# Path: jax_verify/extensions/functional_lagrangian/verify_utils.py
# class AbstractParams(abc.ABC):
# class FCParams(AbstractParams):
# class ConvParams(AbstractParams):
# class SpecType(enum.Enum):
# class Distribution(enum.Enum):
# class NetworkType(enum.Enum):
# class InnerVerifInstance:
#   def __call__(self, inputs: Tensor) -> Tensor:
#   def params(self):
#   def has_bounds(self):
#   def params(self):
#   def params(self):
#   def same_lagrangian_form_pre_post(self) -> bool:
#   UNCERTAINTY = 'uncertainty'
#   ADVERSARIAL = 'adversarial'
#   ADVERSARIAL_SOFTMAX = 'adversarial_softmax'
#   PROBABILITY_THRESHOLD = 'probability_threshold'
#   GAUSSIAN = 'gaussian'
#   BERNOULLI = 'bernoulli'
#   DETERMINISTIC = 'deterministic'
#   STOCHASTIC = 'stochastic'
# 
# Path: jax_verify/extensions/sdp_verify/utils.py
# class SdpDualVerifInstance(_SdpDualVerifInstance):
# class VerifInstanceTypes(enum.Enum):
# class DualVarTypes(enum.Enum):
# def mlp_layer_sizes(params):
# def nn_layer_sizes(params):
# def layer_sizes_from_bounds(bounds):
# def predict_mlp(params, inputs):
# def fwd(inputs, layer_params):
# def predict_cnn(params, inputs, include_preactivations=False):
# def get_network_activs(params, x):
# def get_layer_params(fun_to_extract, example_input):
#   def _get_const_input_arg(eqn):
# def boundprop(params, bounds_in):
# def init_bound(x, epsilon, input_bounds=(0., 1.), add_batch_dim=True):
# def ibp_bound_elided(verif_instance):
# def ibp_bound_nonelided(verif_instance):
# def make_relu_robust_verif_instance(
#     params, bounds=None, target_label=1, label=2, input_bounds=None):
# def make_relu_robust_verif_instance_elided(
#     params, bounds=None, input_bounds=None):
# def output_size_and_verif_type(params, bounds):
# def elide_params(params, label, target_label, op_size):
# def preprocess_cifar(image, inception_preprocess=False, perturbation=False):
# def preprocessed_cifar_eps_and_input_bounds(
#     shape=(32, 32, 3), epsilon=2/255, inception_preprocess=False):
# def adv_objective(model_fn, x, label, target_label):
# def fgsm_single(model_fn, x, label, target_label, epsilon, num_steps,
#                 step_size, input_bounds=(0., 1.)):
# def untargeted_margin_loss(logits, labels):
# def pgd_default(model_fn, x, label, epsilon, num_steps, step_size,
#                 input_bounds=(0., 1.)):
# def pgd(adv_loss, x_init, epsilon, num_steps, step_size, input_bounds=(0., 1.)):
# def scale_by_variable_opt(multipliers):
#   def init_fn(params):
#   def update_fn(updates, _, params=None):
# def flatten(pytree, backend=np):
# def unflatten_like(a, pytree):
# def structure_like(tree1, tree2):
#   MLP_ELIDED = 'mlp_elided'
#   CNN_ELIDED = 'cnn_elided'
#   EQUALITY = 'equality'
#   INEQUALITY = 'inequality'


import dataclasses
import jax
import jax.numpy as jnp
import jax_verify
import optax
from typing import Callable, Union
from jax_verify.extensions.functional_lagrangian import verify_utils
from jax_verify.extensions.sdp_verify import utils as sdp_utils
            std=layer_params.b_std,
            bounds=layer_params.b_bound,
            prng_key=key_b,
        )
        layer_params = dataclasses.replace(layer_params, b=b_sampled)
      sampled_params.append(layer_params)
    return sampled_params

  return sample_fn


def make_forward(
    model_params: ModelParams,
    num_samples: int,
) -> Callable[[Tensor, PRNGKey], Tensor]:
  """Make forward_fn with parameter sampling and averaging in softmax space.

  Args:
    model_params: model parameters.
    num_samples: number of samples drawn per call to forward_fn.

  Returns:
    function that draws parameter samples, averages their results in softmax
      space and takes the log.
  """

  sampling_fn = make_params_sampling_fn(model_params)

  def single_forward(inputs, prng_key):
    sampled_params = sampling_fn(prng_key)

# Path: jax_verify/extensions/functional_lagrangian/verify_utils.py
# class AbstractParams(abc.ABC):
# class FCParams(AbstractParams):
# class ConvParams(AbstractParams):
# class SpecType(enum.Enum):
# class Distribution(enum.Enum):
# class NetworkType(enum.Enum):
# class InnerVerifInstance:
#   def __call__(self, inputs: Tensor) -> Tensor:
#   def params(self):
#   def has_bounds(self):
#   def params(self):
#   def params(self):
#   def same_lagrangian_form_pre_post(self) -> bool:
#   UNCERTAINTY = 'uncertainty'
#   ADVERSARIAL = 'adversarial'
#   ADVERSARIAL_SOFTMAX = 'adversarial_softmax'
#   PROBABILITY_THRESHOLD = 'probability_threshold'
#   GAUSSIAN = 'gaussian'
#   BERNOULLI = 'bernoulli'
#   DETERMINISTIC = 'deterministic'
#   STOCHASTIC = 'stochastic'
# 
# Path: jax_verify/extensions/sdp_verify/utils.py
# class SdpDualVerifInstance(_SdpDualVerifInstance):
# class VerifInstanceTypes(enum.Enum):
# class DualVarTypes(enum.Enum):
# def mlp_layer_sizes(params):
# def nn_layer_sizes(params):
# def layer_sizes_from_bounds(bounds):
# def predict_mlp(params, inputs):
# def fwd(inputs, layer_params):
# def predict_cnn(params, inputs, include_preactivations=False):
# def get_network_activs(params, x):
# def get_layer_params(fun_to_extract, example_input):
#   def _get_const_input_arg(eqn):
# def boundprop(params, bounds_in):
# def init_bound(x, epsilon, input_bounds=(0., 1.), add_batch_dim=True):
# def ibp_bound_elided(verif_instance):
# def ibp_bound_nonelided(verif_instance):
# def make_relu_robust_verif_instance(
#     params, bounds=None, target_label=1, label=2, input_bounds=None):
# def make_relu_robust_verif_instance_elided(
#     params, bounds=None, input_bounds=None):
# def output_size_and_verif_type(params, bounds):
# def elide_params(params, label, target_label, op_size):
# def preprocess_cifar(image, inception_preprocess=False, perturbation=False):
# def preprocessed_cifar_eps_and_input_bounds(
#     shape=(32, 32, 3), epsilon=2/255, inception_preprocess=False):
# def adv_objective(model_fn, x, label, target_label):
# def fgsm_single(model_fn, x, label, target_label, epsilon, num_steps,
#                 step_size, input_bounds=(0., 1.)):
# def untargeted_margin_loss(logits, labels):
# def pgd_default(model_fn, x, label, epsilon, num_steps, step_size,
#                 input_bounds=(0., 1.)):
# def pgd(adv_loss, x_init, epsilon, num_steps, step_size, input_bounds=(0., 1.)):
# def scale_by_variable_opt(multipliers):
#   def init_fn(params):
#   def update_fn(updates, _, params=None):
# def flatten(pytree, backend=np):
# def unflatten_like(a, pytree):
# def structure_like(tree1, tree2):
#   MLP_ELIDED = 'mlp_elided'
#   CNN_ELIDED = 'cnn_elided'
#   EQUALITY = 'equality'
#   INEQUALITY = 'inequality'


# Path: jax_verify/extensions/functional_lagrangian/attacks.py
import dataclasses
import jax
import jax.numpy as jnp
import jax_verify
import optax
from typing import Callable, Union
from jax_verify.extensions.functional_lagrangian import verify_utils
from jax_verify.extensions.sdp_verify import utils as sdp_utils

            std=layer_params.b_std,
            bounds=layer_params.b_bound,
            prng_key=key_b,
        )
        layer_params = dataclasses.replace(layer_params, b=b_sampled)
      sampled_params.append(layer_params)
    return sampled_params

  return sample_fn


def make_forward(
    model_params: ModelParams,
    num_samples: int,
) -> Callable[[Tensor, PRNGKey], Tensor]:
  """Make forward_fn with parameter sampling and averaging in softmax space.

  Args:
    model_params: model parameters.
    num_samples: number of samples drawn per call to forward_fn.

  Returns:
    function that draws parameter samples, averages their results in softmax
      space and takes the log.
  """

  sampling_fn = make_params_sampling_fn(model_params)

  def single_forward(inputs, prng_key):
    sampled_params = sampling_fn(prng_key)

    logits = sdp_utils.predict_cnn(