![]() |
Compute a differentiable approximation to tf.math.floor
.
Inherits From: Bijector
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 betweenR
toR
. - For
t
close to0
, this bijector mimics the identity function. - For
t
approachinginfinity
, this bijector converges pointwise totf.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.]
Args | |
---|---|
graph_parents
|
Python list of graph prerequisites of this Bijector .
|
is_constant_jacobian
|
Python bool indicating that the Jacobian matrix is
not a function of the input.
|
validate_args
|
Python bool , default False . Whether to validate input
with asserts. If validate_args is False , and the inputs are invalid,
correct behavior is not guaranteed.
|
dtype
|
tf.dtype supported by this Bijector . None means dtype is not
enforced. For multipart bijectors, this value is expected to be the
same for all elements of the input and output structures.
|
forward_min_event_ndims
|
Python integer (structure) indicating the
minimum number of dimensions on which forward operates.
|
inverse_min_event_ndims
|
Python integer (structure) indicating the
minimum number of dimensions on which inverse operates. Will be set to
forward_min_event_ndims by default, if no value is provided.
|
parameters
|
Python dict of parameters used to instantiate this
Bijector . Bijector instances with identical types, names, and
parameters share an input/output cache. parameters dicts are
keyed by strings and are identical if their keys are identical and if
corresponding values have identical hashes (or object ids, for
unhashable objects).
|
name
|
The name to give Ops created by the initializer. |
Raises | |
---|---|
ValueError
|
If neither forward_min_event_ndims and
inverse_min_event_ndims are specified, or if either of them is
negative.
|
ValueError
|
If a member of graph_parents is not a Tensor .
|
Attributes | |
---|---|
dtype
|
|
forward_min_event_ndims
|
Returns the minimal number of dimensions bijector.forward operates on.
Multipart bijectors return structured |
graph_parents
|
Returns this Bijector 's graph_parents as a Python list.
|
has_static_min_event_ndims
|
Returns True if the bijector has statically-known min_event_ndims .
|
inverse_min_event_ndims
|
Returns the minimal number of dimensions bijector.inverse operates on.
Multipart bijectors return structured |
is_constant_jacobian
|
Returns true iff the Jacobian matrix is not a function of x. |
name
|
Returns the string name of this Bijector .
|
name_scope
|
Returns a tf.name_scope instance for this class.
|
parameters
|
Dictionary of parameters used to instantiate this Bijector .
|
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).
|
temperature
|
|
trainable_variables
|
Sequence of trainable variables owned by this module and its submodules. |
validate_args
|
Returns True if Tensor arguments will be validated. |
variables
|
Sequence of variables owned by this module and its submodules. |
Methods
forward
forward(
x, name='forward', **kwargs
)
Returns the forward Bijector
evaluation, i.e., X = g(Y).
Args | |
---|---|
x
|
Tensor (structure). The input to the 'forward' evaluation.
|
name
|
The name to give this op. |
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
Tensor (structure).
|
Raises | |
---|---|
TypeError
|
if self.dtype is specified and x.dtype is not
self.dtype .
|
NotImplementedError
|
if _forward is not implemented.
|
forward_dtype
forward_dtype(
dtype=UNSPECIFIED, name='forward_dtype', **kwargs
)
Returns the dtype returned by forward
for the provided input.
forward_event_ndims
forward_event_ndims(
event_ndims, **kwargs
)
Returns the number of event dimensions produced by forward
.
forward_event_shape
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.
Args | |
---|---|
input_shape
|
TensorShape (structure) indicating event-portion shape
passed into forward function.
|
Returns | |
---|---|
forward_event_shape_tensor
|
TensorShape (structure) indicating
event-portion shape after applying forward . Possibly unknown.
|
forward_event_shape_tensor
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
.
Args | |
---|---|
input_shape
|
Tensor , int32 vector (structure) indicating event-portion
shape passed into forward function.
|
name
|
name to give to the op |
Returns | |
---|---|
forward_event_shape_tensor
|
Tensor , int32 vector (structure)
indicating event-portion shape after applying forward .
|
forward_log_det_jacobian
forward_log_det_jacobian(
x, event_ndims, name='forward_log_det_jacobian', **kwargs
)
Returns both the forward_log_det_jacobian.
Args | |
---|---|
x
|
Tensor (structure). The input to the 'forward' Jacobian determinant
evaluation.
|
event_ndims
|
Number of dimensions in the probabilistic events being
transformed. Must be greater than or equal to
self.forward_min_event_ndims . The result is summed over the final
dimensions to produce a scalar Jacobian determinant for each event, i.e.
it has shape rank(x) - event_ndims dimensions.
Multipart bijectors require structured event_ndims, such that
rank(y[i]) - rank(event_ndims[i]) is the same for all elements i of
the structured input. Furthermore, the first event_ndims[i] of each
x[i].shape must be the same for all i (broadcasting is not allowed).
|
name
|
The name to give this op. |
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
Tensor (structure), if this bijector is injective.
If not injective this is not implemented.
|
Raises | |
---|---|
TypeError
|
if y 's dtype is incompatible with the expected output dtype.
|
NotImplementedError
|
if neither _forward_log_det_jacobian
nor {_inverse , _inverse_log_det_jacobian } are implemented, or
this is a non-injective bijector.
|
inverse
inverse(
y, name='inverse', **kwargs
)
Returns the inverse Bijector
evaluation, i.e., X = g^{-1}(Y).
Args | |
---|---|
y
|
Tensor (structure). The input to the 'inverse' evaluation.
|
name
|
The name to give this op. |
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
Tensor (structure), if this bijector is injective.
If not injective, returns the k-tuple containing the unique
k points (x1, ..., xk) such that g(xi) = y .
|
Raises | |
---|---|
TypeError
|
if y 's structured dtype is incompatible with the expected
output dtype.
|
NotImplementedError
|
if _inverse is not implemented.
|
inverse_dtype
inverse_dtype(
dtype=UNSPECIFIED, name='inverse_dtype', **kwargs
)
Returns the dtype returned by inverse
for the provided input.
inverse_event_ndims
inverse_event_ndims(
event_ndims, **kwargs
)
Returns the number of event dimensions produced by inverse
.
inverse_event_shape
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.
Args | |
---|---|
output_shape
|
TensorShape (structure) indicating event-portion shape
passed into inverse function.
|
Returns | |
---|---|
inverse_event_shape_tensor
|
TensorShape (structure) indicating
event-portion shape after applying inverse . Possibly unknown.
|
inverse_event_shape_tensor
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
.
Args | |
---|---|
output_shape
|
Tensor , int32 vector (structure) indicating
event-portion shape passed into inverse function.
|
name
|
name to give to the op |
Returns | |
---|---|
inverse_event_shape_tensor
|
Tensor , int32 vector (structure)
indicating event-portion shape after applying inverse .
|
inverse_log_det_jacobian
inverse_log_det_jacobian(
y, event_ndims, 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)
.
Args | |
---|---|
y
|
Tensor (structure). The input to the 'inverse' Jacobian determinant
evaluation.
|
event_ndims
|
Number of dimensions in the probabilistic events being
transformed. Must be greater than or equal to
self.inverse_min_event_ndims . The result is summed over the final
dimensions to produce a scalar Jacobian determinant for each event, i.e.
it has shape rank(y) - event_ndims dimensions.
Multipart bijectors require structured event_ndims, such that
rank(y[i]) - rank(event_ndims[i]) is the same for all elements i of
the structured input. Furthermore, the first event_ndims[i] of each
x[i].shape must be the same for all i (broadcasting is not allowed).
|
name
|
The name to give this op. |
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
ildj
|
Tensor , if this bijector is injective.
If not injective, returns the tuple of local log det
Jacobians, log(det(Dg_i^{-1}(y))) , where g_i is the restriction
of g to the ith partition Di .
|
Raises | |
---|---|
TypeError
|
if x 's dtype is incompatible with the expected inverse-dtype.
|
NotImplementedError
|
if _inverse_log_det_jacobian is not implemented.
|
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.Variable
s and tf.Tensor
s 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__
__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:
- If the input is a
tfd.Distribution
instance, returntfd.TransformedDistribution(distribution=input, bijector=self)
. - If the input is a
tfb.Bijector
instance, returntfb.Chain([self, input])
. - Otherwise, return
self.forward(input)
Args | |
---|---|
value
|
A tfd.Distribution , tfb.Bijector , or a (structure of) Tensor .
|
name
|
Python str name given to ops created by this function.
|
**kwargs
|
Additional keyword arguments passed into the created
tfd.TransformedDistribution , tfb.Bijector , or self.forward .
|
Returns | |
---|---|
composition
|
A tfd.TransformedDistribution if the input was a
tfd.Distribution , a tfb.Chain if the input was a tfb.Bijector , or
a (structure of) Tensor computed by self.forward .
|
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__
__eq__(
other
)
Return self==value.