init_attack: MinimizationAttack
if self.init_attack is None:
init_attack = LinearSearchBlendedUniformNoiseAttack(steps=50)
logging.info(
f"Neither starting_points nor init_attack given. Falling"
f" back to {init_attack!r} for initialization."
)
else:
init_attack = self.init_attack
# TODO: use call and support all types of attacks (once early_stop is
# possible in __call__)
best_advs = init_attack.run(
model, originals, criterion, early_stop=early_stop
)
else:
best_advs = ep.astensor(starting_points)
is_adv = is_adversarial(best_advs)
if not is_adv.all():
failed = is_adv.logical_not().float32().sum()
if starting_points is None:
raise ValueError(
f"init_attack failed for {failed} of {len(is_adv)} inputs"
)
else:
raise ValueError(
f"{failed} of {len(is_adv)} starting_points are not adversarial"
)
del starting_points
tb = TensorBoard(logdir=self.tensorboard)
N = len(originals)
ndim = originals.ndim
spherical_steps = ep.ones(originals, N) * self.spherical_step
source_steps = ep.ones(originals, N) * self.source_step
tb.scalar("batchsize", N, 0)
# create two queues for each sample to track success rates
# (used to update the hyper parameters)
stats_spherical_adversarial = ArrayQueue(maxlen=100, N=N)
stats_step_adversarial = ArrayQueue(maxlen=30, N=N)
bounds = model.bounds
for step in range(1, self.steps + 1):
converged = source_steps < self.source_step_convergance
if converged.all():
break # pragma: no cover
converged = atleast_kd(converged, ndim)
# TODO: performance: ignore those that have converged
# (we could select the non-converged ones, but we currently
# cannot easily invert this in the end using EagerPy)
unnormalized_source_directions = originals - best_advs
source_norms = ep.norms.l2(flatten(unnormalized_source_directions), axis=-1)
source_directions = unnormalized_source_directions / atleast_kd(
source_norms, ndim
)
# only check spherical candidates every k steps
check_spherical_and_update_stats = step % self.update_stats_every_k == 0
candidates, spherical_candidates = draw_proposals(
bounds,
originals,
best_advs,
unnormalized_source_directions,
source_directions,
source_norms,
spherical_steps,
source_steps,
)
candidates.dtype == originals.dtype
spherical_candidates.dtype == spherical_candidates.dtype
is_adv = is_adversarial(candidates)
spherical_is_adv: Optional[ep.Tensor]
if check_spherical_and_update_stats:
spherical_is_adv = is_adversarial(spherical_candidates)
stats_spherical_adversarial.append(spherical_is_adv)
# TODO: algorithm: the original implementation ignores those samples
# for which spherical is not adversarial and continues with the
# next iteration -> we estimate different probabilities (conditional vs. unconditional)
# TODO: thoughts: should we always track this because we compute it anyway
stats_step_adversarial.append(is_adv)
else:
spherical_is_adv = None
# in theory, we are closer per construction
# but limited numerical precision might break this
distances = ep.norms.l2(flatten(originals - candidates), axis=-1)
closer = distances < source_norms
is_best_adv = ep.logical_and(is_adv, closer)
is_best_adv = atleast_kd(is_best_adv, ndim)
cond = converged.logical_not().logical_and(is_best_adv)
best_advs = ep.where(cond, candidates, best_advs)
tb.probability("converged", converged, step)
tb.scalar("updated_stats", check_spherical_and_update_stats, step)
tb.histogram("norms", source_norms, step)
tb.probability("is_adv", is_adv, step)
if spherical_is_adv is not None:
tb.probability("spherical_is_adv", spherical_is_adv, step)
tb.histogram("candidates/distances", distances, step)
tb.probability("candidates/closer", closer, step)
tb.probability("candidates/is_best_adv", is_best_adv, step)
tb.probability("new_best_adv_including_converged", is_best_adv, step)
tb.probability("new_best_adv", cond, step)
if check_spherical_and_update_stats:
full = stats_spherical_adversarial.isfull()
tb.probability("spherical_stats/full", full, step)
if full.any():
probs = stats_spherical_adversarial.mean()
cond1 = ep.logical_and(probs > 0.5, full)
spherical_steps = ep.where(
cond1, spherical_steps * self.step_adaptation, spherical_steps
)
source_steps = ep.where(
cond1, source_steps * self.step_adaptation, source_steps
)
cond2 = ep.logical_and(probs < 0.2, full)
spherical_steps = ep.where(
cond2, spherical_steps / self.step_adaptation, spherical_steps
)
source_steps = ep.where(
cond2, source_steps / self.step_adaptation, source_steps
)
stats_spherical_adversarial.clear(ep.logical_or(cond1, cond2))
tb.conditional_mean(
"spherical_stats/isfull/success_rate/mean", probs, full, step
)
tb.probability_ratio(
"spherical_stats/isfull/too_linear", cond1, full, step
)
tb.probability_ratio(
"spherical_stats/isfull/too_nonlinear", cond2, full, step
)
full = stats_step_adversarial.isfull()
tb.probability("step_stats/full", full, step)
if full.any():
probs = stats_step_adversarial.mean()
# TODO: algorithm: changed the two values because we are currently tracking p(source_step_sucess)
# instead of p(source_step_success | spherical_step_sucess) that was tracked before
cond1 = ep.logical_and(probs > 0.25, full)
source_steps = ep.where(
cond1, source_steps * self.step_adaptation, source_steps
)
cond2 = ep.logical_and(probs < 0.1, full)
source_steps = ep.where(
cond2, source_steps / self.step_adaptation, source_steps
)
stats_step_adversarial.clear(ep.logical_or(cond1, cond2))
tb.conditional_mean(
"step_stats/isfull/success_rate/mean", probs, full, step
)
tb.probability_ratio(
"step_stats/isfull/success_rate_too_high", cond1, full, step
)
tb.probability_ratio(
"step_stats/isfull/success_rate_too_low", cond2, full, step
)
tb.histogram("spherical_step", spherical_steps, step)
tb.histogram("source_step", source_steps, step)
tb.close()
return restore_type(best_advs)
class ArrayQueue:
def __init__(self, maxlen: int, N: int):
# we use NaN as an indicator for missing data
self.data = np.full((maxlen, N), np.nan)
self.next = 0
# used to infer the correct framework because this class uses NumPy
self.tensor: Optional[ep.Tensor] = None
@property
def maxlen(self) -> int:
return int(self.data.shape[0])
@property
def N(self) -> int:
return int(self.data.shape[1])
def append(self, x: ep.Tensor) -> None:
if self.tensor is None:
self.tensor = x
x = x.numpy()
assert x.shape == (self.N,)
self.data[self.next] = x
self.next = (self.next + 1) % self.maxlen
def clear(self, dims: ep.Tensor) -> None:
if self.tensor is None:
self.tensor = dims # pragma: no cover
dims = dims.numpy()
assert dims.shape == (self.N,)
assert dims.dtype == np.bool_
self.data[:, dims] = np.nan
def mean(self) -> ep.Tensor:
assert self.tensor is not None
result = np.nanmean(self.data, axis=0)
return ep.from_numpy(self.tensor, result)
def isfull(self) -> ep.Tensor:
assert self.tensor is not None
result = ~np.isnan(self.data).any(axis=0)
return ep.from_numpy(self.tensor, result)
def draw_proposals(
bounds: Bounds,
originals: ep.Tensor,
perturbed: ep.Tensor,
unnormalized_source_directions: ep.Tensor,
source_directions: ep.Tensor,
source_norms: ep.Tensor,
spherical_steps: ep.Tensor,
source_steps: ep.Tensor,
) -> Tuple[ep.Tensor, ep.Tensor]:
# remember the actual shape
shape = originals.shape
assert perturbed.shape == shape
assert unnormalized_source_directions.shape == shape
assert source_directions.shape == shape
# flatten everything to (batch, size)
originals = flatten(originals)
perturbed = flatten(perturbed)
unnormalized_source_directions = flatten(unnormalized_source_directions)
source_directions = flatten(source_directions)
N, D = originals.shape
assert source_norms.shape == (N,)
assert spherical_steps.shape == (N,)
assert source_steps.shape == (N,)
# draw from an iid Gaussian (we can share this across the whole batch)
eta = ep.normal(perturbed, (D, 1))
# make orthogonal (source_directions are normalized)
eta = eta.T - ep.matmul(source_directions, eta) * source_directions
assert eta.shape == (N, D)
# rescale
norms = ep.norms.l2(eta, axis=-1)
assert norms.shape == (N,)
eta = eta * atleast_kd(spherical_steps * source_norms / norms, eta.ndim)
# project on the sphere using Pythagoras
distances = atleast_kd((spherical_steps.square() + 1).sqrt(), eta.ndim)
directions = eta - unnormalized_source_directions
spherical_candidates = originals + directions / distances
# clip
min_, max_ = bounds
spherical_candidates = spherical_candidates.clip(min_, max_)
# step towards the original inputs
new_source_directions = originals - spherical_candidates
assert new_source_directions.ndim == 2
new_source_directions_norms = ep.norms.l2(flatten(new_source_directions), axis=-1)
# length if spherical_candidates would be exactly on the sphere
lengths = source_steps * source_norms
# length including correction for numerical deviation from sphere
lengths = lengths + new_source_directions_norms - source_norms
# make sure the step size is positive
lengths = ep.maximum(lengths, 0)
# normalize the length
lengths = lengths / new_source_directions_norms
lengths = atleast_kd(lengths, new_source_directions.ndim)
candidates = spherical_candidates + lengths * new_source_directions
# clip
candidates = candidates.clip(min_, max_)
# restore shape
candidates = candidates.reshape(shape)
spherical_candidates = spherical_candidates.reshape(shape)
return candidates, spherical_candidates