tfc.entropy_models.ContinuousIndexedEntropyModel

Indexed entropy model for continuous random variables.

This entropy model handles quantization of a bottleneck tensor and helps with training of the parameters of the probability distribution modeling the tensor (a shared "prior" between sender and receiver). It also pre-computes integer probability tables, which can then be used to compress and decompress bottleneck tensors reliably across different platforms.

A typical workflow looks like this:

  • Train a model using an instance of this entropy model as a bottleneck, passing the bottleneck tensor through it. With training=True, the model computes a differentiable upper bound on the number of bits needed to compress the bottleneck tensor.
  • For evaluation, get a closer estimate of the number of compressed bits using training=False.
  • Instantiate an entropy model with compression=True (and the same parameters as during training), and share the model between a sender and a receiver.
  • On the sender side, compute the bottleneck tensor and call compress() on it. The output is a compressed string representation of the tensor. Transmit the string to the receiver, and call decompress() there. The output is the quantized bottleneck tensor. Continue processing the tensor on the receiving side.

This class assumes that all scalar elements of the encoded tensor are conditionally independent given some other random variable, possibly depending on data. All dependencies must be represented by the indexes tensor. For each bottleneck tensor element, it selects the appropriate scalar distribution.

The indexes tensor must contain only integer values in a pre-specified range (but may have floating-point type for purposes of backpropagation). To make the distribution conditional on n-dimensional indexes, index_ranges must be specified as an iterable of n integers. indexes must have the same shape as the bottleneck tensor with an additional channel dimension of length n. The position of the channel dimension is given by channel_axis. The index values in the kth channel must be in the range [0, index_ranges[k]). If index_ranges has only one element (i.e. n == 1), channel_axis may be None. In that case, the additional channel dimension is omitted, and the indexes tensor must have the same shape as the bottleneck tensor.

The implied distribution for the bottleneck tensor is determined as:

prior_fn(**{k: f(indexes) for k, f in parameter_fns.items()})

A more detailed description (and motivation) of this indexing scheme can be found in the following paper. Please cite the paper when using this code for derivative work.

"Integer Networks for Data Compression with Latent-Variable Models"
J. Ballé, N. Johnston, D. Minnen
https://openreview.net/forum?id=S1zz2i0cY7

Examples:

To make a parameterized zero-mean normal distribution, one could use:

tfc.ContinuousIndexedEntropyModel(
    prior_fn=tfc.NoisyNormal,
    index_ranges=(64,),
    parameter_fns=dict(
        loc=lambda _: 0.,
        scale=lambda i: tf.exp(i / 8 - 5),
    ),
    coding_rank=1,
    channel_axis=None,
)

Then, each element of indexes in the range [0, 64) would indicate that the corresponding element in bottleneck is normally distributed with zero mean and a standard deviation between exp(-5) and exp(2.875), inclusive.

To make a parameterized logistic mixture distribution, one could use:

tfc.ContinuousIndexedEntropyModel(
    prior_fn=tfc.NoisyLogisticMixture,
    index_ranges=(10, 10, 5),
    parameter_fns=dict(
        loc=lambda i: i[..., 0:2] - 5,
        scale=lambda _: 1,
        weight=lambda i: tf.nn.softmax((i[..., 2:3] - 2) * [-1, 1]),
    ),
    coding_rank=1,
    channel_axis=-1,
)

Then, the last dimension of indexes would consist of triples of elements in the ranges [0, 10), [0, 10), and [0, 5), respectively. Each triple would indicate that the element in bottleneck corresponding to the other dimensions is distributed with a mixture of two logistic distributions, where the components each have one of 10 location parameters between -5 and +4, inclusive, unit scale parameters, and one of five different mixture weightings.

prior_fn A callable returning a tfp.distributions.Distribution object, typically a Distribution class or factory function. This is a density model fitting the marginal distribution of the bottleneck data with additive uniform noise, which is shared a priori between the sender and the receiver. For best results, the distributions should be flexible enough to have a unit-width uniform distribution as a special case, since this is the marginal distribution for bottleneck dimensions that are constant. The callable will receive keyword arguments as determined by parameter_fns.
index_ranges Iterable of integers. indexes must have the same shape as the bottleneck tensor, with an additional dimension at position channel_axis. The values of the kth channel must be in the range [0, index_ranges[k]).
parameter_fns Dict of strings to callables. Functions mapping indexes to each distribution parameter. For each item, indexes is passed to the callable, and the string key and return value make up one keyword argument to prior_fn.
coding_rank Integer. Number of innermost dimensions considered a coding unit. Each coding unit is compressed to its own bit string, and the bits in the __call__ method are summed over each coding unit.
channel_axis Integer or None. Determines the position of the channel axis in indexes. Defaults to the last dimension. If set to None, the index tensor is expected to have the same shape as the bottleneck tensor (only allowed when index_ranges has length 1).
compression Boolean. If set to True, the range coding tables used by compress() and decompress() will be built on instantiation. If set to False, these two methods will not be accessible.
stateless Boolean. If False, range coding tables are created as Variables. This allows the entropy model to be serialized using the SavedModel protocol, so that both the encoder and the decoder use identical tables when loading the stored model. If True, creates range coding tables as Tensors. This makes the entropy model stateless and allows it to be constructed within a tf.function body, for when the range coding tables are provided manually. If compression=False, then stateless=True is implied and the provided value is ignored.
expected_grads If True, will use analytical expected gradients during backpropagation w.r.t. additive uniform noise.
tail_mass Float. Approximate probability mass which is encoded using an Elias gamma code embedded into the range coder.
range_coder_precision Integer. Precision passed to the range coding op.
bottleneck_dtype tf.dtypes.DType. Data type of bottleneck tensor. Defaults to tf.keras.mixed_precision.global_policy().compute_dtype.
prior_dtype tf.dtypes.DType. Data type of prior and probability computations. Defaults to tf.float32.
decode_sanity_check Boolean. If True, an raises an error if the binary strings passed into decompress are not completely decoded.
laplace_tail_mass Float. If positive, will augment the prior with a laplace mixture for training stability. (experimental)

bottleneck_dtype Data type of the bottleneck tensor.
cdf The CDFs used by range coding.
cdf_offset The CDF offsets used by range coding.
channel_axis Position of channel axis in indexes tensor.
coding_rank Number of innermost dimensions considered a coding unit.
compression Whether this entropy model is prepared for compression.
expected_grads Whether to use analytical expected gradients during backpropagation.
index_ranges Upper bound(s) on values allowed in indexes tensor.
laplace_tail_mass Whether to augment the prior with a Laplace mixture.
name Returns the name of this module as passed or determined in the ctor.

name_scope Returns a tf.name_scope instance for this class.
non_trainable_variables Sequence of non-trainable variables owned by this module and its submodules.
parameter_fns Functions mapping indexes to each distribution parameter.
prior Prior distribution, used for deriving range coding tables.
prior_dtype Data type of prior.
prior_fn Class or factory function returning a Distribution object.
range_coder_precision Precision used in range coding op.
stateless Whether range coding tables are created as Tensors or Variables.
submodules Sequence of all sub-modules.

Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on).

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

tail_mass Approximate probability mass which is range encoded with overflow.
trainable_variables Sequence of trainable variables owned by this module and its submodules.

variables Sequence of variables owned by this module and its submodules.

Methods

compress

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Compresses a floating-point tensor.

Compresses the tensor to bit strings. bottleneck is first quantized as in quantize(), and then compressed using the probability tables derived from indexes. The quantized tensor can later be recovered by calling decompress().

The innermost self.coding_rank dimensions are treated as one coding unit, i.e. are compressed into one string each. Any additional dimensions to the left are treated as batch dimensions.

Args
bottleneck tf.Tensor containing the data to be compressed.
indexes tf.Tensor specifying the scalar distribution for each element in bottleneck. See class docstring for examples.

Returns
A tf.Tensor having the same shape as bottleneck without the self.coding_rank innermost dimensions, containing a string for each coding unit.

decompress

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Decompresses a tensor.

Reconstructs the quantized tensor from bit strings produced by compress().

Args
strings tf.Tensor containing the compressed bit strings.
indexes tf.Tensor specifying the scalar distribution for each output element. See class docstring for examples.

Returns
A tf.Tensor of the same shape as indexes (without the optional channel dimension).

from_config

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Instantiates an entropy model from a configuration dictionary.

get_config

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Returns the configuration of the entropy model.

get_weights

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quantize

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Quantizes a floating-point tensor.

To use this entropy model as an information bottleneck during training, pass a tensor through this function. The tensor is rounded to integer values.

The gradient of this rounding operation is overridden with the identity (straight-through gradient estimator).

Args
bottleneck tf.Tensor containing the data to be quantized.

Returns
A tf.Tensor containing the quantized values.

set_weights

View source

with_name_scope

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)>

Args
method The method to wrap.

Returns
The original method wrapped such that it enters the module's name scope.

__call__

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Perturbs a tensor with (quantization) noise and estimates rate.

Args
bottleneck tf.Tensor containing the data to be compressed.
indexes tf.Tensor specifying the scalar distribution for each element in bottleneck. See class docstring for examples.
training Boolean. If False, computes the Shannon information of bottleneck under the distribution computed by self.prior_fn, which is a non-differentiable, tight lower bound on the number of bits needed to compress bottleneck using compress(). If True, returns a somewhat looser, but differentiable upper bound on this quantity.

Returns
A tuple (bottleneck_perturbed, bits) where bottleneck_perturbed is bottleneck perturbed with (quantization) noise and bits is the rate. bits has the same shape as bottleneck without the self.coding_rank innermost dimensions.