tfp.bijectors.Softfloor

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Compute a differentiable approximation to tf.math.floor.

Inherits From: AutoCompositeTensorBijector, Bijector, AutoCompositeTensor

tfp.bijectors.Softfloor(
    temperature, validate_args=False, name='softfloor'
)

Given x, compute a differentiable approximation to tf.math.floor(x). It is parameterized by a temperature parameter t to control the closeness of the approximation at the cost of numerical stability of the inverse.

This Bijector has the following properties:

• This Bijector is a map between R to R.
• For t close to 0, this bijector mimics the identity function.
• For t approaching infinity, this bijector converges pointwise to tf.math.floor (except at integer points).

Note that for lower temperatures t, this bijector becomes more numerically unstable. In particular, the inverse for this bijector is not numerically stable at lower temperatures, because flooring is not a bijective function ( and hence any pointwise limit towards the floor function will start to have a non-numerically stable inverse).

Mathematical details

Let x be in [0.5, 1.5]. We would like to simulate the floor function on this interval. We will do this via a shifted and rescaled sigmoid.

floor(x) = 0 for x < 1 and floor(x) = 1 for x >= 1. If we take f(x) = sigmoid((x - 1.) / t), where t > 0, we can see that when t goes to zero, we get that when x > 1, the f(x) tends towards 1 while f(x) tends to 0 when x < 1, thus giving us a function that looks like the floor function. If we shift f(x) by -sigmoid(-0.5 / t) and rescale by 1 / (sigmoid(0.5 / t) - sigmoid(-0.5 / t)), we preserve the pointwise limit, but also fix f(0.5) = 0. and f(1.5) = 1..

Thus we can define softfloor(x, t) = a * sigmoid((x - 1.) / t) + b

where

• a = 1 / (sigmoid(0.5 / t) - sigmoid(-0.5 / t))
• b = -sigmoid(-0.5 / t) / (sigmoid(0.5 / t) - sigmoid(-0.5 / t))

The implementation of the Softfloor bijector follows this, with the caveat that we extend the function to all of the real line, by appropriately shifting this function for each integer.

Examples

Example use:

# High temperature.
soft_floor = Softfloor(temperature=100.)
x = [2.1, 3.2, 5.5]
soft_floor.forward(x)

# Low temperature. This acts like a floor.
soft_floor = Softfloor(temperature=0.01)
soft_floor.forward(x) # Should be close to [2., 3., 5.]

# Ceiling is just a shifted floor at non-integer points.
soft_ceiling = tfb.Chain(
  [tfb.Shift(1.),
   tfb.Softfloor(temperature=1.)])
soft_ceiling.forward(x) # Should be close to [3., 5., 6.]

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

copy

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copy(
    **override_parameters_kwargs
)

Creates a copy of the bijector.

experimental_batch_shape

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experimental_batch_shape(
    x_event_ndims=None, y_event_ndims=None
)

Returns the batch shape of this bijector for inputs of the given rank.

The batch shape of a bijector decribes the set of distinct transformations it represents on events of a given size. For example: the bijector tfb.Scale([1., 2.]) has batch shape [2] for scalar events (event_ndims = 0), because applying it to a scalar event produces two scalar outputs, the result of two different scaling transformations. The same bijector has batch shape [] for vector events, because applying it to a vector produces (via elementwise multiplication) a single vector output.

Bijectors that operate independently on multiple state parts, such as tfb.JointMap, must broadcast to a coherent batch shape. Some events may not be valid: for example, the bijector tfd.JointMap([tfb.Scale([1., 2.]), tfb.Scale([1., 2., 3.])]) does not produce a valid batch shape when event_ndims = [0, 0], since the batch shapes of the two parts are inconsistent. The same bijector does define valid batch shapes of [], [2], and [3] if event_ndims is [1, 1], [0, 1], or [1, 0], respectively.

Since transforming a single event produces a scalar log-det-Jacobian, the batch shape of a bijector with non-constant Jacobian is expected to equal the shape of forward_log_det_jacobian(x, event_ndims=x_event_ndims) or inverse_log_det_jacobian(y, event_ndims=y_event_ndims), for x or y of the specified ndims.

experimental_batch_shape_tensor

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experimental_batch_shape_tensor(
    x_event_ndims=None, y_event_ndims=None
)

Returns the batch shape of this bijector for inputs of the given rank.

The batch shape of a bijector decribes the set of distinct transformations it represents on events of a given size. For example: the bijector tfb.Scale([1., 2.]) has batch shape [2] for scalar events (event_ndims = 0), because applying it to a scalar event produces two scalar outputs, the result of two different scaling transformations. The same bijector has batch shape [] for vector events, because applying it to a vector produces (via elementwise multiplication) a single vector output.

Bijectors that operate independently on multiple state parts, such as tfb.JointMap, must broadcast to a coherent batch shape. Some events may not be valid: for example, the bijector tfd.JointMap([tfb.Scale([1., 2.]), tfb.Scale([1., 2., 3.])]) does not produce a valid batch shape when event_ndims = [0, 0], since the batch shapes of the two parts are inconsistent. The same bijector does define valid batch shapes of [], [2], and [3] if event_ndims is [1, 1], [0, 1], or [1, 0], respectively.

Since transforming a single event produces a scalar log-det-Jacobian, the batch shape of a bijector with non-constant Jacobian is expected to equal the shape of forward_log_det_jacobian(x, event_ndims=x_event_ndims) or inverse_log_det_jacobian(y, event_ndims=y_event_ndims), for x or y of the specified ndims.

forward

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forward(
    x, name='forward', **kwargs
)

Returns the forward Bijector evaluation, i.e., X = g(Y).

forward_dtype

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forward_dtype(
    dtype=UNSPECIFIED, name='forward_dtype', **kwargs
)

Returns the dtype returned by forward for the provided input.

forward_event_ndims

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forward_event_ndims(
    event_ndims, **kwargs
)

Returns the number of event dimensions produced by forward.

forward_event_shape

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forward_event_shape(
    input_shape
)

Shape of a single sample from a single batch as a TensorShape.

Same meaning as forward_event_shape_tensor. May be only partially defined.

forward_event_shape_tensor

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forward_event_shape_tensor(
    input_shape, name='forward_event_shape_tensor'
)

Shape of a single sample from a single batch as an int32 1D Tensor.

forward_log_det_jacobian

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forward_log_det_jacobian(
    x, event_ndims=None, name='forward_log_det_jacobian', **kwargs
)

Returns both the forward_log_det_jacobian.

inverse

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inverse(
    y, name='inverse', **kwargs
)

Returns the inverse Bijector evaluation, i.e., X = g^{-1}(Y).

inverse_dtype

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inverse_dtype(
    dtype=UNSPECIFIED, name='inverse_dtype', **kwargs
)

Returns the dtype returned by inverse for the provided input.

inverse_event_ndims

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inverse_event_ndims(
    event_ndims, **kwargs
)

Returns the number of event dimensions produced by inverse.

inverse_event_shape

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inverse_event_shape(
    output_shape
)

Shape of a single sample from a single batch as a TensorShape.

Same meaning as inverse_event_shape_tensor. May be only partially defined.

inverse_event_shape_tensor

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inverse_event_shape_tensor(
    output_shape, name='inverse_event_shape_tensor'
)

Shape of a single sample from a single batch as an int32 1D Tensor.

inverse_log_det_jacobian

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inverse_log_det_jacobian(
    y, event_ndims=None, name='inverse_log_det_jacobian', **kwargs
)

Returns the (log o det o Jacobian o inverse)(y).

Mathematically, returns: log(det(dX/dY))(Y). (Recall that: X=g^{-1}(Y).)

Note that forward_log_det_jacobian is the negative of this function, evaluated at g^{-1}(y).

parameter_properties

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@classmethod
parameter_properties(
    dtype=tf.float32
)

Returns a dict mapping constructor arg names to property annotations.

This dict should include an entry for each of the bijector's Tensor-valued constructor arguments.

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__(
    value, name=None, **kwargs
)

Applies or composes the Bijector, depending on input type.

This is a convenience function which applies the Bijector instance in three different ways, depending on the input:

1. If the input is a tfd.Distribution instance, return tfd.TransformedDistribution(distribution=input, bijector=self).
2. If the input is a tfb.Bijector instance, return tfb.Chain([self, input]).
3. Otherwise, return self.forward(input)

Examples

sigmoid = tfb.Reciprocal()(
    tfb.Shift(shift=1.)(
      tfb.Exp()(
        tfb.Scale(scale=-1.))))
# ==> `tfb.Chain([
#         tfb.Reciprocal(),
#         tfb.Shift(shift=1.),
#         tfb.Exp(),
#         tfb.Scale(scale=-1.),
#      ])`  # ie, `tfb.Sigmoid()`

log_normal = tfb.Exp()(tfd.Normal(0, 1))
# ==> `tfd.TransformedDistribution(tfd.Normal(0, 1), tfb.Exp())`

tfb.Exp()([-1., 0., 1.])
# ==> tf.exp([-1., 0., 1.])

__eq__

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__eq__(
    other
)

Return self==value.