tfp.experimental.nn.AffineVariationalReparameterizationLocal

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Densely-connected layer class with local reparameterization estimator.

Inherits From: VariationalLayer, Layer

tfp.experimental.nn.AffineVariationalReparameterizationLocal(
    input_size,
    output_size,
    kernel_initializer=None,
    bias_initializer=None,
    make_posterior_fn=tfp.experimental.nn.util.make_kernel_bias_posterior_mvn_diag,
    make_prior_fn=tfp.experimental.nn.util.make_kernel_bias_prior_spike_and_slab,
    posterior_value_fn=tfp.distributions.Distribution.sample,
    unpack_weights_fn=unpack_kernel_and_bias,
    dtype=tf.float32,
    activation_fn=None,
    seed=None,
    validate_args=False,
    name=None
)

This layer implements the Bayesian variational inference analogue to a dense layer by assuming the kernel and/or the bias are drawn from distributions. By default, the layer implements a stochastic forward pass via sampling from the kernel and bias posteriors,

kernel, bias ~ posterior
outputs = matmul(inputs, kernel) + bias

It uses the local reparameterization estimator [(Kingma et al., 2015)][1], which performs a Monte Carlo approximation of the distribution on the hidden units induced by the kernel and bias. The default kernel_posterior_fn is a normal distribution which factorizes across all elements of the weight matrix and bias vector. Unlike [1]'s multiplicative parameterization, this distribution has trainable location and scale parameters which is known as an additive noise parameterization [(Molchanov et al., 2017)][2].

The arguments permit separate specification of the surrogate posterior (q(W|x)), prior (p(W)), and divergence for both the kernel and bias distributions.

Upon being built, this layer adds losses (accessible via the losses property) representing the divergences of kernel and/or bias surrogate posteriors and their respective priors. When doing minibatch stochastic optimization, make sure to scale this loss such that it is applied just once per epoch (e.g. if kl is the sum of losses for each element of the batch, you should pass kl / num_examples_per_epoch to your optimizer).

You can access the kernel and/or bias posterior and prior distributions after the layer is built via the kernel_posterior, kernel_prior, bias_posterior and bias_prior properties.

Examples

We illustrate a Bayesian neural network with variational inference, assuming a dataset of images and length-10 one-hot targets.

# Using the following substitution, see:
tfn = tfp.experimental.nn
help(tfn.AffineVariationalReparameterization)
BayesAffine =  tfn.AffineVariationalReparameterizationLocal

This example uses reparameterization gradients to minimize the Kullback-Leibler divergence up to a constant, also known as the negative Evidence Lower Bound. It consists of the sum of two terms: the expected negative log-likelihood, which we approximate via Monte Carlo; and the KL divergence, which is added via regularizer terms which are arguments to the layer.

References

[1]: Diederik Kingma, Tim Salimans, and Max Welling. Variational Dropout and the Local Reparameterization Trick. In Neural Information Processing Systems, 2015. https://arxiv.org/abs/1506.02557 [2]: Dmitry Molchanov, Arsenii Ashukha, Dmitry Vetrov. Variational Dropout Sparsifies Deep Neural Networks. In International Conference on Machine Learning, 2017. https://arxiv.org/abs/1701.05369

a = tf.Module()
b = tf.Module()
c = tf.Module()
a.b = b
b.c = c
list(a.submodules) == [b, c]
True
list(b.submodules) == [c]
True
list(c.submodules) == []
True

Methods

load

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load(
    filename
)

save

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save(
    filename
)

summary

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summary()

with_name_scope

@classmethod
with_name_scope(
    method
)

Decorator to automatically enter the module name scope.

class MyModule(tf.Module):
  @tf.Module.with_name_scope
  def __call__(self, x):
    if not hasattr(self, 'w'):
      self.w = tf.Variable(tf.random.normal([x.shape[1], 3]))
    return tf.matmul(x, self.w)

Using the above module would produce tf.Variables and tf.Tensors whose names included the module name:

mod = MyModule()
mod(tf.ones([1, 2]))
<tf.Tensor: shape=(1, 3), dtype=float32, numpy=..., dtype=float32)>
mod.w
<tf.Variable 'my_module/Variable:0' shape=(2, 3) dtype=float32,
numpy=..., dtype=float32)>

__call__

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__call__(
    x
)

Call self as a function.