Embed trainable bijector into Keras model

Question

I am trying to implement normalizing flows embedded in a Keras model. In all examples I can find, such as the documentation of MAF , the bijectors which constitute the normalizing flows are embedded into a TransformedDistribution and exposed directly for training etc.

I am trying to embed this TransformedDistribution in a keras Model to match the architecture of other models I have which are inheriting from keras Model.

Unfortunately all my attempts (see code) so far fail at transferring the trainable variables inside the transformed distribution to the keras Model.

I have tried to make the bijector inherit from tf.keras.layers.Layer , which did not change anything.

import tensorflow as tf
import tensorflow_probability as tfp

tfd = tfp.distributions
tfb = tfp.bijectors


class Flow(tfb.Bijector, tf.Module):
    """
    tf.Module to register trainable_variables
    """

    def __init__(self, d, init_sigma=0.1, **kwargs):
        super(Flow, self).__init__(
            dtype=tf.float32,
            forward_min_event_ndims=0,
            inverse_min_event_ndims=0,
            **kwargs
        )
        # Shape of the flow goes from Rd to Rd
        self.d = d
        # Weights/Variables initializer
        self.init_sigma = init_sigma
        w_init = tf.random_normal_initializer(stddev=self.init_sigma)
        # Variables
        self.u = tf.Variable(
            w_init(shape=[1, self.d], dtype=tf.float32),
            dtype=tf.float32,
            name='u',
            trainable=True,
        )

    def _forward(self, x):
        return x

    def _inverse(self, y):
        return y


class Flows(tf.keras.Model):

    def __init__(self, d=2, shape=(100, 2), n_flows=10, ):
        super(Flows, self).__init__()
        # Parameters
        self.d = d
        self.shape = shape
        self.n_flows = n_flows
        # Base distribution - MF = Multivariate normal diag
        base_distribution = tfd.MultivariateNormalDiag(
            loc=tf.zeros(shape=shape, dtype=tf.float32)
        )
        # Flows as chain of bijector
        flows = []
        for n in range(n_flows):
            flows.append(Flow(self.d, name=f"flow_{n + 1}"))
        bijector = tfb.Chain(list(reversed(flows)))
        self.flow = tfd.TransformedDistribution(
            distribution=base_distribution,
            bijector=bijector
        )

    def call(self, *inputs):
        return self.flow.bijector.forward(*inputs)

    def log_prob(self, *inputs):
        return self.flow.log_prob(*inputs)

    def sample(self, num):
        return self.flow.sample(num)


q = Flows()
# Call to instantiate variables
q(tf.zeros(q.shape))
# Prints no trainable params
print(q.summary())
# Prints expected trainable params
print(q.flow.trainable_variables)

Any idea if this is even possible? Thanks!

Answer 1

I bumped into this issue as well. It seems to be caused by the incompatibility issues between TFP and TF 2.0 (a couple relevant issues https://github.com/tensorflow/probability/issues/355 and https://github.com/tensorflow/probability/issues/946 ).

As a workaround, you need to add the (trainable) variables of your transformed distribution / bijector as an attribute to your Keras Model:

class Flows(tf.keras.Model):

    def __init__(self, d=2, shape=(100, 2), n_flows=10, ):
        super(Flows, self).__init__()
        # Parameters
        self.d = d
        self.shape = shape
        self.n_flows = n_flows
        # Base distribution - MF = Multivariate normal diag
        base_distribution = tfd.MultivariateNormalDiag(
            loc=tf.zeros(shape=shape, dtype=tf.float32)
        )
        # Flows as chain of bijector
        flows = []
        for n in range(n_flows):
            flows.append(Flow(self.d, name=f"flow_{n + 1}"))
        bijector = tfb.Chain(list(reversed(flows)))
        self.flow = tfd.TransformedDistribution(
            distribution=base_distribution,
            bijector=bijector
        )
        # issue: https://github.com/tensorflow/probability/issues/355, https://github.com/tensorflow/probability/issues/946
        # need to add bijector's trainable variables as an attribute (name does not matter)
        # otherwise this layer has zero trainable variables
        self._variables = self.flow.variables # https://github.com/tensorflow/probability/issues/355

    def call(self, *inputs):
        return self.flow.bijector.forward(*inputs)

    def log_prob(self, *inputs):
        return self.flow.log_prob(*inputs)

    def sample(self, num):
        return self.flow.sample(num)

After adding this your model should have trainable variables and weights to optimize.