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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.

There are upper and lower bound constraints on the output.

Input shape:

  • 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))

Output shape:

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 tf.keras.layers.Layer initializer.

    ValueError If layer hyperparameters are invalid.

    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 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):
        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 Inputs. 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))
    

    Arguments
    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(x))
        self.add_metric(tf.reduce_sum(x), 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 Inputs. 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.

    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

    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

    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).

    Arguments
    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.

    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-- per-output 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

    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-- per-output 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

    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.Variables and tf.Tensors 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.

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