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## Class `Lattice`

Lattice layer.

### Used in the notebooks

Used in the tutorials |
---|

Layer performs interpolation using one of `units`

d-dimension 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
d-dimensional 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:

```
o---o---o
| | |
o---o---o
```

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.**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 in-dependently, 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 of`len(lattice_sizes)`

tensors of same shape:`(batch_size, ..., 1)`

- if
`units > 1`

: tensor of shape:`(batch_size, ..., units, len(lattice_sizes))`

or list of`len(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)`

#### Attributes:

All

`__init__`

arguments.: weights of the lattice.`kernel`

#### 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)
```

`__init__`

```
__init__(
lattice_sizes,
units=1,
monotonicities=None,
unimodalities=None,
edgeworth_trusts=None,
trapezoid_trusts=None,
monotonic_dominances=None,
joint_monotonicities=None,
output_min=None,
output_max=None,
num_projection_iterations=10,
monotonic_at_every_step=True,
clip_inputs=True,
kernel_initializer='linear_initializer',
kernel_regularizer=None,
**kwargs
)
```

Initializes an instance of `Lattice`

.

#### Args:

: 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.`lattice_sizes`

: Output dimension of the layer. See class comments for details.`units`

: 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.`monotonicities`

: None or list or tuple of same length as lattice_sizes of {'none', 'valley', 0, 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 and 'none' or 0 to indicate no unimodality constraints.`unimodalities`

: None or three-element tuple or iterable of three-element 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.`edgeworth_trusts`

: None or three-element tuple or iterable of three-element 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 two-element tuple or iterable of two-element tuples. First element is the index of the dominant feature. Second element is the index of the weak feature.`monotonic_dominances`

: None or two-element tuple or iterable of two-element tuples which represents indices of two features requiring joint monotonicity.`joint_monotonicities`

: None or lower bound of the output.`output_min`

: None or upper bound of the output.`output_max`

: 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.`num_projection_iterations`

: 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.`monotonic_at_every_step`

: If inputs should be clipped to the input range of the lattice.`clip_inputs`

: None or one of:`kernel_initializer`

`'linear_initializer'`

: initialize parameters to form a linear function with positive and equal coefficients for monotonic dimensions and 0.0 coefficients for other dimensions. Linear function is such that minimum possible output is equal to output_min and maximum possible output is equal to output_max. See`tfl.lattice_layer.LinearInitializer`

class docstring for more details.`'random_monotonic_initializer'`

: initialize parameters uniformly at random such that all parameters are monotonically increasing for each input. Parameters will be sampled uniformly at random from the range`[output_min, output_max]`

. See`tfl.lattice_layer.RandomMonotonicInitializer`

class docstring for more details.- Any Keras initializer object.

: None or a single element or a list of following:`kernel_regularizer`

- Tuple
`('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. - Tuple
`('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. - Any Keras regularizer object.

- Tuple
: Other args passed to`**kwargs`

`tf.keras.layers.Layer`

initializer.

#### Raises:

: If layer hyperparameters are invalid.`ValueError`

## Properties

`activity_regularizer`

Optional regularizer function for the output of this layer.

`dtype`

`dynamic`

`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.

#### Returns:

Input tensor or list of input tensors.

#### Raises:

: If called in Eager mode.`RuntimeError`

: If no inbound nodes are found.`AttributeError`

`input_mask`

Retrieves the input mask tensor(s) of a layer.

Only applicable if the layer has exactly one inbound node, i.e. if it is connected to one incoming layer.

#### Returns:

Input mask tensor (potentially None) or list of input mask tensors.

#### Raises:

: if the layer is connected to more than one incoming layers.`AttributeError`

`input_shape`

Retrieves the input shape(s) of a layer.

Only applicable if the layer has exactly one input, i.e. if it is connected to one incoming layer, or if all inputs have the same shape.

#### Returns:

Input shape, as an integer shape tuple (or list of shape tuples, one tuple per input tensor).

#### Raises:

: if the layer has no defined input_shape.`AttributeError`

: if called in Eager mode.`RuntimeError`

`input_spec`

`losses`

Losses which are associated with this `Layer`

.

Variable regularization tensors are created when this property is accessed,
so it is eager safe: accessing `losses`

under a `tf.GradientTape`

will
propagate gradients back to the corresponding variables.

#### Returns:

A list of tensors.

`metrics`

`name`

Returns the name of this module as passed or determined in the ctor.

NOTE: This is not the same as the `self.name_scope.name`

which includes
parent module names.

`name_scope`

Returns a `tf.name_scope`

instance for this class.

`non_trainable_variables`

`non_trainable_weights`

`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.

#### Returns:

Output tensor or list of output tensors.

#### Raises:

: if the layer is connected to more than one incoming layers.`AttributeError`

: if called in Eager mode.`RuntimeError`

`output_mask`

Retrieves the output mask tensor(s) of a layer.

Only applicable if the layer has exactly one inbound node, i.e. if it is connected to one incoming layer.

#### Returns:

Output mask tensor (potentially None) or list of output mask tensors.

#### Raises:

: if the layer is connected to more than one incoming layers.`AttributeError`

`output_shape`

Retrieves the output shape(s) of a layer.

Only applicable if the layer has one output, or if all outputs have the same shape.

#### Returns:

Output shape, as an integer shape tuple (or list of shape tuples, one tuple per output tensor).

#### Raises:

: if the layer has no defined output shape.`AttributeError`

: if called in Eager mode.`RuntimeError`

`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
assert list(a.submodules) == [b, c]
assert list(b.submodules) == [c]
assert list(c.submodules) == []
```

#### Returns:

A sequence of all submodules.

`trainable`

`trainable_variables`

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

#### Returns:

A sequence of variables for the current module (sorted by attribute name) followed by variables from all submodules recursively (breadth first).

`trainable_weights`

`updates`

`variables`

Returns the list of all layer variables/weights.

Alias of `self.weights`

.

#### Returns:

A list of variables.

`weights`

Returns the list of all layer variables/weights.

#### Returns:

A list of variables.

## Methods

`__call__`

```
__call__(
inputs,
*args,
**kwargs
)
```

Wraps `call`

, applying pre- and post-processing steps.

#### Arguments:

: input tensor(s).`inputs`

: additional positional arguments to be passed to`*args`

`self.call`

.: additional keyword arguments to be passed to`**kwargs`

`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 the`call`

is meant for training or inference.`mask`

: Boolean input mask.

- If the layer's
`call`

method takes a`mask`

argument (as some Keras layers do), its default value will be set to the mask generated for`inputs`

by the previous layer (if`input`

did come from a layer that generated a corresponding mask, i.e. if it came from a Keras layer with masking support.

#### Raises:

: if the layer's`ValueError`

`call`

method returns None (an invalid value).

`assert_constraints`

```
assert_constraints(eps=1e-06)
```

Asserts that weights satisfy all constraints.

In graph mode builds and returns list of assertion ops. In eager mode directly executes assetions.

#### Args:

: allowed constraints violation.`eps`

#### Returns:

List of assertion ops in graph mode or immideately 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:

: Tensor or list of tensors.`inputs`

: Tensor or list of tensors.`mask`

#### 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:

: if the layer isn't yet built (in which case its weights aren't yet defined).`ValueError`

`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(
cls,
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:

: A Python dictionary, typically the output of get_config.`config`

#### Returns:

A layer instance.

`get_config`

```
get_config()
```

Standard Keras config for serialization.

`get_input_at`

```
get_input_at(node_index)
```

Retrieves the input tensor(s) of a layer at a given node.

#### Arguments:

: Integer, index of the node from which to retrieve the attribute. E.g.`node_index`

`node_index=0`

will correspond to the first time the layer was called.

#### Returns:

A tensor (or list of tensors if the layer has multiple inputs).

#### Raises:

: If called in Eager mode.`RuntimeError`

`get_input_mask_at`

```
get_input_mask_at(node_index)
```

Retrieves the input mask tensor(s) of a layer at a given node.

#### Arguments:

: Integer, index of the node from which to retrieve the attribute. E.g.`node_index`

`node_index=0`

will correspond to the first time the layer was called.

#### Returns:

A mask tensor (or list of tensors if the layer has multiple inputs).

`get_input_shape_at`

```
get_input_shape_at(node_index)
```

Retrieves the input shape(s) of a layer at a given node.

#### Arguments:

: Integer, index of the node from which to retrieve the attribute. E.g.`node_index`

`node_index=0`

will correspond to the first time the layer was called.

#### Returns:

A shape tuple (or list of shape tuples if the layer has multiple inputs).

#### Raises:

: If called in Eager mode.`RuntimeError`

`get_losses_for`

```
get_losses_for(inputs)
```

Retrieves losses relevant to a specific set of inputs.

#### Arguments:

: Input tensor or list/tuple of input tensors.`inputs`

#### Returns:

List of loss tensors of the layer that depend on `inputs`

.

`get_output_at`

```
get_output_at(node_index)
```

Retrieves the output tensor(s) of a layer at a given node.

#### Arguments:

: Integer, index of the node from which to retrieve the attribute. E.g.`node_index`

`node_index=0`

will correspond to the first time the layer was called.

#### Returns:

A tensor (or list of tensors if the layer has multiple outputs).

#### Raises:

: If called in Eager mode.`RuntimeError`

`get_output_mask_at`

```
get_output_mask_at(node_index)
```

Retrieves the output mask tensor(s) of a layer at a given node.

#### Arguments:

: Integer, index of the node from which to retrieve the attribute. E.g.`node_index`

`node_index=0`

will correspond to the first time the layer was called.

#### Returns:

A mask tensor (or list of tensors if the layer has multiple outputs).

`get_output_shape_at`

```
get_output_shape_at(node_index)
```

Retrieves the output shape(s) of a layer at a given node.

#### Arguments:

: Integer, index of the node from which to retrieve the attribute. E.g.`node_index`

`node_index=0`

will correspond to the first time the layer was called.

#### Returns:

A shape tuple (or list of shape tuples if the layer has multiple outputs).

#### Raises:

: If called in Eager mode.`RuntimeError`

`get_updates_for`

```
get_updates_for(inputs)
```

Retrieves updates relevant to a specific set of inputs.

#### Arguments:

: Input tensor or list/tuple of input tensors.`inputs`

#### Returns:

List of update ops of the layer that depend on `inputs`

.

`get_weights`

```
get_weights()
```

Returns the current weights of the layer.

#### Returns:

Weights values as a list of numpy arrays.

`set_weights`

```
set_weights(weights)
```

Sets the weights of the layer, from Numpy arrays.

#### Arguments:

: 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`weights`

`get_weights`

).

#### Raises:

: If the provided weights list does not match the layer's specifications.`ValueError`

`with_name_scope`

```
@classmethod
with_name_scope(
cls,
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], 64]))
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([8, 32]))
# ==> <tf.Tensor: ...>
mod.w
# ==> <tf.Variable ...'my_module/w:0'>
```

#### Args:

: The method to wrap.`method`

#### Returns:

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