# tfl.layers.Lattice

Lattice layer.

### Used in the notebooks

Used in the tutorials

Layer performs interpolation using one of `units` d-dimensional 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.
• 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 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)`

#### 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)
``````

`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 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 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.
`monotonic_dominances` 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.
`range_dominances` 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.
`joint_monotonicities` None or two-element tuple or iterable of two-element 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 d-dimensional 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:

• `'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.
• `random_uniform_or_linear_initializer`: if the lattice has a single joint unimodality constraint group encompassing all features then use the Keras 'random_uniform' initializer; otherwise, use TFL's 'linear_initializer'.
• Any Keras initializer object.
`kernel_regularizer` None or a single element or a list of following:
• 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.
• `**kwargs` Other args passed to `tf.keras.layers.Layer` initializer.

`ValueError` If layer hyperparameters are invalid.

`kernel` weights of the lattice.
`activity_regularizer` Optional regularizer function for the output of this layer.
`compute_dtype` The dtype of the layer's computations.

This is equivalent to `Layer.dtype_policy.compute_dtype`. Unless mixed precision is used, this is the same as `Layer.dtype`, the dtype of the weights.

Layers automatically cast their inputs to the compute dtype, which causes computations and the output to be in the compute dtype as well. This is done by the base Layer class in `Layer.call`, so you do not have to insert these casts if implementing your own layer.

Layers often perform certain internal computations in higher precision when `compute_dtype` is float16 or bfloat16 for numeric stability. The output will still typically be float16 or bfloat16 in such cases.

`dtype` The dtype of the layer weights.

This is equivalent to `Layer.dtype_policy.variable_dtype`. Unless mixed precision is used, this is the same as `Layer.compute_dtype`, the dtype of the layer's computations.

`dtype_policy` The dtype policy associated with this layer.

This is an instance of a `tf.keras.mixed_precision.Policy`.

`dynamic` Whether the layer is dynamic (eager-only); 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 `self.input_spec` to enable the layer to run input compatibility checks when it is called. Consider a `Conv2D` layer: it can only be called on a single input tensor of rank 4. As such, you can set, in `__init__()`:

``````self.input_spec = tf.keras.layers.InputSpec(ndim=4)
``````

Now, if you try to call the layer on an input that isn't rank 4 (for instance, an input of shape `(2,)`, it will raise a nicely-formatted error:

``````ValueError: Input 0 of layer conv2d is incompatible with the layer:
expected ndim=4, found ndim=1. Full shape received: [2]
``````

Input checks that can be specified via `input_spec` include:

• Structure (e.g. a single input, a list of 2 inputs, etc)
• Shape
• Rank (ndim)
• Dtype

For more information, see `tf.keras.layers.InputSpec`.

`losses` List of losses added using the `add_loss()` API.

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.

````class MyLayer(tf.keras.layers.Layer):`
`  def call(self, inputs):`
`    self.add_loss(tf.abs(tf.reduce_mean(inputs)))`
`    return inputs`
`l = MyLayer()`
`l(np.ones((10, 1)))`
`l.losses`
`[1.0]`
```
````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.`
`len(model.losses)`
`0`
`model.add_loss(tf.abs(tf.reduce_mean(x)))`
`len(model.losses)`
`1`
```
````inputs = tf.keras.Input(shape=(10,))`
`d = tf.keras.layers.Dense(10, kernel_initializer='ones')`
`x = d(inputs)`
`outputs = tf.keras.layers.Dense(1)(x)`
`model = tf.keras.Model(inputs, outputs)`
`# Weight regularization.`
`model.add_loss(lambda: tf.reduce_mean(d.kernel))`
`model.losses`
`[<tf.Tensor: shape=(), dtype=float32, numpy=1.0>]`
```

`metrics` List of metrics added using the `add_metric()` API.

````input = tf.keras.layers.Input(shape=(3,))`
`d = tf.keras.layers.Dense(2)`
`output = d(input)`
`d.add_metric(tf.reduce_max(output), name='max')`
`d.add_metric(tf.reduce_min(output), name='min')`
`[m.name for m in d.metrics]`
`['max', 'min']`
```

`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 non-trainable weights tracked by this layer.

Non-trainable weights are not updated during training. They are expected to be updated manually in `call()`.

`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 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`
```

`supports_masking` Whether this layer supports computing a mask using `compute_mask`.
`trainable`

`trainable_weights` List of all trainable weights tracked by this layer.

Trainable weights are updated via gradient descent during training.

`variable_dtype` Alias of `Layer.dtype`, the dtype of the weights.
`weights` Returns the list of all layer variables/weights.

## Methods

### `add_loss`

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(self, inputs):
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.
``````

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 zero-argument 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,))
d = tf.keras.layers.Dense(10)
x = d(inputs)
outputs = tf.keras.layers.Dense(1)(x)
model = tf.keras.Model(inputs, outputs)
# Weight regularization.
``````

Args
`losses` Loss tensor, or list/tuple of tensors. Rather than tensors, losses may also be zero-argument callables which create a loss tensor.
`**kwargs` Additional keyword arguments for backward compatibility. Accepted values: inputs - Deprecated, will be automatically inferred.

### `add_metric`

Adds metric tensor to the layer.

This method can be used inside the `call()` method of a subclassed layer or model.

``````class MyMetricLayer(tf.keras.layers.Layer):
def __init__(self):
super(MyMetricLayer, self).__init__(name='my_metric_layer')
self.mean = tf.keras.metrics.Mean(name='metric_1')

def call(self, inputs):
return inputs
``````

This method can also be called directly on a Functional Model during construction. In this case, any tensor passed to this Model must be symbolic and be able to be traced back to the model's `Input`s. These metrics become part of the model's topology and are tracked when you save the model via `save()`.

``````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)
``````
``````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)
``````

Args
`value` Metric tensor.
`name` String metric name.
`**kwargs` Additional keyword arguments for backward compatibility. Accepted values: `aggregation` - When the `value` tensor provided is not the result of calling a `keras.Metric` instance, it will be aggregated by default using a `keras.Metric.Mean`.

### `assert_constraints`

View source

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`

View source

Standard Keras build() method.

### `compute_mask`

Args
`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`

View source

Standard Keras compute_output_shape() method.

### `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`

View source

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`

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`).

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

Returns
A layer instance.

### `get_config`

View source

Standard Keras config for serialization.

### `get_weights`

Returns the current weights of the layer, as NumPy arrays.

The weights of a layer represent the state of the layer. This function returns both trainable and non-trainable 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: the kernel matrix and the bias vector. These can be used to set the weights of another `Dense` layer:

````layer_a = tf.keras.layers.Dense(1,`
`  kernel_initializer=tf.constant_initializer(1.))`
`a_out = layer_a(tf.convert_to_tensor([[1., 2., 3.]]))`
`layer_a.get_weights()`
`[array([[1.],`
`       [1.],`
`       [1.]], dtype=float32), array([0.], dtype=float32)]`
`layer_b = tf.keras.layers.Dense(1,`
`  kernel_initializer=tf.constant_initializer(2.))`
`b_out = layer_b(tf.convert_to_tensor([[10., 20., 30.]]))`
`layer_b.get_weights()`
`[array([[2.],`
`       [2.],`
`       [2.]], dtype=float32), array([0.], dtype=float32)]`
`layer_b.set_weights(layer_a.get_weights())`
`layer_b.get_weights()`
`[array([[1.],`
`       [1.],`
`       [1.]], dtype=float32), array([0.], dtype=float32)]`
```

Returns
Weights values as a list of NumPy arrays.

### `set_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: the kernel matrix and the bias vector. These can be used to set the weights of another `Dense` layer:

````layer_a = tf.keras.layers.Dense(1,`
`  kernel_initializer=tf.constant_initializer(1.))`
`a_out = layer_a(tf.convert_to_tensor([[1., 2., 3.]]))`
`layer_a.get_weights()`
`[array([[1.],`
`       [1.],`
`       [1.]], dtype=float32), array([0.], dtype=float32)]`
`layer_b = tf.keras.layers.Dense(1,`
`  kernel_initializer=tf.constant_initializer(2.))`
`b_out = layer_b(tf.convert_to_tensor([[10., 20., 30.]]))`
`layer_b.get_weights()`
`[array([[2.],`
`       [2.],`
`       [2.]], dtype=float32), array([0.], dtype=float32)]`
`layer_b.set_weights(layer_a.get_weights())`
`layer_b.get_weights()`
`[array([[1.],`
`       [1.],`
`       [1.]], dtype=float32), array([0.], dtype=float32)]`
```

Args
`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`

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__`

Wraps `call`, applying pre- and post-processing steps.

Args
`*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 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.
• If the layer is not built, the method will call `build`.

Raises
`ValueError` if the layer's `call` method returns None (an invalid value).
`RuntimeError` if `super().__init__()` was not called in the constructor.

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