# Source code for pyro.contrib.bnn.hidden_layer

```
# Copyright (c) 2017-2019 Uber Technologies, Inc.
# SPDX-License-Identifier: Apache-2.0
import torch
import torch.nn.functional as F
from torch.distributions.utils import lazy_property
from pyro.contrib.bnn.utils import adjoin_ones_vector
from pyro.distributions.torch_distribution import TorchDistribution
[docs]class HiddenLayer(TorchDistribution):
r"""
This distribution is a basic building block in a Bayesian neural network.
It represents a single hidden layer, i.e. an affine transformation applied
to a set of inputs `X` followed by a non-linearity. The uncertainty in the
weights is encoded in a Normal variational distribution specified by the
parameters `A_scale` and `A_mean`. The so-called 'local reparameterization
trick' is used to reduce variance (see reference below). In effect, this
means the weights are never sampled directly; instead one samples in
pre-activation space (i.e. before the non-linearity is applied). Since the
weights are never directly sampled, when this distribution is used within
the context of variational inference, care must be taken to correctly scale
the KL divergence term that corresponds to the weight matrix. This term is
folded into the `log_prob` method of this distributions.
In effect, this distribution encodes the following generative process:
A ~ Normal(A_mean, A_scale)
output ~ non_linearity(AX)
:param torch.Tensor X: B x D dimensional mini-batch of inputs
:param torch.Tensor A_mean: D x H dimensional specifiying weight mean
:param torch.Tensor A_scale: D x H dimensional (diagonal covariance matrix)
specifying weight uncertainty
:param callable non_linearity: a callable that specifies the
non-linearity used. defaults to ReLU.
:param float KL_factor: scaling factor for the KL divergence. prototypically
this is equal to the size of the mini-batch divided
by the size of the whole dataset. defaults to `1.0`.
:param A_prior: the prior over the weights is assumed to be normal with
mean zero and scale factor `A_prior`. default value is 1.0.
:type A_prior: float or torch.Tensor
:param bool include_hidden_bias: controls whether the activations should be
augmented with a 1, which can be used to
incorporate bias terms. defaults to `True`.
:param bool weight_space_sampling: controls whether the local reparameterization
trick is used. this is only intended to be
used for internal testing.
defaults to `False`.
Reference:
Kingma, Diederik P., Tim Salimans, and Max Welling.
"Variational dropout and the local reparameterization trick."
Advances in Neural Information Processing Systems. 2015.
"""
has_rsample = True
def __init__(self, X=None, A_mean=None, A_scale=None, non_linearity=F.relu,
KL_factor=1.0, A_prior_scale=1.0, include_hidden_bias=True,
weight_space_sampling=False):
self.X = X
self.dim_X = X.size(-1)
self.dim_H = A_mean.size(-1)
assert A_mean.size(0) == self.dim_X, \
"The dimensions of X and A_mean and A_scale must match accordingly; see documentation"
self.A_mean = A_mean
self.A_scale = A_scale
self.non_linearity = non_linearity
assert callable(non_linearity), "non_linearity must be callable"
if A_scale.dim() != 2:
raise NotImplementedError("A_scale must be 2-dimensional")
self.KL_factor = KL_factor
self.A_prior_scale = A_prior_scale
self.weight_space_sampling = weight_space_sampling
self.include_hidden_bias = include_hidden_bias
def log_prob(self, value):
return -self.KL_factor * self.KL
@lazy_property
def KL(self):
KL_A = torch.pow(self.A_mean / self.A_prior_scale, 2.0).sum()
KL_A -= self.dim_X * self.dim_H
KL_A += torch.pow(self.A_scale / self.A_prior_scale, 2.0).sum()
KL_A -= 2.0 * torch.log(self.A_scale / self.A_prior_scale).sum()
return 0.5 * KL_A
def rsample(self, sample_shape=torch.Size()):
# note: weight space sampling is only meant for testing
if self.weight_space_sampling:
A = self.A_mean + torch.randn(sample_shape + self.A_scale.shape).type_as(self.A_mean) * self.A_scale
activation = torch.matmul(self.X, A)
else:
_mean = torch.matmul(self.X, self.A_mean)
X_sqr = torch.pow(self.X, 2.0).unsqueeze(-1)
A_scale_sqr = torch.pow(self.A_scale, 2.0)
_std = (X_sqr * A_scale_sqr).sum(-2).sqrt()
activation = _mean + torch.randn(sample_shape + _std.shape).type_as(_std) * _std
# apply non-linearity
activation = self.non_linearity(activation)
# add 1 element to activations
if self.include_hidden_bias:
activation = adjoin_ones_vector(activation)
return activation
```