Mixing TensorFlow models with GPflow

This notebook explores the combination of Keras TensorFlow neural networks with GPflow models.

import numpy as np
import tensorflow as tf
from matplotlib import pyplot as plt
import gpflow
from gpflow.ci_utils import ci_niter
from scipy.cluster.vq import kmeans2

from typing import Dict, Optional, Tuple
import tensorflow as tf
import tensorflow_datasets as tfds
import gpflow
from gpflow.utilities import to_default_float

iterations = ci_niter(100)

2022-05-10 11:16:52.747241: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcudart.so.11.0'; dlerror: libcudart.so.11.0: cannot open shared object file: No such file or directory
2022-05-10 11:16:52.747269: I tensorflow/stream_executor/cuda/cudart_stub.cc:29] Ignore above cudart dlerror if you do not have a GPU set up on your machine.

Convolutional network inside a GPflow model

original_dataset, info = tfds.load(name="mnist", split=tfds.Split.TRAIN, with_info=True)
total_num_data = info.splits["train"].num_examples
image_shape = info.features["image"].shape
image_size = tf.reduce_prod(image_shape)
batch_size = 32


def map_fn(input_slice: Dict[str, tf.Tensor]):
    updated = input_slice
    image = to_default_float(updated["image"]) / 255.0
    label = to_default_float(updated["label"])
    return tf.reshape(image, [-1, image_size]), label


autotune = tf.data.experimental.AUTOTUNE
dataset = (
    original_dataset.shuffle(1024)
    .batch(batch_size, drop_remainder=True)
    .map(map_fn, num_parallel_calls=autotune)
    .prefetch(autotune)
    .repeat()
)

2022-05-10 11:16:56.558368: W tensorflow/core/platform/cloud/google_auth_provider.cc:184] All attempts to get a Google authentication bearer token failed, returning an empty token. Retrieving token from files failed with "NOT_FOUND: Could not locate the credentials file.". Retrieving token from GCE failed with "FAILED_PRECONDITION: Error executing an HTTP request: libcurl code 6 meaning 'Couldn't resolve host name', error details: Could not resolve host: metadata".

Downloading and preparing dataset 11.06 MiB (download: 11.06 MiB, generated: 21.00 MiB, total: 32.06 MiB) to /home/circleci/tensorflow_datasets/mnist/3.0.1...

Dataset mnist downloaded and prepared to /home/circleci/tensorflow_datasets/mnist/3.0.1. Subsequent calls will reuse this data.

2022-05-10 11:16:57.870264: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcuda.so.1'; dlerror: libcuda.so.1: cannot open shared object file: No such file or directory
2022-05-10 11:16:57.870297: W tensorflow/stream_executor/cuda/cuda_driver.cc:269] failed call to cuInit: UNKNOWN ERROR (303)
2022-05-10 11:16:57.870315: I tensorflow/stream_executor/cuda/cuda_diagnostics.cc:156] kernel driver does not appear to be running on this host (49c966262641): /proc/driver/nvidia/version does not exist
2022-05-10 11:16:57.870570: I tensorflow/core/platform/cpu_feature_guard.cc:151] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  AVX2 AVX512F FMA
To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.

Here we’ll use the GPflow functionality, but put a non-GPflow model inside the kernel.

Vanilla ConvNet. This gets 97.3% accuracy on MNIST when used on its own (+ final linear layer) after 20K iterations

class KernelWithConvNN(gpflow.kernels.Kernel):
    def __init__(
        self,
        image_shape: Tuple,
        output_dim: int,
        base_kernel: gpflow.kernels.Kernel,
        batch_size: Optional[int] = None,
    ):
        super().__init__()
        with self.name_scope:
            self.base_kernel = base_kernel
            input_size = int(tf.reduce_prod(image_shape))
            input_shape = (input_size,)

            self.cnn = tf.keras.Sequential(
                [
                    tf.keras.layers.InputLayer(input_shape=input_shape, batch_size=batch_size),
                    tf.keras.layers.Reshape(image_shape),
                    tf.keras.layers.Conv2D(
                        filters=32, kernel_size=image_shape[:-1], padding="same", activation="relu"
                    ),
                    tf.keras.layers.MaxPool2D(pool_size=(2, 2), strides=2),
                    tf.keras.layers.Conv2D(
                        filters=64, kernel_size=(5, 5), padding="same", activation="relu"
                    ),
                    tf.keras.layers.MaxPool2D(pool_size=(2, 2), strides=2),
                    tf.keras.layers.Flatten(),
                    tf.keras.layers.Dense(output_dim, activation="relu"),
                    tf.keras.layers.Lambda(to_default_float),
                ]
            )

            self.cnn.build()

    def K(self, a_input: tf.Tensor, b_input: Optional[tf.Tensor] = None) -> tf.Tensor:
        transformed_a = self.cnn(a_input)
        transformed_b = self.cnn(b_input) if b_input is not None else b_input
        return self.base_kernel.K(transformed_a, transformed_b)

    def K_diag(self, a_input: tf.Tensor) -> tf.Tensor:
        transformed_a = self.cnn(a_input)
        return self.base_kernel.K_diag(transformed_a)

\(K_{uf}\) is in ConvNN output space, therefore we need to update Kuf multidispatch.

class KernelSpaceInducingPoints(gpflow.inducing_variables.InducingPoints):
    pass


@gpflow.covariances.Kuu.register(KernelSpaceInducingPoints, KernelWithConvNN)
def Kuu(inducing_variable, kernel, jitter=None):
    func = gpflow.covariances.Kuu.dispatch(
        gpflow.inducing_variables.InducingPoints, gpflow.kernels.Kernel
    )
    return func(inducing_variable, kernel.base_kernel, jitter=jitter)


@gpflow.covariances.Kuf.register(KernelSpaceInducingPoints, KernelWithConvNN, object)
def Kuf(inducing_variable, kernel, a_input):
    return kernel.base_kernel(inducing_variable.Z, kernel.cnn(a_input))

Now we are ready to create and initialize the model:

num_mnist_classes = 10
output_dim = 5
num_inducing_points = 100
images_subset, labels_subset = next(iter(dataset.batch(32)))
images_subset = tf.reshape(images_subset, [-1, image_size])
labels_subset = tf.reshape(labels_subset, [-1, 1])

kernel = KernelWithConvNN(
    image_shape, output_dim, gpflow.kernels.SquaredExponential(), batch_size=batch_size
)

likelihood = gpflow.likelihoods.MultiClass(num_mnist_classes)

inducing_variable_kmeans = kmeans2(images_subset.numpy(), num_inducing_points, minit="points")[0]
inducing_variable_cnn = kernel.cnn(inducing_variable_kmeans)
inducing_variable = KernelSpaceInducingPoints(inducing_variable_cnn)

model = gpflow.models.SVGP(
    kernel,
    likelihood,
    inducing_variable=inducing_variable,
    num_data=total_num_data,
    num_latent_gps=num_mnist_classes,
)

2022-05-10 11:16:58.295643: W tensorflow/core/kernels/data/cache_dataset_ops.cc:768] The calling iterator did not fully read the dataset being cached. In order to avoid unexpected truncation of the dataset, the partially cached contents of the dataset  will be discarded. This can happen if you have an input pipeline similar to `dataset.cache().take(k).repeat()`. You should use `dataset.take(k).cache().repeat()` instead.

And start optimization:

data_iterator = iter(dataset)
adam_opt = tf.optimizers.Adam(0.001)

training_loss = model.training_loss_closure(data_iterator)


@tf.function
def optimization_step():
    adam_opt.minimize(training_loss, var_list=model.trainable_variables)


for _ in range(iterations):
    optimization_step()

2022-05-10 11:17:03.457744: W tensorflow/python/util/util.cc:368] Sets are not currently considered sequences, but this may change in the future, so consider avoiding using them.

Let’s do predictions after training. Don’t expect that we will get a good accuracy, because we haven’t run training for long enough.

m, v = model.predict_y(images_subset)
preds = np.argmax(m, 1).reshape(labels_subset.numpy().shape)
correct = preds == labels_subset.numpy().astype(int)
acc = np.average(correct.astype(float)) * 100.0

print("Accuracy is {:.4f}%".format(acc))

Accuracy is 71.1914%