MultiTaskGaussianProcessRegressionModel issue with tf.function

Hi, I have encountered an error when using tf.function decorator on a function calling MultiTaskGaussianProcessRegressionModel from the experimental package. The error occurs specifically when passing input_signature of unknown dimension to tf.function. Below are the details. Thanks!

Code

import tensorflow as tf
import tensorflow_probability as tfp

tfde = tfp.experimental.distributions
tfk = tfp.math.psd_kernels
tfke = tfp.experimental.psd_kernels

base_kernel = tfk.ExponentiatedQuadratic(
    amplitude=tf.convert_to_tensor(0.6, tf.float64),
    length_scale=tf.convert_to_tensor(0.5, tf.float64),
)
kernel = tfke.Independent(num_tasks=2, base_kernel=base_kernel)
observations = tf.constant([[0., 1.],[-0.5, -1.0]], tf.float64)
observation_index_points = tf.constant([[0],[1.0]], tf.float64)

@tf.function(input_signature=[tf.TensorSpec(shape=[None, 1], dtype=tf.float64)])
def predict(index_points):
    gp = tfde.MultiTaskGaussianProcessRegressionModel(
        kernel=kernel,
        observations=observations,
        observation_index_points=observation_index_points,
        index_points=index_points,
    )
    return gp.mean()

predict(tf.constant([[0.2],[0.4],[0.6]], tf.float64))

The code above works:

• if we remove tf.function, or
• if we remove input_signature inside with tf.function

We get the following error if we set shape=[None, 1] inside tf.TensorSpec:

UnboundLocalError: in user code:

    File "/tmp/ipykernel_299029/1064227357.py", line 24, in predict  *
        return gp.mean()
    File "/usr/.local/lib/python3.12/site-packages/tensorflow_probability/python/distributions/distribution.py", line 1536, in mean  **
        return self._mean(**kwargs)
    File "/usr/.local/lib/python3.12/site-packages/tensorflow_probability/python/experimental/distributions/multitask_gaussian_process_regression_model.py", line 852, in _mean
        self._get_flattened_marginal_distribution(
    File "/usr/.local/lib/python3.12/site-packages/tensorflow_probability/python/experimental/distributions/multitask_gaussian_process_regression_model.py", line 831, in _get_flattened_marginal_distribution
        covariance = self._compute_flattened_covariance(index_points)
    File "/usr/.local/lib/python3.12/site-packages/tensorflow_probability/python/experimental/distributions/multitask_gaussian_process_regression_model.py", line 811, in _compute_flattened_covariance
        cholinv_kzx = observation_scale.solve(kxz, adjoint_arg=True)

    UnboundLocalError: cannot access local variable 'dim' where it is not associated with a value

Start by reproducing the example with tf.function and input_signature shape [None, 1]. Inspect tensorflow_probability/python/experimental/distributions/multitask_gaussian_process_regression_model.py, especially _compute_flattened_covariance and the reported dim handling, then verify that the example no longer raises UnboundLocalError for unknown dimensions.