tfl.layers.Lattice

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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.
  • 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.
    dtype Dtype used by the weights of the layer, set in the constructor.
    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 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.

    metrics List of tf.keras.metrics.Metric instances tracked by 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
    

    trainable

    trainable_weights List of all trainable weights tracked by this layer.

    Trainable weights are updated via gradient descent during training.

    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(inputs, self):
        self.add_loss(tf.abs(tf.reduce_mean(inputs)), inputs=True)
        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,))
    x = tf.keras.layers.Dense(10)(inputs)
    outputs = tf.keras.layers.Dense(1)(x)
    model = tf.keras.Model(inputs, outputs)
    # Weight regularization.
    model.add_loss(lambda: tf.reduce_mean(x.kernel))
    

    The get_losses_for method allows to retrieve the losses relevant to a specific set of inputs.

    Arguments
    losses Loss tensor, or list/tuple of tensors. Rather than tensors, losses may also be zero-argument callables which create a loss tensor.
    inputs Ignored when executing eagerly. If anything other than None is passed, it signals the losses are conditional on some of the layer's inputs, and thus they should only be run where these inputs are available. This is the case for activity regularization losses, for instance. If None is passed, the losses are assumed to be unconditional, and will apply across all dataflows of the layer (e.g. weight regularization losses).

    add_metric

    Adds metric tensor to the layer.

    Args
    value Metric tensor.
    aggregation Sample-wise metric reduction function. If aggregation=None, it indicates that the metric tensor provided has been aggregated already. eg, bin_acc = BinaryAccuracy(name='acc') followed by model.add_metric(bin_acc(y_true, y_pred)). If aggregation='mean', the given metric tensor will be sample-wise reduced using mean function. eg, model.add_metric(tf.reduce_sum(outputs), name='output_mean', aggregation='mean').
    name String metric name.

    Raises
    ValueError If aggregation is anything other than None or 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. 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).

    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.