# Source code for pyro.distributions.transforms.batchnorm

# Copyright (c) 2017-2019 Uber Technologies, Inc.

import torch
import torch.nn as nn
import torch.nn.functional as F

from .. import constraints
from ..torch_transform import TransformModule
from ..util import copy_docs_from

[docs]@copy_docs_from(TransformModule)
class BatchNorm(TransformModule):
r"""
A type of batch normalization that can be used to stabilize training in
normalizing flows. The inverse operation is defined as

:math:x = (y - \hat{\mu}) \oslash \sqrt{\hat{\sigma^2}} \otimes \gamma + \beta

that is, the standard batch norm equation, where :math:x is the input,
:math:y is the output, :math:\gamma,\beta are learnable parameters, and
:math:\hat{\mu}/:math:\hat{\sigma^2} are smoothed running averages of
the sample mean and variance, respectively. The constraint :math:\gamma>0 is
enforced to ease calculation of the log-det-Jacobian term.

This is an element-wise transform, and when applied to a vector, learns two
parameters (:math:\gamma,\beta) for each dimension of the input.

When the module is set to training mode, the moving averages of the sample mean
and variance are updated every time the inverse operator is called, e.g., when a
normalizing flow scores a minibatch with the log_prob method.

Also, when the module is set to training mode, the sample mean and variance on
the current minibatch are used in place of the smoothed averages,
:math:\hat{\mu} and :math:\hat{\sigma^2}, for the inverse operator. For
this reason it is not the case that :math:x=g(g^{-1}(x)) during training,
i.e., that the inverse operation is the inverse of the forward one.

Example usage:

>>> from pyro.nn import AutoRegressiveNN
>>> from pyro.distributions.transforms import AffineAutoregressive
>>> base_dist = dist.Normal(torch.zeros(10), torch.ones(10))
>>> iafs = [AffineAutoregressive(AutoRegressiveNN(10, [40])) for _ in range(2)]
>>> bn = BatchNorm(10)
>>> flow_dist = dist.TransformedDistribution(base_dist, [iafs[0], bn, iafs[1]])
>>> flow_dist.sample()  # doctest: +SKIP

:param input_dim: the dimension of the input
:type input_dim: int
:param momentum: momentum parameter for updating moving averages
:type momentum: float
:param epsilon: small number to add to variances to ensure numerical stability
:type epsilon: float

References:

[1] Sergey Ioffe and Christian Szegedy. Batch Normalization: Accelerating Deep
Network Training by Reducing Internal Covariate Shift. In International
Conference on Machine Learning, 2015. https://arxiv.org/abs/1502.03167

[2] Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio. Density Estimation
using Real NVP. In International Conference on Learning Representations, 2017.
https://arxiv.org/abs/1605.08803

[3] George Papamakarios, Theo Pavlakou, and Iain Murray. Masked Autoregressive
Flow for Density Estimation. In Neural Information Processing Systems, 2017.
https://arxiv.org/abs/1705.07057

"""

domain = constraints.real
codomain = constraints.real
bijective = True

def __init__(self, input_dim, momentum=0.1, epsilon=1e-5):
super().__init__()

self.input_dim = input_dim
self.gamma = nn.Parameter(torch.ones(input_dim))
self.beta = nn.Parameter(torch.zeros(input_dim))
self.momentum = momentum
self.epsilon = epsilon

self.register_buffer("moving_mean", torch.zeros(input_dim))
self.register_buffer("moving_variance", torch.ones(input_dim))

@property
def constrained_gamma(self):
return F.relu(self.gamma) + 1e-6

def _call(self, x):
"""
:param x: the input into the bijection
:type x: torch.Tensor

Invokes the bijection x=>y; in the prototypical context of a
:class:~pyro.distributions.TransformedDistribution x is a sample from
the base distribution (or the output of a previous transform)
"""
# Enforcing the constraint that gamma is positive
return (x - self.beta) / self.constrained_gamma * torch.sqrt(
self.moving_variance + self.epsilon
) + self.moving_mean

def _inverse(self, y):
"""
:param y: the output of the bijection
:type y: torch.Tensor

Inverts y => x.
"""
# During training, keep smoothed average of sample mean and variance
if self.training:
mean, var = y.mean(0), y.var(0)

# NOTE: The momentum variable agrees with the definition in e.g. torch.nn.BatchNorm1d

# During test time, use smoothed averages rather than the sample ones
else:
mean, var = self.moving_mean, self.moving_variance

return (y - mean) * self.constrained_gamma / torch.sqrt(
var + self.epsilon
) + self.beta

[docs]    def log_abs_det_jacobian(self, x, y):
"""
Calculates the elementwise determinant of the log Jacobian, dx/dy
"""
if self.training:
var = torch.var(y, dim=0, keepdim=True)
else:
# NOTE: You wouldn't typically run this function in eval mode, but included for gradient tests
var = self.moving_variance
return -self.constrained_gamma.log() + 0.5 * torch.log(var + self.epsilon)

[docs]def batchnorm(input_dim, **kwargs):
"""
A helper function to create a :class:~pyro.distributions.transforms.BatchNorm
object for consistency with other helpers.

:param input_dim: Dimension of input variable
:type input_dim: int
:param momentum: momentum parameter for updating moving averages
:type momentum: float
:param epsilon: small number to add to variances to ensure numerical stability
:type epsilon: float

"""
bn = BatchNorm(input_dim, **kwargs)
return bn