Implements the Glow Bijector from Kingma & Dhariwal (2018).

Overview: Glow is a chain of bijectors which transforms a rank-1 tensor (vector) into a rank-3 tensor (e.g. an RGB image). Glow does this by chaining together an alternating series of "Blocks," "Squeezes," and "Exits" which are each themselves special chains of other bijectors. The intended use of Glow is as part of a tfd_transformed_distribution, in which the base distribution over the vector space is used to generate samples in the image space. In the paper, an Independent Normal distribution is used as the base distribution.

tfb_glow(
  output_shape = c(32, 32, 3),
  num_glow_blocks = 3,
  num_steps_per_block = 32,
  coupling_bijector_fn = NULL,
  exit_bijector_fn = NULL,
  grab_after_block = NULL,
  use_actnorm = TRUE,
  seed = NULL,
  validate_args = FALSE,
  name = "glow"
)

Arguments

output_shape	A list of integers, specifying the event shape of the output, of the bijectors forward pass (the image). Specified as `[H, W, C]`. Default Value: (32, 32, 3)
num_glow_blocks	An integer, specifying how many downsampling levels to include in the model. This must divide equally into both H and W, otherwise the bijector would not be invertible. Default Value: 3
num_steps_per_block	An integer specifying how many Affine Coupling and 1x1 convolution layers to include at each level of the spatial hierarchy. Default Value: 32 (i.e. the value used in the original glow paper).
coupling_bijector_fn	A function which takes the argument `input_shape` and returns a callable neural network (e.g. a `keras_model_sequential()`). The network should either return a tensor with the same event shape as `input_shape` (this will employ additive coupling), a tensor with the same height and width as `input_shape` but twice the number of channels (this will employ affine coupling), or a bijector which takes in a tensor with event shape `input_shape`, and returns a tensor with shape `input_shape`.
exit_bijector_fn	Similar to coupling_bijector_fn, exit_bijector_fn is a function which takes the argument `input_shape` and `output_chan` and returns a callable neural network. The neural network it returns should take a tensor of shape `input_shape` as the input, and return one of three options: A tensor with `output_chan` channels, a tensor with `2 * output_chan` channels, or a bijector. Additional details can be found in the documentation for ExitBijector.
grab_after_block	A tuple of floats, specifying what fraction of the remaining channels to remove following each glow block. Glow will take the integer floor of this number multiplied by the remaining number of channels. The default is half at each spatial hierarchy. Default value: None (this will take out half of the channels after each block.
use_actnorm	A boolean deciding whether or not to use actnorm. Data-dependent initialization is used to initialize this layer. Default value: `FALSE`
seed	A seed to control randomness in the 1x1 convolution initialization. Default value: `NULL` (i.e., non-reproducible sampling).
validate_args	Logical, default FALSE. Whether to validate input with asserts. If validate_args is FALSE, and the inputs are invalid, correct behavior is not guaranteed.
name	name prefixed to Ops created by this class.

Value

a bijector instance.

Details

A "Block" (implemented as the GlowBlock Bijector) performs much of the transformations which allow glow to produce sophisticated and complex mappings between the image space and the latent space and therefore achieve rich image generation performance. A Block is composed of num_steps_per_block steps, which are each implemented as a Chain containing an ActivationNormalization (ActNorm) bijector, followed by an (invertible) OneByOneConv bijector, and finally a coupling bijector. The coupling bijector is an instance of a RealNVP bijector, and uses the coupling_bijector_fn function to instantiate the coupling bijector function which is given to the RealNVP. This function returns a bijector which defines the coupling (e.g. Shift(Scale) for affine coupling or Shift for additive coupling).

A "Squeeze" converts spatial features into channel features. It is implemented using the Expand bijector. The difference in names is due to the fact that the forward function from glow is meant to ultimately correspond to sampling from a tfp$util$TransformedDistribution object, which would use Expand (Squeeze is just Invert(Expand)). The Expand bijector takes a tensor with shape [H, W, C] and returns a tensor with shape [2H, 2W, C / 4], such that each 2x2x1 spatial tile in the output is composed from a single 1x1x4 tile in the input tensor, as depicted in the figure below.

Forward pass (Expand)

\     \       \    \    \
\\     \ ----> \  1 \  2 \
\\\__1__\       \____\____\
\\\__2__\        \    \    \
\\__3__\  <----  \  3 \  4 \
\__4__\          \____\____\

Inverse pass (Squeeze) This is implemented using a chain of Reshape -> Transpose -> Reshape bijectors. Note that on an inverse pass through the bijector, each Squeeze will cause the width/height of the image to decrease by a factor of 2. Therefore, the input image must be evenly divisible by 2 at least num_glow_blocks times, since it will pass through a Squeeze step that many times.

An "Exit" is simply a junction at which some of the tensor "exits" from the glow bijector and therefore avoids any further alteration. Each exit is implemented as a Blockwise bijector, where some channels are given to the rest of the glow model, and the rest are given to a bypass implemented using the Identity bijector. The fraction of channels to be removed at each exit is determined by the grab_after_block arg, indicates the fraction of remaining channels which join the identity bypass. The fraction is converted to an integer number of channels by multiplying by the remaining number of channels and rounding. Additionally, at each exit, glow couples the tensor exiting the highway to the tensor continuing onward. This makes small scale features in the image dependent on larger scale features, since the larger scale features dictate the mean and scale of the distribution over the smaller scale features. This coupling is done similarly to the Coupling bijector in each step of the flow (i.e. using a RealNVP bijector). However for the exit bijector, the coupling is instantiated using exit_bijector_fn rather than coupling bijector fn, allowing for different behaviors between standard coupling and exit coupling. Also note that because the exit utilizes a coupling bijector, there are two special cases (all channels exiting and no channels exiting). The full Glow bijector consists of num_glow_blocks Blocks each of which contains num_steps_per_block steps. Each step implements a coupling using bijector_coupling_fn. Between blocks, glow converts between spatial pixels and channels using the Expand Bijector, and splits channels out of the bijector using the Exit Bijector. The channels which have exited continue onward through Identity bijectors and those which have not exited are given to the next block. After passing through all Blocks, the tensor is reshaped to a rank-1 tensor with the same number of elements. This is where the distribution will be defined. A schematic diagram of Glow is shown below. The forward function of the bijector starts from the bottom and goes upward, while the inverse function starts from the top and proceeds downward.

#' ```

Glow Schematic Diagram Input Image ######################## shape = [H, W, C] \ /<- Expand Bijector turns spatial \ / dimensions into channels. | XXXXXXXXXXXXXXXXXXXX | XXXXXXXXXXXXXXXXXXXX | XXXXXXXXXXXXXXXXXXXX A single step of the flow consists Glow Block - | XXXXXXXXXXXXXXXXXXXX <- of ActNorm -> 1x1Conv -> Coupling. | XXXXXXXXXXXXXXXXXXXX there are num_steps_per_block | XXXXXXXXXXXXXXXXXXXX steps of the flow in each block. |_ XXXXXXXXXXXXXXXXXXXX \ / <-- Expand bijectors follow each glow \ / block XXXXXXXX\\\\ <-- Exit Bijector removes channels _ _ from additional alteration. | XXXXXXXX ! | ! | XXXXXXXX ! | ! | XXXXXXXX ! | ! After exiting, channels are passed Glow Block - | XXXXXXXX ! | ! <--- downward using the Blockwise and | XXXXXXXX ! | ! Identify bijectors. | XXXXXXXX ! | ! |_ XXXXXXXX ! | ! \ / <---- Expand Bijector \ / XXX\\ | ! <---- Exit Bijector _ | XXX ! | | ! | XXX ! | | ! | XXX ! | | ! low Block - | XXX ! | | ! | XXX ! | | ! | XXX ! | | ! |_ XXX ! | | ! XX\ ! | | ! <----- (Optional) Exit Bijector | | | v v v Output Distribution ########## shape = [H * W * C]

    Legend

| XX = Step of flow | | X\ = Exit bijector | | \/ = Expand bijector | | !|! = Identity bijector | | | | up = Forward pass | | dn = Inverse pass | |_________________________|

[H, W, C]: R:H,%20W,%20C
[2H, 2W, C / 4]: R:2H,%202W,%20C%20/%204
[H, W, C]: R:H,%20W,%20C
[H * W * C]: R:H%20*%20W%20*%20C