# tfl.layers.KroneckerFactoredLattice

Kronecker-Factored Lattice layer.

A Kronecker-Factored Lattice is a reparameterization of a Lattice using kronecker-facotrization, which gives us linear time and space complexity. While the underlying representation is different, the input-output behavior remains the same.

A Kronecker-Factored Lattice consists of 'units' lattices. Each unit computes the function described below on a distinct 'dims'-dimensional vector x taken from the input tensor. Each unit has its own set of parameters. The function each unit computes is given by:

f(x) = b + (1/numterms) * sum{t=1}^{num_terms} scalet * prod{d=1}^{dims} PLF(x[d];w[d])

where bias and each scale_t are scalar parameters, w[d] is a 'lattice_size'-dimensional vector of parameters, and PLF(;w) denotes the one-dimensional piecewise-linear function with domain [0, lattice_sizes-1] whose graph consists of lattice_sizes-1 linear segments interpolating the points (i, w[i]), for i=0,1,...,lattice_size-1.

There is currently one type of constraint on the shape of the learned function.

• Monotonicity: constrains the function to be increasing in the corresponding dimension. To achieve decreasing monotonicity, either pass the inputs through a `tfl.layers.PWLCalibration` with `decreasing` monotonicity, or manually reverse the inputs as `lattice_size - 1 - inputs`.

There are upper and lower bound constraints on the output.

• if `units == 1`: tensor of shape: `(batch_size, ..., dims)` or list of `dims` tensors of same shape: `(batch_size, ..., 1)`
• if `units > 1`: tensor of shape: `(batch_size, ..., units, dims)` or list of `dims` tensors of same shape: `(batch_size, ..., units, 1)`

A typical shape is: `(batch_size, len(monotonicities))`

Tensor of shape: `(batch_size, ..., units)`

#### Example:

``````kfl = tfl.layers.KroneckerFactoredLattice(
# Number of vertices along each dimension.
lattice_sizes=2,
# Number of output units.
units=2,
# Number of independently trained submodels per unit, the outputs
# of which are averaged to get the final output.
num_terms=4,
# You can specify monotonicity constraints.
monotonicities=['increasing', 'none', 'increasing', 'increasing',
'increasing', 'increasing', 'increasing'])
``````

`lattice_sizes` Number of vertices per dimension (minimum is 2).
`units` Output dimension of the layer. See class comments for details.
`num_terms` Number of independently trained submodels per unit, the outputs of which are averaged to get the final output.
`monotonicities` None or list or tuple of same length as input dimension of {'none', 'increasing', 0, 1} which specifies if the model output should be monotonic in the corresponding feature, using 'increasing' or 1 to indicate increasing monotonicity and 'none' or 0 to indicate no monotonicity constraints.
`output_min` None or lower bound of the output.
`output_max` None or upper bound of the output.
`clip_inputs` If inputs should be clipped to the input range of the Kronecker-Factored Lattice.
`kernel_initializer` None or one of:

• `'kfl_random_monotonic_initializer'`: initializes parameters as uniform random functions that are monotonic in monotonic dimensions.
• Any Keras initializer object.
`scale_initializer` None or one of:
• `'scale_initializer'`: Initializes scale depending on output_min and output_max. If both output_min and output_max are set, scale is initialized to half their difference, alternating signs for each term. If only output_min is set, scale is initialized to 1 for each term. If only output_max is set, scale is initialized to -1 for each term. Otherwise scale is initialized to alternate between 1 and -1 for each term.
• `**kwargs` Other args passed to `keras.layers.Layer` initializer.

`ValueError` If layer hyperparameters are invalid.

• All `__init__` arguments.
`scale` A tensor of shape `(units, num_terms)`. Contains the `scale_t` parameter for each unit for each term.
`bias` A tensor of shape `(units)`. Contains the `b` parameter for each unit.
`kernel` The `w` weights parameter of the Kronecker-Factored Lattice of shape: `(1, lattice_sizes, units * dims, num_terms)`. Note that the kernel is unit-major in its second to last dimension.
`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 attached to 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 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):
self.add_loss(tf.abs(tf.reduce_mean(inputs)))
return inputs
``````

The same code works in distributed training: the input to `add_loss()` is treated like a regularization loss and averaged across replicas by the training loop (both built-in `Model.fit()` and compliant custom training loops).

The `add_loss` 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 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.
model.add_loss(lambda: tf.reduce_mean(d.kernel))
``````

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` Used for backwards compatibility only.

### `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.

### `build_from_config`

Builds the layer's states with the supplied config dict.

By default, this method calls the `build(config["input_shape"])` method, which creates weights based on the layer's input shape in the supplied config. If your config contains other information needed to load the layer's state, you should override this method.

Args
`config` Dict containing the input shape associated with this layer.

### `compute_mask`

Computes an output mask tensor.

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.

Returns
In eager mode directly updates kernel and scale and returns the variables which store them. In graph mode returns a `group` op containing the `assign_add` ops which have to be executed to update the kernel and scale.

### `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_build_config`

Returns a dictionary with the layer's input shape.

This method returns a config dict that can be used by `build_from_config(config)` to create all states (e.g. Variables and Lookup tables) needed by the layer.

By default, the config only contains the input shape that the layer was built with. If you're writing a custom layer that creates state in an unusual way, you should override this method to make sure this state is already created when TF-Keras attempts to load its value upon model loading.

Returns
A dict containing the input shape associated with the layer.

### `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.

### `load_own_variables`

Loads the state of the layer.

You can override this method to take full control of how the state of the layer is loaded upon calling `keras.models.load_model()`.

Args
`store` Dict from which the state of the model will be loaded.

### `save_own_variables`

Saves the state of the layer.

You can override this method to take full control of how the state of the layer is saved upon calling `model.save()`.

Args
`store` Dict where the state of the model will be saved.

### `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 TF-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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