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# tfp.bijectors.AutoregressiveNetwork

Masked Autoencoder for Distribution Estimation [Germain et al. (2015)].

A `AutoregressiveNetwork` takes as input a Tensor of shape `[..., event_size]` and returns a Tensor of shape `[..., event_size, params]`.

The output satisfies the autoregressive property. That is, the layer is configured with some permutation `ord` of `{0, ..., event_size-1}` (i.e., an ordering of the input dimensions), and the output `output[batch_idx, i, ...]` for input dimension `i` depends only on inputs `x[batch_idx, j]` where `ord(j) < ord(i)`. The autoregressive property allows us to use `output[batch_idx, i]` to parameterize conditional distributions: `p(x[batch_idx, i] | x[batch_idx, j] for ord(j) < ord(i))` which give us a tractable distribution over input `x[batch_idx]`: `p(x[batch_idx]) = prod_i p(x[batch_idx, ord(i)] | x[batch_idx, ord(0:i)])`

For example, when `params` is 2, the output of the layer can parameterize the location and log-scale of an autoregressive Gaussian distribution.

#### Example

The `AutoregressiveNetwork` can be used to do density estimation as is shown in the below example:

``````# Generate data -- as in Figure 1 in [Papamakarios et al. (2017)]).
n = 2000
x2 = np.random.randn(n).astype(dtype=np.float32) * 2.
x1 = np.random.randn(n).astype(dtype=np.float32) + (x2 * x2 / 4.)
data = np.stack([x1, x2], axis=-1)

# Density estimation with MADE.
made = tfb.AutoregressiveNetwork(params=2, hidden_units=[10, 10])

distribution = tfd.TransformedDistribution(
distribution=tfd.Sample(tfd.Normal(loc=0., scale=1.), sample_shape=),
bijector=tfb.MaskedAutoregressiveFlow(made))

# Construct and fit model.
x_ = tfkl.Input(shape=(2,), dtype=tf.float32)
log_prob_ = distribution.log_prob(x_)
model = tfk.Model(x_, log_prob_)

model.compile(optimizer=tf.optimizers.Adam(),
loss=lambda _, log_prob: -log_prob)

batch_size = 25
model.fit(x=data,
y=np.zeros((n, 0), dtype=np.float32),
batch_size=batch_size,
epochs=1,
steps_per_epoch=1,  # Usually `n // batch_size`.
shuffle=True,
verbose=True)

# Use the fitted distribution.
distribution.sample((3, 1))
distribution.log_prob(np.ones((3, 2), dtype=np.float32))
``````

The `conditional` argument can be used to instead build a conditional density estimator. To do this the conditioning variable must be passed as a `kwarg`:

``````# Generate data as the mixture of two distributions.
n = 2000
c = np.r_[
np.zeros(n//2),
np.ones(n//2)
]
mean_0, mean_1 = 0, 5
x = np.r_[
np.random.randn(n//2).astype(dtype=np.float32) + mean_0,
np.random.randn(n//2).astype(dtype=np.float32) + mean_1
]

# Density estimation with MADE.
made = tfb.AutoregressiveNetwork(
params=2,
hidden_units=[2, 2],
event_shape=(1,),
conditional=True,
kernel_initializer=tfk.initializers.VarianceScaling(0.1),
conditional_event_shape=(1,)
)

distribution = tfd.TransformedDistribution(
distribution=tfd.Sample(tfd.Normal(loc=0., scale=1.), sample_shape=),
bijector=tfb.MaskedAutoregressiveFlow(made))

# Construct and fit model.
x_ = tfkl.Input(shape=(1,), dtype=tf.float32)
c_ = tfkl.Input(shape=(1,), dtype=tf.float32)
log_prob_ = distribution.log_prob(
x_, bijector_kwargs={'conditional_input': c_})
model = tfk.Model([x_, c_], log_prob_)

model.compile(optimizer=tf.optimizers.Adam(learning_rate=0.1),
loss=lambda _, log_prob: -log_prob)

batch_size = 25
model.fit(x=[x, c],
y=np.zeros((n, 0), dtype=np.float32),
batch_size=batch_size,
epochs=3,
steps_per_epoch=n // batch_size,
shuffle=True,
verbose=True)

# Use the fitted distribution to sample condition on c = 1
n_samples = 1000
cond = 1
samples = distribution.sample(
(n_samples,),
bijector_kwargs={'conditional_input': cond * np.ones((n_samples, 1))})
``````

#### Examples: Handling Rank-2+ Tensors

`AutoregressiveNetwork` can be used as a building block to achieve different autoregressive structures over rank-2+ tensors. For example, suppose we want to build an autoregressive distribution over images with dimension ```[weight, height, channels]``` with `channels = 3`:

1. We can parameterize a 'fully autoregressive' distribution, with cross-channel and within-pixel autoregressivity:

``````    r0    g0   b0     r0    g0   b0       r0   g0    b0
^   ^      ^         ^   ^   ^         ^      ^   ^
|  /  ____/           \  |  /           \____  \  |
| /__/                 \ | /                 \__\ |
r1    g1   b1     r1 <- g1   b1       r1   g1 <- b1
^          |
\_________/
``````

as:

``````# Generate random images for training data.
images = np.random.uniform(size=(100, 8, 8, 3)).astype(np.float32)
n, width, height, channels = images.shape

# Reshape images to achieve desired autoregressivity.
event_shape = [height * width * channels]
reshaped_images = tf.reshape(images, [n, event_shape])

# Density estimation with MADE.
made = tfb.AutoregressiveNetwork(params=2, event_shape=event_shape,
hidden_units=[20, 20], activation='relu')
distribution = tfd.TransformedDistribution(
distribution=tfd.Sample(
tfd.Normal(loc=0., scale=1.), sample_shape=[dims]),
bijector=tfb.MaskedAutoregressiveFlow(made))

# Construct and fit model.
x_ = tfkl.Input(shape=event_shape, dtype=tf.float32)
log_prob_ = distribution.log_prob(x_)
model = tfk.Model(x_, log_prob_)

model.compile(optimizer=tf.optimizers.Adam(),
loss=lambda _, log_prob: -log_prob)

batch_size = 10
model.fit(x=data,
y=np.zeros((n, 0), dtype=np.float32),
batch_size=batch_size,
epochs=10,
steps_per_epoch=n // batch_size,
shuffle=True,
verbose=True)

# Use the fitted distribution.
distribution.sample((3, 1))
distribution.log_prob(np.ones((5, 8, 8, 3), dtype=np.float32))
``````
2. We can parameterize a distribution with neither cross-channel nor within-pixel autoregressivity:

``````    r0    g0   b0
^     ^    ^
|     |    |
|     |    |
r1    g1   b1
``````

as:

``````# Generate fake images.
images = np.random.choice([0, 1], size=(100, 8, 8, 3))
n, width, height, channels = images.shape

# Reshape images to achieve desired autoregressivity.
reshaped_images = np.transpose(
np.reshape(images, [n, width * height, channels]),
axes=[0, 2, 1])

made = tfb.AutoregressiveNetwork(params=1, event_shape=[width * height],
hidden_units=[20, 20], activation='relu')

# Density estimation with MADE.
#
# NOTE: Parameterize an autoregressive distribution over an event_shape of
# [channels, width * height], with univariate Bernoulli conditional
# distributions.
distribution = tfd.Autoregressive(
lambda x: tfd.Independent(
tfd.Bernoulli(logits=tf.unstack(made(x), axis=-1),
dtype=tf.float32),
reinterpreted_batch_ndims=2),
sample0=tf.zeros([channels, width * height], dtype=tf.float32))

# Construct and fit model.
x_ = tfkl.Input(shape=(channels, width * height), dtype=tf.float32)
log_prob_ = distribution.log_prob(x_)
model = tfk.Model(x_, log_prob_)

model.compile(optimizer=tf.optimizers.Adam(),
loss=lambda _, log_prob: -log_prob)

batch_size = 10
model.fit(x=reshaped_images,
y=np.zeros((n, 0), dtype=np.float32),
batch_size=batch_size,
epochs=10,
steps_per_epoch=n // batch_size,
shuffle=True,
verbose=True)

distribution.sample(7)
distribution.log_prob(np.ones((4, 8, 8, 3), dtype=np.float32))
``````

Note that one set of weights is shared for the mapping for each channel from image to distribution parameters -- i.e., the mapping `layer(reshaped_images[..., channel, :])`, where `channel` is 0, 1, or 2.

To use separate weights for each channel, we could construct an `AutoregressiveNetwork` and `TransformedDistribution` for each channel, and combine them with a `tfd.Blockwise` distribution.

: Mathieu Germain, Karol Gregor, Iain Murray, and Hugo Larochelle. MADE: Masked Autoencoder for Distribution Estimation. In International Conference on Machine Learning, 2015. https://arxiv.org/abs/1502.03509

: George Papamakarios, Theo Pavlakou, Iain Murray, Masked Autoregressive Flow for Density Estimation. In Neural Information Processing Systems, 2017. https://arxiv.org/abs/1705.07057

`params` Python integer specifying the number of parameters to output per input.
`event_shape` Python `list`-like of positive integers (or a single int), specifying the shape of the input to this layer, which is also the event_shape of the distribution parameterized by this layer. Currently only rank-1 shapes are supported. That is, event_shape must be a single integer. If not specified, the event shape is inferred when this layer is first called or built.
`conditional` Python boolean describing whether to add conditional inputs.
`conditional_event_shape` Python `list`-like of positive integers (or a single int), specifying the shape of the conditional input to this layer (without the batch dimensions). This must be specified if `conditional` is `True`.
`conditional_input_layers` Python `str` describing how to add conditional parameters to the autoregressive network. When "all_layers" the conditional input will be combined with the network at every layer, whilst "first_layer" combines the conditional input only at the first layer which is then passed through the network autoregressively. Default: 'all_layers'.
`hidden_units` Python `list`-like of non-negative integers, specifying the number of units in each hidden layer.
`input_order` Order of degrees to the input units: 'random', 'left-to-right', 'right-to-left', or an array of an explicit order. For example, 'left-to-right' builds an autoregressive model: `p(x) = p(x1) p(x2 | x1) ... p(xD | x<D)`. Default: 'left-to-right'.
`hidden_degrees` Method for assigning degrees to the hidden units: 'equal', 'random'. If 'equal', hidden units in each layer are allocated equally (up to a remainder term) to each degree. Default: 'equal'.
`activation` An activation function. See `tf.keras.layers.Dense`. Default: `None`.
`use_bias` Whether or not the dense layers constructed in this layer should have a bias term. See `tf.keras.layers.Dense`. Default: `True`.
`kernel_initializer` Initializer for the `Dense` kernel weight matrices. Default: 'glorot_uniform'.
`bias_initializer` Initializer for the `Dense` bias vectors. Default: 'zeros'.
`kernel_regularizer` Regularizer function applied to the `Dense` kernel weight matrices. Default: None.
`bias_regularizer` Regularizer function applied to the `Dense` bias weight vectors. Default: None.
`kernel_constraint` Constraint function applied to the `Dense` kernel weight matrices. Default: None.
`bias_constraint` Constraint function applied to the `Dense` bias weight vectors. Default: None.
`validate_args` Python `bool`, default `False`. When `True`, layer parameters are checked for validity despite possibly degrading runtime performance. When `False` invalid inputs may silently render incorrect outputs.
`**kwargs` Additional keyword arguments passed to this layer (but not to the `tf.keras.layer.Dense` layers constructed by this layer).

`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.
`event_shape`

`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: 
``````

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.

`params`

`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
``````

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 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` 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):
self.add_metric(self.mean(inputs))
self.add_metric(tf.reduce_sum(inputs), name='metric_2')
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)
model.add_metric(math_ops.reduce_sum(x), name='metric_1')
``````
``````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)
model.add_metric(tf.keras.metrics.Mean()(x), name='metric_1')
``````

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`.

### `build`

View source

See tfkl.Layer.build.

### `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

See tfkl.Layer.compute_output_shape.

### `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).

### `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`

Returns the config of the layer.

A layer config is a Python dictionary (serializable) containing the configuration of a layer. The same layer can be reinstantiated later (without its trained weights) from this configuration.

The config of a layer does not include connectivity information, nor the layer class name. These are handled by `Network` (one layer of abstraction above).

Note that `get_config()` does not guarantee to return a fresh copy of dict every time it is called. The callers should make a copy of the returned dict if they want to modify it.

Returns
Python dictionary.

### `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, 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.