Densely-connected layer class with local reparameterization estimator.

This layer implements the Bayesian variational inference analogue to a dense layer by assuming the kernel and/or the bias are drawn from distributions.

layer_dense_local_reparameterization(
  object,
  units,
  activation = NULL,
  activity_regularizer = NULL,
  trainable = TRUE,
  kernel_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(),
  kernel_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  kernel_prior_fn = tfp$layers$util$default_multivariate_normal_fn,
  kernel_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  bias_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(is_singular = TRUE),
  bias_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  bias_prior_fn = NULL,
  bias_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  ...
)

Arguments

object	Model or layer object
units	integer dimensionality of the output space
activation	Activation function. Set it to None to maintain a linear activation.
activity_regularizer	Regularizer function for the output.
trainable	Whether the layer weights will be updated during training.
kernel_posterior_fn	Function which creates tfd$Distribution instance representing the surrogate posterior of the kernel parameter. Default value: default_mean_field_normal_fn().
kernel_posterior_tensor_fn	Function which takes a tfd$Distribution instance and returns a representative value. Default value: function(d) d %>% tfd_sample().
kernel_prior_fn	Function which creates tfd$Distribution instance. See default_mean_field_normal_fn docstring for required parameter signature. Default value: tfd_normal(loc = 0, scale = 1).
kernel_divergence_fn	Function which takes the surrogate posterior distribution, prior distribution and random variate sample(s) from the surrogate posterior and computes or approximates the KL divergence. The distributions are tfd$Distribution-like instances and the sample is a Tensor.
bias_posterior_fn	Function which creates a tfd$Distribution instance representing the surrogate posterior of the bias parameter. Default value: default_mean_field_normal_fn(is_singular = TRUE) (which creates an instance of tfd_deterministic).
bias_posterior_tensor_fn	Function which takes a tfd$Distribution instance and returns a representative value. Default value: function(d) d %>% tfd_sample().
bias_prior_fn	Function which creates tfd instance. See default_mean_field_normal_fn docstring for required parameter signature. Default value: NULL (no prior, no variational inference)
bias_divergence_fn	Function which takes the surrogate posterior distribution, prior distribution and random variate sample(s) from the surrogate posterior and computes or approximates the KL divergence. The distributions are tfd$Distribution-like instances and the sample is a Tensor.
...	Additional keyword arguments passed to the keras::layer_dense constructed by this layer.

Value

a Keras layer

Details

By default, the layer implements a stochastic forward pass via sampling from the kernel and bias posteriors,

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

It uses the local reparameterization estimator (Kingma et al., 2015), 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 that paper's multiplicative parameterization, this distribution has trainable location and scale parameters which is known as an additive noise parameterization (Molchanov et al., 2017).

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.

References

• Diederik Kingma, Tim Salimans, and Max Welling. Variational Dropout and the Local Reparameterization Trick. In Neural Information Processing Systems, 2015.

• Dmitry Molchanov, Arsenii Ashukha, Dmitry Vetrov. Variational Dropout Sparsifies Deep Neural Networks. In International Conference on Machine Learning, 2017.

See also

Other layers: layer_autoregressive(), layer_conv_1d_flipout(), layer_conv_1d_reparameterization(), layer_conv_2d_flipout(), layer_conv_2d_reparameterization(), layer_conv_3d_flipout(), layer_conv_3d_reparameterization(), layer_dense_flipout(), layer_dense_reparameterization(), layer_dense_variational(), layer_variable()