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Lattice layer.
tfl.layers.Lattice(
lattice_sizes, units=1, monotonicities=None, unimodalities=None,
edgeworth_trusts=None, trapezoid_trusts=None, monotonic_dominances=None,
range_dominances=None, joint_monotonicities=None, joint_unimodalities=None,
output_min=None, output_max=None, num_projection_iterations=10,
monotonic_at_every_step=True, clip_inputs=True, interpolation='hypercube',
kernel_initializer='random_uniform_or_linear_initializer',
kernel_regularizer=None, **kwargs
)
Used in the notebooks
Used in the tutorials 

Layer performs interpolation using one of units
ddimension lattices with
arbitrary number of keypoints per dimension. There are trainable weights
associated with lattice vertices. Input to this layer is considered to be a
ddimensional point within the lattice. If point coincides with one of the
lattice vertex then interpolation result for this point is equal to weight
associated with that vertex. Otherwise, all surrounding vertices contribute to
the interpolation result inversely proportional to the distance from them.
For example lattice sizes: [2, 3] produce following lattice:
ooo
  
ooo
First coordinate of input tensor must be within [0, 1], and the second within [0, 2]. If coordinates are outside of this range they will be clipped into it.
There are several types of constraints on the shape of the learned function that are either 1 or 2 dimensional:
 Monotonicity: constrains the function to be either increasing or decreasing in that dimension.
 Unimodality: constrains the function to be unimodal in that dimension with minimum being in the center lattice vertex of that dimension. Single dimension can not be constrained to be both monotonic and unimodal. Unimodal dimensions must have at least 3 lattice vertices.
 Edgeworth Trust: constrains the function to be more responsive to a main feature as a secondary conditional feature increases or decreases. For example, we may want the model to rely more on average rating (main feature) when the number of reviews (conditional feature) is high. In particular, the constraint guarantees that a given change in the main feature's value will change the model output by more when a secondary feature indicates higher trust in the main feature. Note that the constraint only works when the model is monotonic in the main feature.
 Trapezoid Trust: conceptually similar to edgeworth trust, but this constraint guarantees that the range of possible outputs along the main feature dimension, when a conditional feature indicates low trust, is a subset of the range of outputs when a conditional feature indicates high trust. When lattices have 2 vertices in each constrained dimension, this implies edgeworth trust (which only constrains the size of the relevant ranges). With more than 2 lattice vertices per dimension, the two constraints diverge and are not necessarily 'weaker' or 'stronger' than each other  edgeworth trust acts throughout the lattice interior on delta shifts in the main feature, while trapezoid trust only acts on the min and max extremes of the main feature, constraining the overall range of outputs across the domain of the main feature. The two types of trust constraints can be applied jointly.
 Monotonic Dominance: constrains the function to require the effect (slope) in the direction of the dominant dimension to be greater than that of the weak dimension for any point in the lattice. Both dominant and weak dimensions must be monotonic. Note that this constraint might not be strictly satisified at the end of training. In such cases, increase the number of projection iterations.
 Range Dominance: constraints the function to require the range of possible outputs to be greater than if one varies the dominant dimension than if one varies the weak dimension for any point. Both dominant and weak dimensions must be monotonic. Note that this constraint might not be strictly satisified at the end of training. In such cases, increase the number of projection iterations.
 Joint Monotonicity: constrains the function to be monotonic along a diagonal direction of a two dimensional subspace when all other dimensions are fixed. For example, if our function is scoring the profit given A hotel guests and B hotel beds, it may be wrong to constrain the profit to be increasing in either hotel guests or hotel beds independently, but along the diagonal (+ 1 guest and +1 bed), the profit should be monotonic. Note that this constraint might not be strictly satisified at the end of training. In such cases, increase the number of projection iterations.
There are upper and lower bound constraints on the output.
All units share the same layer configuration, but each has their separate set of trained parameters.
Input shape:
 if
units == 1
: tensor of shape:(batch_size, ..., len(lattice_sizes))
or list oflen(lattice_sizes)
tensors of same shape:(batch_size, ..., 1)
 if
units > 1
: tensor of shape:(batch_size, ..., units, len(lattice_sizes))
or list oflen(lattice_sizes)
tensors of same shape:(batch_size, ..., units, 1)
A typical shape is: (batch_size, len(lattice_sizes))
Output shape:
Tensor of shape: (batch_size, ..., units)
Example:
lattice = tfl.layers.Lattice(
# Number of vertices along each dimension.
lattice_sizes=[2, 2, 3, 4, 2, 2, 3],
# You can specify monotonicity constraints.
monotonicities=['increasing', 'none', 'increasing', 'increasing',
'increasing', 'increasing', 'increasing'],
# You can specify trust constraints between pairs of features. Here we
# constrain the function to be more responsive to a main feature (index 4)
# as a secondary conditional feature (index 3) increases (positive
# direction).
edgeworth_trusts=(4, 3, 'positive'),
# Output can be bounded.
output_min=0.0,
output_max=1.0)
Args  

lattice_sizes

List or tuple of length d of integers which represents number of lattice vertices per dimension (minimum is 2). Second dimension of input shape must match the number of elements in lattice sizes. 
units

Output dimension of the layer. See class comments for details. 
monotonicities

None or list or tuple of same length as lattice_sizes of {'none', 'increasing', 0, 1} which specifies if the model output should be monotonic in corresponding feature, using 'increasing' or 1 to indicate increasing monotonicity and 'none' or 0 to indicate no monotonicity constraints. 
unimodalities

None or list or tuple of same length as lattice_sizes of {'none', 'valley', 'peak', 0, 1, 1} which specifies if the model output should be unimodal in corresponding feature, using 'valley' or 1 to indicate that function first decreases then increases, using 'peak' or 1 to indicate that funciton first increases then decreases, using 'none' or 0 to indicate no unimodality constraints. 
edgeworth_trusts

None or threeelement tuple or iterable of threeelement tuples. First element is the index of the main (monotonic) feature. Second element is the index of the conditional feature. Third element is the direction of trust: 'positive' or 1 if higher values of the conditional feature should increase trust in the main feature and 'negative' or 1 otherwise. 
trapezoid_trusts

None or threeelement tuple or iterable of threeelement tuples. First element is the index of the main (monotonic) feature. Second element is the index of the conditional feature. Third element is the direction of trust: 'positive' or 1 if higher values of the conditional feature should increase trust in the main feature and 'negative' or 1 otherwise. 
monotonic_dominances

None or twoelement tuple or iterable of twoelement tuples. First element is the index of the dominant feature. Second element is the index of the weak feature. 
range_dominances

None or twoelement tuple or iterable of twoelement tuples. First element is the index of the dominant feature. Second element is the index of the weak feature. 
joint_monotonicities

None or twoelement tuple or iterable of twoelement tuples which represents indices of two features requiring joint monotonicity. 
joint_unimodalities

None or tuple or iterable of tuples. Each tuple contains 2 elements: iterable of indices of single group of jointly unimodal features followed by string 'valley' or 'peak', using 'valley' to indicate that function first decreases then increases, using 'peak' to indicate that funciton first increases then decreases. For example: ([0, 3, 4], 'valley'). 
output_min

None or lower bound of the output. 
output_max

None or upper bound of the output. 
num_projection_iterations

Number of iterations of Dykstra projections algorithm. Projection updates will be closer to a true projection (with respect to the L2 norm) with higher number of iterations. Increasing this number has diminishing return on projection precsion. Infinite number of iterations would yield perfect projection. Increasing this number might slightly improve convergence by cost of slightly increasing running time. Most likely you want this number to be proportional to number of lattice vertices in largest constrained dimension. 
monotonic_at_every_step

Whether to strictly enforce monotonicity and trust constraints after every gradient update by applying a final imprecise projection. Setting this parameter to True together with small num_projection_iterations parameter is likely to hurt convergence. 
clip_inputs

If inputs should be clipped to the input range of the lattice. 
interpolation

One of 'hypercube' or 'simplex' interpolation. For a
ddimensional lattice, 'hypercube' interpolates 2^d parameters, whereas
'simplex' uses d+1 parameters and thus scales better. For details see
tfl.lattice_lib.evaluate_with_simplex_interpolation and
tfl.lattice_lib.evaluate_with_hypercube_interpolation .

kernel_initializer

None or one of:

kernel_regularizer

None or a single element or a list of following:
('torsion', l1, l2) where l1 and l2 represent corresponding
regularization amount for graph Torsion regularizer. l1 and l2 can
either be single floats or lists of floats to specify different
regularization amount for every dimension.('laplacian', l1, l2) where l1 and l2 represent corresponding
regularization amount for graph Laplacian regularizer. l1 and l2 can
either be single floats or lists of floats to specify different
regularization amount for every dimension. 
**kwargs

Other args passed to tf.keras.layers.Layer initializer.

Raises  

ValueError

If layer hyperparameters are invalid. 
Attributes  

kernel

weights of the lattice. 
activity_regularizer

Optional regularizer function for the output of this layer. 
dtype

Dtype used by the weights of the layer, set in the constructor. 
dynamic

Whether the layer is dynamic (eageronly); set in the constructor. 
input

Retrieves the input tensor(s) of a layer.
Only applicable if the layer has exactly one input, i.e. if it is connected to one incoming layer. 
input_spec

InputSpec instance(s) describing the input format for this layer.
When you create a layer subclass, you can set
Now, if you try to call the layer on an input that isn't rank 4
(for instance, an input of shape
Input checks that can be specified via
For more information, see 
losses

Losses which are associated with this Layer .
Variable regularization tensors are created when this property is accessed,
so it is eager safe: accessing 
metrics

List of tf.keras.metrics.Metric instances tracked by the layer.

name

Name of the layer (string), set in the constructor. 
name_scope

Returns a tf.name_scope instance for this class.

non_trainable_weights

List of all nontrainable weights tracked by this layer.
Nontrainable weights are not updated during training. They are expected
to be updated manually in 
output

Retrieves the output tensor(s) of a layer.
Only applicable if the layer has exactly one output, i.e. if it is connected to one incoming layer. 
submodules

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

trainable


trainable_weights

List of all trainable weights tracked by this layer.
Trainable weights are updated via gradient descent during training. 
weights

Returns the list of all layer variables/weights. 
Methods
add_loss
add_loss(
losses, inputs=None
)
Add loss tensor(s), potentially dependent on layer inputs.
Some losses (for instance, activity regularization losses) may be dependent
on the inputs passed when calling a layer. Hence, when reusing the same
layer on different inputs a
and b
, some entries in layer.losses
may
be dependent on a
and some on b
. This method automatically keeps track
of dependencies.
This method can be used inside a subclassed layer or model's call
function, in which case losses
should be a Tensor or list of Tensors.
Example:
class MyLayer(tf.keras.layers.Layer):
def call(inputs, self):
self.add_loss(tf.abs(tf.reduce_mean(inputs)), inputs=True)
return inputs
This method can also be called directly on a Functional Model during
construction. In this case, any loss Tensors passed to this Model must
be symbolic and be able to be traced back to the model's Input
s. These
losses become part of the model's topology and are tracked in get_config
.
Example:
inputs = tf.keras.Input(shape=(10,))
x = tf.keras.layers.Dense(10)(inputs)
outputs = tf.keras.layers.Dense(1)(x)
model = tf.keras.Model(inputs, outputs)
# Activity regularization.
model.add_loss(tf.abs(tf.reduce_mean(x)))
If this is not the case for your loss (if, for example, your loss references
a Variable
of one of the model's layers), you can wrap your loss in a
zeroargument lambda. These losses are not tracked as part of the model's
topology since they can't be serialized.
Example:
inputs = tf.keras.Input(shape=(10,))
x = tf.keras.layers.Dense(10)(inputs)
outputs = tf.keras.layers.Dense(1)(x)
model = tf.keras.Model(inputs, outputs)
# Weight regularization.
model.add_loss(lambda: tf.reduce_mean(x.kernel))
The get_losses_for
method allows to retrieve the losses relevant to a
specific set of inputs.
Arguments  

losses

Loss tensor, or list/tuple of tensors. Rather than tensors, losses may also be zeroargument callables which create a loss tensor. 
inputs

Ignored when executing eagerly. If anything other than None is
passed, it signals the losses are conditional on some of the layer's
inputs, and thus they should only be run where these inputs are
available. This is the case for activity regularization losses, for
instance. If None is passed, the losses are assumed
to be unconditional, and will apply across all dataflows of the layer
(e.g. weight regularization losses).

add_metric
add_metric(
value, aggregation=None, name=None
)
Adds metric tensor to the layer.
Args  

value

Metric tensor. 
aggregation

Samplewise metric reduction function. If aggregation=None ,
it indicates that the metric tensor provided has been aggregated
already. eg, bin_acc = BinaryAccuracy(name='acc') followed by
model.add_metric(bin_acc(y_true, y_pred)) . If aggregation='mean', the
given metric tensor will be samplewise reduced using mean function.
eg, model.add_metric(tf.reduce_sum(outputs), name='output_mean',
aggregation='mean') .

name

String metric name. 
Raises  

ValueError

If aggregation is anything other than None or mean .

assert_constraints
assert_constraints(
eps=1e06
)
Asserts that weights satisfy all constraints.
In graph mode builds and returns list of assertion ops. In eager mode directly executes assertions.
Args  

eps

allowed constraints violation. 
Returns  

List of assertion ops in graph mode or immediately asserts in eager mode. 
build
build(
input_shape
)
Standard Keras build() method.
compute_mask
compute_mask(
inputs, mask=None
)
Computes an output mask tensor.
Arguments  

inputs

Tensor or list of tensors. 
mask

Tensor or list of tensors. 
Returns  

None or a tensor (or list of tensors, one per output tensor of the layer). 
compute_output_shape
compute_output_shape(
input_shape
)
Standard Keras compute_output_shape() method.
count_params
count_params()
Count the total number of scalars composing the weights.
Returns  

An integer count. 
Raises  

ValueError

if the layer isn't yet built (in which case its weights aren't yet defined). 
finalize_constraints
finalize_constraints()
Ensures layers weights strictly satisfy constraints.
Applies approximate projection to strictly satisfy specified constraints.
If monotonic_at_every_step == True
there is no need to call this function.
Returns  

In eager mode directly updates weights and returns variable which stores
them. In graph mode returns assign_add op which has to be executed to
updates weights.

from_config
@classmethod
from_config( config )
Creates a layer from its config.
This method is the reverse of get_config
,
capable of instantiating the same layer from the config
dictionary. It does not handle layer connectivity
(handled by Network), nor weights (handled by set_weights
).
Arguments  

config

A Python dictionary, typically the output of get_config. 
Returns  

A layer instance. 
get_config
get_config()
Standard Keras config for serialization.
get_weights
get_weights()
Returns the current weights of the layer.
The weights of a layer represent the state of the layer. This function returns both trainable and nontrainable weight values associated with this layer as a list of Numpy arrays, which can in turn be used to load state into similarly parameterized layers.
For example, a Dense layer returns a list of two values peroutput weights and the bias value. These can be used to set the weights of another Dense layer:
a = tf.keras.layers.Dense(1,
kernel_initializer=tf.constant_initializer(1.))
a_out = a(tf.convert_to_tensor([[1., 2., 3.]]))
a.get_weights()
[array([[1.],
[1.],
[1.]], dtype=float32), array([0.], dtype=float32)]
b = tf.keras.layers.Dense(1,
kernel_initializer=tf.constant_initializer(2.))
b_out = b(tf.convert_to_tensor([[10., 20., 30.]]))
b.get_weights()
[array([[2.],
[2.],
[2.]], dtype=float32), array([0.], dtype=float32)]
b.set_weights(a.get_weights())
b.get_weights()
[array([[1.],
[1.],
[1.]], dtype=float32), array([0.], dtype=float32)]
Returns  

Weights values as a list of numpy arrays. 
set_weights
set_weights(
weights
)
Sets the weights of the layer, from Numpy arrays.
The weights of a layer represent the state of the layer. This function sets the weight values from numpy arrays. The weight values should be passed in the order they are created by the layer. Note that the layer's weights must be instantiated before calling this function by calling the layer.
For example, a Dense layer returns a list of two values peroutput weights and the bias value. These can be used to set the weights of another Dense layer:
a = tf.keras.layers.Dense(1,
kernel_initializer=tf.constant_initializer(1.))
a_out = a(tf.convert_to_tensor([[1., 2., 3.]]))
a.get_weights()
[array([[1.],
[1.],
[1.]], dtype=float32), array([0.], dtype=float32)]
b = tf.keras.layers.Dense(1,
kernel_initializer=tf.constant_initializer(2.))
b_out = b(tf.convert_to_tensor([[10., 20., 30.]]))
b.get_weights()
[array([[2.],
[2.],
[2.]], dtype=float32), array([0.], dtype=float32)]
b.set_weights(a.get_weights())
b.get_weights()
[array([[1.],
[1.],
[1.]], dtype=float32), array([0.], dtype=float32)]
Arguments  

weights

a list of Numpy arrays. The number
of arrays and their shape must match
number of the dimensions of the weights
of the layer (i.e. it should match the
output of get_weights ).

Raises  

ValueError

If the provided weights list does not match the layer's specifications. 
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__(
*args, **kwargs
)
Wraps call
, applying pre and postprocessing steps.
Arguments  

*args

Positional arguments to be passed to self.call .

**kwargs

Keyword arguments to be passed to self.call .

Returns  

Output tensor(s). 
Note:
 The following optional keyword arguments are reserved for specific uses:
training
: Boolean scalar tensor of Python boolean indicating whether thecall
is meant for training or inference.mask
: Boolean input mask.
 If the layer's
call
method takes amask
argument (as some Keras layers do), its default value will be set to the mask generated forinputs
by the previous layer (ifinput
did come from a layer that generated a corresponding mask, i.e. if it came from a Keras layer with masking support.
Raises  

ValueError

if the layer's call method returns None (an invalid value).

RuntimeError

if super().__init__() was not called in the constructor.
