Graph regularization for document classification using natural graphs

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Overview

Graph regularization is a specific technique under the broader paradigm of Neural Graph Learning (Bui et al., 2018). The core idea is to train neural network models with a graph-regularized objective, harnessing both labeled and unlabeled data.

In this tutorial, we will explore the use of graph regularization to classify documents that form a natural (organic) graph.

The general recipe for creating a graph-regularized model using the Neural Structured Learning (NSL) framework is as follows:

  1. Generate training data from the input graph and sample features. Nodes in the graph correspond to samples and edges in the graph correspond to similarity between pairs of samples. The resulting training data will contain neighbor features in addition to the original node features.
  2. Create a neural network as a base model using the Keras sequential, functional, or subclass API.
  3. Wrap the base model with the GraphRegularization wrapper class, which is provided by the NSL framework, to create a new graph Keras model. This new model will include a graph regularization loss as the regularization term in its training objective.
  4. Train and evaluate the graph Keras model.

Setup

Install the Neural Structured Learning package.

pip install --quiet neural-structured-learning

Dependencies and imports

import neural_structured_learning as nsl

import tensorflow as tf

# Resets notebook state
tf.keras.backend.clear_session()

print("Version: ", tf.__version__)
print("Eager mode: ", tf.executing_eagerly())
print(
    "GPU is",
    "available" if tf.config.list_physical_devices("GPU") else "NOT AVAILABLE")
2023-11-16 12:04:49.460421: E external/local_xla/xla/stream_executor/cuda/cuda_dnn.cc:9261] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
2023-11-16 12:04:49.460472: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:607] Unable to register cuFFT factory: Attempting to register factory for plugin cuFFT when one has already been registered
2023-11-16 12:04:49.461916: E external/local_xla/xla/stream_executor/cuda/cuda_blas.cc:1515] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
Version:  2.15.0
Eager mode:  True
GPU is NOT AVAILABLE
2023-11-16 12:04:51.768240: E external/local_xla/xla/stream_executor/cuda/cuda_driver.cc:274] failed call to cuInit: CUDA_ERROR_NO_DEVICE: no CUDA-capable device is detected

Cora dataset

The Cora dataset is a citation graph where nodes represent machine learning papers and edges represent citations between pairs of papers. The task involved is document classification where the goal is to categorize each paper into one of 7 categories. In other words, this is a multi-class classification problem with 7 classes.

Graph

The original graph is directed. However, for the purpose of this example, we consider the undirected version of this graph. So, if paper A cites paper B, we also consider paper B to have cited A. Although this is not necessarily true, in this example, we consider citations as a proxy for similarity, which is usually a commutative property.

Features

Each paper in the input effectively contains 2 features:

  1. Words: A dense, multi-hot bag-of-words representation of the text in the paper. The vocabulary for the Cora dataset contains 1433 unique words. So, the length of this feature is 1433, and the value at position 'i' is 0/1 indicating whether word 'i' in the vocabulary exists in the given paper or not.

  2. Label: A single integer representing the class ID (category) of the paper.

Download the Cora dataset

wget --quiet -P /tmp https://linqs-data.soe.ucsc.edu/public/lbc/cora.tgz
tar -C /tmp -xvzf /tmp/cora.tgz
cora/
cora/README
cora/cora.cites
cora/cora.content

Convert the Cora data to the NSL format

In order to preprocess the Cora dataset and convert it to the format required by Neural Structured Learning, we will run the 'preprocess_cora_dataset.py' script, which is included in the NSL github repository. This script does the following:

  1. Generate neighbor features using the original node features and the graph.
  2. Generate train and test data splits containing tf.train.Example instances.
  3. Persist the resulting train and test data in the TFRecord format.
!wget https://raw.githubusercontent.com/tensorflow/neural-structured-learning/master/neural_structured_learning/examples/preprocess/cora/preprocess_cora_dataset.py

!python preprocess_cora_dataset.py \
--input_cora_content=/tmp/cora/cora.content \
--input_cora_graph=/tmp/cora/cora.cites \
--max_nbrs=5 \
--output_train_data=/tmp/cora/train_merged_examples.tfr \
--output_test_data=/tmp/cora/test_examples.tfr
--2023-11-16 12:04:52--  https://raw.githubusercontent.com/tensorflow/neural-structured-learning/master/neural_structured_learning/examples/preprocess/cora/preprocess_cora_dataset.py
Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.108.133, 185.199.109.133, 185.199.110.133, ...
Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.108.133|:443... connected.
HTTP request sent, awaiting response... 200 OK
Length: 11640 (11K) [text/plain]
Saving to: ‘preprocess_cora_dataset.py’

preprocess_cora_dat 100%[===================>]  11.37K  --.-KB/s    in 0s      

2023-11-16 12:04:53 (75.6 MB/s) - ‘preprocess_cora_dataset.py’ saved [11640/11640]

2023-11-16 12:04:53.758687: E external/local_xla/xla/stream_executor/cuda/cuda_dnn.cc:9261] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
2023-11-16 12:04:53.758743: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:607] Unable to register cuFFT factory: Attempting to register factory for plugin cuFFT when one has already been registered
2023-11-16 12:04:53.760530: E external/local_xla/xla/stream_executor/cuda/cuda_blas.cc:1515] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
2023-11-16 12:04:55.968449: E external/local_xla/xla/stream_executor/cuda/cuda_driver.cc:274] failed call to cuInit: CUDA_ERROR_NO_DEVICE: no CUDA-capable device is detected
Reading graph file: /tmp/cora/cora.cites...
Done reading 5429 edges from: /tmp/cora/cora.cites (0.01 seconds).
Making all edges bi-directional...
Done (0.01 seconds). Total graph nodes: 2708
Joining seed and neighbor tf.train.Examples with graph edges...
Done creating and writing 2155 merged tf.train.Examples (1.44 seconds).
Out-degree histogram: [(1, 386), (2, 468), (3, 452), (4, 309), (5, 540)]
Output training data written to TFRecord file: /tmp/cora/train_merged_examples.tfr.
Output test data written to TFRecord file: /tmp/cora/test_examples.tfr.
Total running time: 0.05 minutes.

Global variables

The file paths to the train and test data are based on the command line flag values used to invoke the 'preprocess_cora_dataset.py' script above.

### Experiment dataset
TRAIN_DATA_PATH = '/tmp/cora/train_merged_examples.tfr'
TEST_DATA_PATH = '/tmp/cora/test_examples.tfr'

### Constants used to identify neighbor features in the input.
NBR_FEATURE_PREFIX = 'NL_nbr_'
NBR_WEIGHT_SUFFIX = '_weight'

Hyperparameters

We will use an instance of HParams to include various hyperparameters and constants used for training and evaluation. We briefly describe each of them below:

  • num_classes: There are a total 7 different classes

  • max_seq_length: This is the size of the vocabulary and all instances in the input have a dense multi-hot, bag-of-words representation. In other words, a value of 1 for a word indicates that the word is present in the input and a value of 0 indicates that it is not.

  • distance_type: This is the distance metric used to regularize the sample with its neighbors.

  • graph_regularization_multiplier: This controls the relative weight of the graph regularization term in the overall loss function.

  • num_neighbors: The number of neighbors used for graph regularization. This value has to be less than or equal to the max_nbrs command-line argument used above when running preprocess_cora_dataset.py.

  • num_fc_units: The number of fully connected layers in our neural network.

  • train_epochs: The number of training epochs.

  • batch_size: Batch size used for training and evaluation.

  • dropout_rate: Controls the rate of dropout following each fully connected layer

  • eval_steps: The number of batches to process before deeming evaluation is complete. If set to None, all instances in the test set are evaluated.

class HParams(object):
  """Hyperparameters used for training."""
  def __init__(self):
    ### dataset parameters
    self.num_classes = 7
    self.max_seq_length = 1433
    ### neural graph learning parameters
    self.distance_type = nsl.configs.DistanceType.L2
    self.graph_regularization_multiplier = 0.1
    self.num_neighbors = 1
    ### model architecture
    self.num_fc_units = [50, 50]
    ### training parameters
    self.train_epochs = 100
    self.batch_size = 128
    self.dropout_rate = 0.5
    ### eval parameters
    self.eval_steps = None  # All instances in the test set are evaluated.

HPARAMS = HParams()

Load train and test data

As described earlier in this notebook, the input training and test data have been created by the 'preprocess_cora_dataset.py'. We will load them into two tf.data.Dataset objects -- one for train and one for test.

In the input layer of our model, we will extract not just the 'words' and the 'label' features from each sample, but also corresponding neighbor features based on the hparams.num_neighbors value. Instances with fewer neighbors than hparams.num_neighbors will be assigned dummy values for those non-existent neighbor features.

def make_dataset(file_path, training=False):
  """Creates a `tf.data.TFRecordDataset`.

  Args:
    file_path: Name of the file in the `.tfrecord` format containing
      `tf.train.Example` objects.
    training: Boolean indicating if we are in training mode.

  Returns:
    An instance of `tf.data.TFRecordDataset` containing the `tf.train.Example`
    objects.
  """

  def parse_example(example_proto):
    """Extracts relevant fields from the `example_proto`.

    Args:
      example_proto: An instance of `tf.train.Example`.

    Returns:
      A pair whose first value is a dictionary containing relevant features
      and whose second value contains the ground truth label.
    """
    # The 'words' feature is a multi-hot, bag-of-words representation of the
    # original raw text. A default value is required for examples that don't
    # have the feature.
    feature_spec = {
        'words':
            tf.io.FixedLenFeature([HPARAMS.max_seq_length],
                                  tf.int64,
                                  default_value=tf.constant(
                                      0,
                                      dtype=tf.int64,
                                      shape=[HPARAMS.max_seq_length])),
        'label':
            tf.io.FixedLenFeature((), tf.int64, default_value=-1),
    }
    # We also extract corresponding neighbor features in a similar manner to
    # the features above during training.
    if training:
      for i in range(HPARAMS.num_neighbors):
        nbr_feature_key = '{}{}_{}'.format(NBR_FEATURE_PREFIX, i, 'words')
        nbr_weight_key = '{}{}{}'.format(NBR_FEATURE_PREFIX, i,
                                         NBR_WEIGHT_SUFFIX)
        feature_spec[nbr_feature_key] = tf.io.FixedLenFeature(
            [HPARAMS.max_seq_length],
            tf.int64,
            default_value=tf.constant(
                0, dtype=tf.int64, shape=[HPARAMS.max_seq_length]))

        # We assign a default value of 0.0 for the neighbor weight so that
        # graph regularization is done on samples based on their exact number
        # of neighbors. In other words, non-existent neighbors are discounted.
        feature_spec[nbr_weight_key] = tf.io.FixedLenFeature(
            [1], tf.float32, default_value=tf.constant([0.0]))

    features = tf.io.parse_single_example(example_proto, feature_spec)

    label = features.pop('label')
    return features, label

  dataset = tf.data.TFRecordDataset([file_path])
  if training:
    dataset = dataset.shuffle(10000)
  dataset = dataset.map(parse_example)
  dataset = dataset.batch(HPARAMS.batch_size)
  return dataset


train_dataset = make_dataset(TRAIN_DATA_PATH, training=True)
test_dataset = make_dataset(TEST_DATA_PATH)

Let's peek into the train dataset to look at its contents.

for feature_batch, label_batch in train_dataset.take(1):
  print('Feature list:', list(feature_batch.keys()))
  print('Batch of inputs:', feature_batch['words'])
  nbr_feature_key = '{}{}_{}'.format(NBR_FEATURE_PREFIX, 0, 'words')
  nbr_weight_key = '{}{}{}'.format(NBR_FEATURE_PREFIX, 0, NBR_WEIGHT_SUFFIX)
  print('Batch of neighbor inputs:', feature_batch[nbr_feature_key])
  print('Batch of neighbor weights:',
        tf.reshape(feature_batch[nbr_weight_key], [-1]))
  print('Batch of labels:', label_batch)
Feature list: ['NL_nbr_0_weight', 'NL_nbr_0_words', 'words']
Batch of inputs: tf.Tensor(
[[0 0 0 ... 0 0 0]
 [0 0 0 ... 0 0 0]
 [0 0 0 ... 0 0 0]
 ...
 [0 0 0 ... 0 0 0]
 [0 0 0 ... 0 0 0]
 [0 0 0 ... 0 0 0]], shape=(128, 1433), dtype=int64)
Batch of neighbor inputs: tf.Tensor(
[[0 0 0 ... 0 0 0]
 [0 0 0 ... 0 0 0]
 [0 0 1 ... 0 0 0]
 ...
 [0 0 0 ... 0 0 0]
 [0 0 0 ... 0 0 0]
 [0 0 0 ... 0 0 0]], shape=(128, 1433), dtype=int64)
Batch of neighbor weights: tf.Tensor(
[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.

 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
 1. 1. 1. 1. 1. 1. 1. 1.], shape=(128,), dtype=float32)
Batch of labels: tf.Tensor(
[2 2 3 6 6 4 3 1 3 4 2 5 4 5 6 4 1 5 1 0 5 6 3 0 4 2 4 4 1 1 1 6 2 2 5 3 3
 5 3 2 0 0 1 5 5 0 4 6 1 4 2 0 2 4 4 1 3 2 2 2 1 2 2 5 2 2 4 1 2 6 1 6 3 0
 5 2 6 4 3 2 4 0 2 1 2 2 2 2 2 2 1 1 6 3 2 4 1 2 1 0 3 0 0 3 2 6 1 2 2 1 2
 2 2 3 2 0 2 3 2 5 3 0 1 1 2 0 2 1], shape=(128,), dtype=int64)

Let's peek into the test dataset to look at its contents.

for feature_batch, label_batch in test_dataset.take(1):
  print('Feature list:', list(feature_batch.keys()))
  print('Batch of inputs:', feature_batch['words'])
  print('Batch of labels:', label_batch)
Feature list: ['words']
Batch of inputs: tf.Tensor(
[[0 0 0 ... 0 0 0]
 [0 0 0 ... 0 0 0]
 [0 0 0 ... 0 0 0]
 ...
 [0 0 0 ... 0 0 0]
 [0 0 0 ... 0 0 0]
 [0 0 0 ... 0 0 0]], shape=(128, 1433), dtype=int64)
Batch of labels: tf.Tensor(
[5 2 2 2 1 2 6 3 2 3 6 1 3 6 4 4 2 3 3 0 2 0 5 2 1 0 6 3 6 4 2 2 3 0 4 2 2
 2 2 3 2 2 2 0 2 2 2 2 4 2 3 4 0 2 6 2 1 4 2 0 0 1 4 2 6 0 5 2 2 3 2 5 2 5
 2 3 2 2 2 2 2 6 6 3 2 4 2 6 3 2 2 6 2 4 2 2 1 3 4 6 0 0 2 4 2 1 3 6 6 2 6
 6 6 1 4 6 4 3 6 6 0 0 2 6 2 4 0 0], shape=(128,), dtype=int64)

Model definition

In order to demonstrate the use of graph regularization, we build a base model for this problem first. We will use a simple feed-forward neural network with 2 hidden layers and dropout in between. We illustrate the creation of the base model using all model types supported by the tf.Keras framework -- sequential, functional, and subclass.

Sequential base model

def make_mlp_sequential_model(hparams):
  """Creates a sequential multi-layer perceptron model."""
  model = tf.keras.Sequential()
  model.add(
      tf.keras.layers.InputLayer(
          input_shape=(hparams.max_seq_length,), name='words'))
  # Input is already one-hot encoded in the integer format. We cast it to
  # floating point format here.
  model.add(
      tf.keras.layers.Lambda(lambda x: tf.keras.backend.cast(x, tf.float32)))
  for num_units in hparams.num_fc_units:
    model.add(tf.keras.layers.Dense(num_units, activation='relu'))
    # For sequential models, by default, Keras ensures that the 'dropout' layer
    # is invoked only during training.
    model.add(tf.keras.layers.Dropout(hparams.dropout_rate))
  model.add(tf.keras.layers.Dense(hparams.num_classes))
  return model

Functional base model

def make_mlp_functional_model(hparams):
  """Creates a functional API-based multi-layer perceptron model."""
  inputs = tf.keras.Input(
      shape=(hparams.max_seq_length,), dtype='int64', name='words')

  # Input is already one-hot encoded in the integer format. We cast it to
  # floating point format here.
  cur_layer = tf.keras.layers.Lambda(
      lambda x: tf.keras.backend.cast(x, tf.float32))(
          inputs)

  for num_units in hparams.num_fc_units:
    cur_layer = tf.keras.layers.Dense(num_units, activation='relu')(cur_layer)
    # For functional models, by default, Keras ensures that the 'dropout' layer
    # is invoked only during training.
    cur_layer = tf.keras.layers.Dropout(hparams.dropout_rate)(cur_layer)

  outputs = tf.keras.layers.Dense(hparams.num_classes)(cur_layer)

  model = tf.keras.Model(inputs, outputs=outputs)
  return model

Subclass base model

def make_mlp_subclass_model(hparams):
  """Creates a multi-layer perceptron subclass model in Keras."""

  class MLP(tf.keras.Model):
    """Subclass model defining a multi-layer perceptron."""

    def __init__(self):
      super(MLP, self).__init__()
      # Input is already one-hot encoded in the integer format. We create a
      # layer to cast it to floating point format here.
      self.cast_to_float_layer = tf.keras.layers.Lambda(
          lambda x: tf.keras.backend.cast(x, tf.float32))
      self.dense_layers = [
          tf.keras.layers.Dense(num_units, activation='relu')
          for num_units in hparams.num_fc_units
      ]
      self.dropout_layer = tf.keras.layers.Dropout(hparams.dropout_rate)
      self.output_layer = tf.keras.layers.Dense(hparams.num_classes)

    def call(self, inputs, training=False):
      cur_layer = self.cast_to_float_layer(inputs['words'])
      for dense_layer in self.dense_layers:
        cur_layer = dense_layer(cur_layer)
        cur_layer = self.dropout_layer(cur_layer, training=training)

      outputs = self.output_layer(cur_layer)

      return outputs

  return MLP()

Create base model(s)

# Create a base MLP model using the functional API.
# Alternatively, you can also create a sequential or subclass base model using
# the make_mlp_sequential_model() or make_mlp_subclass_model() functions
# respectively, defined above. Note that if a subclass model is used, its
# summary cannot be generated until it is built.
base_model_tag, base_model = 'FUNCTIONAL', make_mlp_functional_model(HPARAMS)
base_model.summary()
Model: "model"
_________________________________________________________________
 Layer (type)                Output Shape              Param #   
=================================================================
 words (InputLayer)          [(None, 1433)]            0         
                                                                 
 lambda (Lambda)             (None, 1433)              0         
                                                                 
 dense (Dense)               (None, 50)                71700     
                                                                 
 dropout (Dropout)           (None, 50)                0         
                                                                 
 dense_1 (Dense)             (None, 50)                2550      
                                                                 
 dropout_1 (Dropout)         (None, 50)                0         
                                                                 
 dense_2 (Dense)             (None, 7)                 357       
                                                                 
=================================================================
Total params: 74607 (291.43 KB)
Trainable params: 74607 (291.43 KB)
Non-trainable params: 0 (0.00 Byte)
_________________________________________________________________

Train base MLP model

# Compile and train the base MLP model
base_model.compile(
    optimizer='adam',
    loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True),
    metrics=['accuracy'])
base_model.fit(train_dataset, epochs=HPARAMS.train_epochs, verbose=1)
Epoch 1/100
/tmpfs/src/tf_docs_env/lib/python3.9/site-packages/keras/src/engine/functional.py:642: UserWarning: Input dict contained keys ['NL_nbr_0_weight', 'NL_nbr_0_words'] which did not match any model input. They will be ignored by the model.
  inputs = self._flatten_to_reference_inputs(inputs)
17/17 [==============================] - 1s 6ms/step - loss: 1.9105 - accuracy: 0.2260
Epoch 2/100
17/17 [==============================] - 0s 3ms/step - loss: 1.8280 - accuracy: 0.3044
Epoch 3/100
17/17 [==============================] - 0s 3ms/step - loss: 1.7240 - accuracy: 0.3299
Epoch 4/100
17/17 [==============================] - 0s 3ms/step - loss: 1.5969 - accuracy: 0.3745
Epoch 5/100
17/17 [==============================] - 0s 3ms/step - loss: 1.4765 - accuracy: 0.4492
Epoch 6/100
17/17 [==============================] - 0s 3ms/step - loss: 1.3235 - accuracy: 0.5276
Epoch 7/100
17/17 [==============================] - 0s 3ms/step - loss: 1.1913 - accuracy: 0.5889
Epoch 8/100
17/17 [==============================] - 0s 3ms/step - loss: 1.0604 - accuracy: 0.6432
Epoch 9/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9628 - accuracy: 0.6821
Epoch 10/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8601 - accuracy: 0.7234
Epoch 11/100
17/17 [==============================] - 0s 3ms/step - loss: 0.7914 - accuracy: 0.7480
Epoch 12/100
17/17 [==============================] - 0s 3ms/step - loss: 0.7230 - accuracy: 0.7633
Epoch 13/100
17/17 [==============================] - 0s 3ms/step - loss: 0.6783 - accuracy: 0.7791
Epoch 14/100
17/17 [==============================] - 0s 3ms/step - loss: 0.6019 - accuracy: 0.8070
Epoch 15/100
17/17 [==============================] - 0s 3ms/step - loss: 0.5587 - accuracy: 0.8367
Epoch 16/100
17/17 [==============================] - 0s 3ms/step - loss: 0.5295 - accuracy: 0.8450
Epoch 17/100
17/17 [==============================] - 0s 3ms/step - loss: 0.4789 - accuracy: 0.8599
Epoch 18/100
17/17 [==============================] - 0s 3ms/step - loss: 0.4474 - accuracy: 0.8650
Epoch 19/100
17/17 [==============================] - 0s 3ms/step - loss: 0.4148 - accuracy: 0.8701
Epoch 20/100
17/17 [==============================] - 0s 3ms/step - loss: 0.3812 - accuracy: 0.8896
Epoch 21/100
17/17 [==============================] - 0s 3ms/step - loss: 0.3656 - accuracy: 0.8863
Epoch 22/100
17/17 [==============================] - 0s 3ms/step - loss: 0.3544 - accuracy: 0.8923
Epoch 23/100
17/17 [==============================] - 0s 3ms/step - loss: 0.3050 - accuracy: 0.9165
Epoch 24/100
17/17 [==============================] - 0s 3ms/step - loss: 0.2858 - accuracy: 0.9216
Epoch 25/100
17/17 [==============================] - 0s 3ms/step - loss: 0.2821 - accuracy: 0.9234
Epoch 26/100
17/17 [==============================] - 0s 3ms/step - loss: 0.2543 - accuracy: 0.9276
Epoch 27/100
17/17 [==============================] - 0s 3ms/step - loss: 0.2477 - accuracy: 0.9285
Epoch 28/100
17/17 [==============================] - 0s 3ms/step - loss: 0.2413 - accuracy: 0.9295
Epoch 29/100
17/17 [==============================] - 0s 3ms/step - loss: 0.2153 - accuracy: 0.9415
Epoch 30/100
17/17 [==============================] - 0s 3ms/step - loss: 0.2241 - accuracy: 0.9290
Epoch 31/100
17/17 [==============================] - 0s 3ms/step - loss: 0.2118 - accuracy: 0.9374
Epoch 32/100
17/17 [==============================] - 0s 3ms/step - loss: 0.2041 - accuracy: 0.9471
Epoch 33/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1951 - accuracy: 0.9392
Epoch 34/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1841 - accuracy: 0.9443
Epoch 35/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1783 - accuracy: 0.9522
Epoch 36/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1742 - accuracy: 0.9485
Epoch 37/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1705 - accuracy: 0.9541
Epoch 38/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1507 - accuracy: 0.9592
Epoch 39/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1513 - accuracy: 0.9555
Epoch 40/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1378 - accuracy: 0.9652
Epoch 41/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1471 - accuracy: 0.9587
Epoch 42/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1309 - accuracy: 0.9661
Epoch 43/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1288 - accuracy: 0.9596
Epoch 44/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1327 - accuracy: 0.9629
Epoch 45/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1170 - accuracy: 0.9675
Epoch 46/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1198 - accuracy: 0.9666
Epoch 47/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1183 - accuracy: 0.9680
Epoch 48/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1025 - accuracy: 0.9740
Epoch 49/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0981 - accuracy: 0.9754
Epoch 50/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1076 - accuracy: 0.9708
Epoch 51/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0874 - accuracy: 0.9796
Epoch 52/100
17/17 [==============================] - 0s 3ms/step - loss: 0.1027 - accuracy: 0.9735
Epoch 53/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0993 - accuracy: 0.9740
Epoch 54/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0934 - accuracy: 0.9759
Epoch 55/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0932 - accuracy: 0.9759
Epoch 56/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0787 - accuracy: 0.9810
Epoch 57/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0890 - accuracy: 0.9754
Epoch 58/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0918 - accuracy: 0.9749
Epoch 59/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0908 - accuracy: 0.9717
Epoch 60/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0825 - accuracy: 0.9777
Epoch 61/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0926 - accuracy: 0.9684
Epoch 62/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0702 - accuracy: 0.9800
Epoch 63/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0720 - accuracy: 0.9842
Epoch 64/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0792 - accuracy: 0.9773
Epoch 65/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0760 - accuracy: 0.9782
Epoch 66/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0736 - accuracy: 0.9800
Epoch 67/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0838 - accuracy: 0.9773
Epoch 68/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0639 - accuracy: 0.9824
Epoch 69/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0742 - accuracy: 0.9805
Epoch 70/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0798 - accuracy: 0.9782
Epoch 71/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0694 - accuracy: 0.9805
Epoch 72/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0635 - accuracy: 0.9833
Epoch 73/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0587 - accuracy: 0.9824
Epoch 74/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0689 - accuracy: 0.9828
Epoch 75/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0628 - accuracy: 0.9828
Epoch 76/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0570 - accuracy: 0.9842
Epoch 77/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0632 - accuracy: 0.9824
Epoch 78/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0673 - accuracy: 0.9782
Epoch 79/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0573 - accuracy: 0.9828
Epoch 80/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0640 - accuracy: 0.9824
Epoch 81/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0610 - accuracy: 0.9810
Epoch 82/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0553 - accuracy: 0.9861
Epoch 83/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0482 - accuracy: 0.9879
Epoch 84/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0548 - accuracy: 0.9842
Epoch 85/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0537 - accuracy: 0.9865
Epoch 86/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0540 - accuracy: 0.9828
Epoch 87/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0528 - accuracy: 0.9838
Epoch 88/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0505 - accuracy: 0.9865
Epoch 89/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0473 - accuracy: 0.9833
Epoch 90/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0604 - accuracy: 0.9810
Epoch 91/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0469 - accuracy: 0.9879
Epoch 92/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0554 - accuracy: 0.9810
Epoch 93/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0427 - accuracy: 0.9875
Epoch 94/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0581 - accuracy: 0.9824
Epoch 95/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0488 - accuracy: 0.9842
Epoch 96/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0466 - accuracy: 0.9875
Epoch 97/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0465 - accuracy: 0.9875
Epoch 98/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0411 - accuracy: 0.9879
Epoch 99/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0539 - accuracy: 0.9852
Epoch 100/100
17/17 [==============================] - 0s 3ms/step - loss: 0.0451 - accuracy: 0.9870
<keras.src.callbacks.History at 0x7f459c2e9e50>

Evaluate base MLP model

# Helper function to print evaluation metrics.
def print_metrics(model_desc, eval_metrics):
  """Prints evaluation metrics.

  Args:
    model_desc: A description of the model.
    eval_metrics: A dictionary mapping metric names to corresponding values. It
      must contain the loss and accuracy metrics.
  """
  print('\n')
  print('Eval accuracy for ', model_desc, ': ', eval_metrics['accuracy'])
  print('Eval loss for ', model_desc, ': ', eval_metrics['loss'])
  if 'graph_loss' in eval_metrics:
    print('Eval graph loss for ', model_desc, ': ', eval_metrics['graph_loss'])
eval_results = dict(
    zip(base_model.metrics_names,
        base_model.evaluate(test_dataset, steps=HPARAMS.eval_steps)))
print_metrics('Base MLP model', eval_results)
5/5 [==============================] - 0s 5ms/step - loss: 1.4164 - accuracy: 0.7758


Eval accuracy for  Base MLP model :  0.775768518447876
Eval loss for  Base MLP model :  1.4164185523986816

Train MLP model with graph regularization

Incorporating graph regularization into the loss term of an existing tf.Keras.Model requires just a few lines of code. The base model is wrapped to create a new tf.Keras subclass model, whose loss includes graph regularization.

To assess the incremental benefit of graph regularization, we will create a new base model instance. This is because base_model has already been trained for a few iterations, and reusing this trained model to create a graph-regularized model will not be a fair comparison for base_model.

# Build a new base MLP model.
base_reg_model_tag, base_reg_model = 'FUNCTIONAL', make_mlp_functional_model(
    HPARAMS)
# Wrap the base MLP model with graph regularization.
graph_reg_config = nsl.configs.make_graph_reg_config(
    max_neighbors=HPARAMS.num_neighbors,
    multiplier=HPARAMS.graph_regularization_multiplier,
    distance_type=HPARAMS.distance_type,
    sum_over_axis=-1)
graph_reg_model = nsl.keras.GraphRegularization(base_reg_model,
                                                graph_reg_config)
graph_reg_model.compile(
    optimizer='adam',
    loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True),
    metrics=['accuracy'])
graph_reg_model.fit(train_dataset, epochs=HPARAMS.train_epochs, verbose=1)
Epoch 1/100
17/17 [==============================] - 2s 7ms/step - loss: 1.9586 - accuracy: 0.2107 - scaled_graph_loss: 0.0319
Epoch 2/100
17/17 [==============================] - 0s 3ms/step - loss: 1.8903 - accuracy: 0.2942 - scaled_graph_loss: 0.0282
Epoch 3/100
17/17 [==============================] - 0s 3ms/step - loss: 1.8290 - accuracy: 0.3262 - scaled_graph_loss: 0.0411
Epoch 4/100
17/17 [==============================] - 0s 3ms/step - loss: 1.7762 - accuracy: 0.3248 - scaled_graph_loss: 0.0604
Epoch 5/100
17/17 [==============================] - 0s 3ms/step - loss: 1.7334 - accuracy: 0.3568 - scaled_graph_loss: 0.0792
Epoch 6/100
17/17 [==============================] - 0s 3ms/step - loss: 1.6859 - accuracy: 0.3735 - scaled_graph_loss: 0.0920
Epoch 7/100
17/17 [==============================] - 0s 3ms/step - loss: 1.6506 - accuracy: 0.3935 - scaled_graph_loss: 0.1086
Epoch 8/100
17/17 [==============================] - 0s 3ms/step - loss: 1.6028 - accuracy: 0.4520 - scaled_graph_loss: 0.1249
Epoch 9/100
17/17 [==============================] - 0s 3ms/step - loss: 1.5690 - accuracy: 0.5012 - scaled_graph_loss: 0.1386
Epoch 10/100
17/17 [==============================] - 0s 3ms/step - loss: 1.5332 - accuracy: 0.5420 - scaled_graph_loss: 0.1577
Epoch 11/100
17/17 [==============================] - 0s 3ms/step - loss: 1.4792 - accuracy: 0.5842 - scaled_graph_loss: 0.1642
Epoch 12/100
17/17 [==============================] - 0s 3ms/step - loss: 1.4438 - accuracy: 0.6306 - scaled_graph_loss: 0.1909
Epoch 13/100
17/17 [==============================] - 0s 3ms/step - loss: 1.4155 - accuracy: 0.6617 - scaled_graph_loss: 0.2009
Epoch 14/100
17/17 [==============================] - 0s 3ms/step - loss: 1.3596 - accuracy: 0.6896 - scaled_graph_loss: 0.1964
Epoch 15/100
17/17 [==============================] - 0s 3ms/step - loss: 1.3462 - accuracy: 0.7077 - scaled_graph_loss: 0.2294
Epoch 16/100
17/17 [==============================] - 0s 3ms/step - loss: 1.3151 - accuracy: 0.7295 - scaled_graph_loss: 0.2312
Epoch 17/100
17/17 [==============================] - 0s 3ms/step - loss: 1.2848 - accuracy: 0.7555 - scaled_graph_loss: 0.2319
Epoch 18/100
17/17 [==============================] - 0s 3ms/step - loss: 1.2643 - accuracy: 0.7759 - scaled_graph_loss: 0.2469
Epoch 19/100
17/17 [==============================] - 0s 3ms/step - loss: 1.2434 - accuracy: 0.7921 - scaled_graph_loss: 0.2544
Epoch 20/100
17/17 [==============================] - 0s 3ms/step - loss: 1.2005 - accuracy: 0.8093 - scaled_graph_loss: 0.2473
Epoch 21/100
17/17 [==============================] - 0s 3ms/step - loss: 1.2007 - accuracy: 0.8070 - scaled_graph_loss: 0.2688
Epoch 22/100
17/17 [==============================] - 0s 3ms/step - loss: 1.1876 - accuracy: 0.8135 - scaled_graph_loss: 0.2708
Epoch 23/100
17/17 [==============================] - 0s 3ms/step - loss: 1.1729 - accuracy: 0.8274 - scaled_graph_loss: 0.2662
Epoch 24/100
17/17 [==============================] - 0s 3ms/step - loss: 1.1543 - accuracy: 0.8376 - scaled_graph_loss: 0.2707
Epoch 25/100
17/17 [==============================] - 0s 3ms/step - loss: 1.1228 - accuracy: 0.8538 - scaled_graph_loss: 0.2677
Epoch 26/100
17/17 [==============================] - 0s 3ms/step - loss: 1.1166 - accuracy: 0.8603 - scaled_graph_loss: 0.2785
Epoch 27/100
17/17 [==============================] - 0s 3ms/step - loss: 1.1176 - accuracy: 0.8473 - scaled_graph_loss: 0.2807
Epoch 28/100
17/17 [==============================] - 0s 3ms/step - loss: 1.1085 - accuracy: 0.8473 - scaled_graph_loss: 0.2649
Epoch 29/100
17/17 [==============================] - 0s 3ms/step - loss: 1.0751 - accuracy: 0.8691 - scaled_graph_loss: 0.2858
Epoch 30/100
17/17 [==============================] - 0s 3ms/step - loss: 1.0851 - accuracy: 0.8696 - scaled_graph_loss: 0.2996
Epoch 31/100
17/17 [==============================] - 0s 3ms/step - loss: 1.0932 - accuracy: 0.8770 - scaled_graph_loss: 0.2892
Epoch 32/100
17/17 [==============================] - 0s 3ms/step - loss: 1.0619 - accuracy: 0.8821 - scaled_graph_loss: 0.2880
Epoch 33/100
17/17 [==============================] - 0s 3ms/step - loss: 1.0531 - accuracy: 0.8886 - scaled_graph_loss: 0.2847
Epoch 34/100
17/17 [==============================] - 0s 3ms/step - loss: 1.0558 - accuracy: 0.8863 - scaled_graph_loss: 0.2962
Epoch 35/100
17/17 [==============================] - 0s 3ms/step - loss: 1.0375 - accuracy: 0.8891 - scaled_graph_loss: 0.2780
Epoch 36/100
17/17 [==============================] - 0s 3ms/step - loss: 1.0310 - accuracy: 0.8858 - scaled_graph_loss: 0.2932
Epoch 37/100
17/17 [==============================] - 0s 3ms/step - loss: 1.0269 - accuracy: 0.8872 - scaled_graph_loss: 0.2916
Epoch 38/100
17/17 [==============================] - 0s 3ms/step - loss: 1.0273 - accuracy: 0.8928 - scaled_graph_loss: 0.2948
Epoch 39/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9935 - accuracy: 0.9123 - scaled_graph_loss: 0.2910
Epoch 40/100
17/17 [==============================] - 0s 3ms/step - loss: 1.0083 - accuracy: 0.9104 - scaled_graph_loss: 0.2951
Epoch 41/100
17/17 [==============================] - 0s 3ms/step - loss: 1.0196 - accuracy: 0.8951 - scaled_graph_loss: 0.2982
Epoch 42/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9941 - accuracy: 0.9007 - scaled_graph_loss: 0.2898
Epoch 43/100
17/17 [==============================] - 0s 3ms/step - loss: 1.0069 - accuracy: 0.9012 - scaled_graph_loss: 0.3076
Epoch 44/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9816 - accuracy: 0.9049 - scaled_graph_loss: 0.2930
Epoch 45/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9910 - accuracy: 0.9104 - scaled_graph_loss: 0.2954
Epoch 46/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9949 - accuracy: 0.9026 - scaled_graph_loss: 0.3111
Epoch 47/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9715 - accuracy: 0.9114 - scaled_graph_loss: 0.2830
Epoch 48/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9796 - accuracy: 0.9067 - scaled_graph_loss: 0.2970
Epoch 49/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9570 - accuracy: 0.9114 - scaled_graph_loss: 0.2936
Epoch 50/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9691 - accuracy: 0.9049 - scaled_graph_loss: 0.2940
Epoch 51/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9803 - accuracy: 0.9114 - scaled_graph_loss: 0.3083
Epoch 52/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9612 - accuracy: 0.9128 - scaled_graph_loss: 0.2860
Epoch 53/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9627 - accuracy: 0.9216 - scaled_graph_loss: 0.3077
Epoch 54/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9516 - accuracy: 0.9151 - scaled_graph_loss: 0.2906
Epoch 55/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9431 - accuracy: 0.9197 - scaled_graph_loss: 0.2967
Epoch 56/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9622 - accuracy: 0.9132 - scaled_graph_loss: 0.3053
Epoch 57/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9410 - accuracy: 0.9188 - scaled_graph_loss: 0.2830
Epoch 58/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9531 - accuracy: 0.9230 - scaled_graph_loss: 0.3049
Epoch 59/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9309 - accuracy: 0.9193 - scaled_graph_loss: 0.3009
Epoch 60/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9300 - accuracy: 0.9248 - scaled_graph_loss: 0.2988
Epoch 61/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9173 - accuracy: 0.9244 - scaled_graph_loss: 0.2884
Epoch 62/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9228 - accuracy: 0.9248 - scaled_graph_loss: 0.2960
Epoch 63/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9394 - accuracy: 0.9174 - scaled_graph_loss: 0.3102
Epoch 64/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9182 - accuracy: 0.9174 - scaled_graph_loss: 0.2899
Epoch 65/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9276 - accuracy: 0.9253 - scaled_graph_loss: 0.2996
Epoch 66/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9229 - accuracy: 0.9244 - scaled_graph_loss: 0.2912
Epoch 67/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9325 - accuracy: 0.9142 - scaled_graph_loss: 0.3088
Epoch 68/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9091 - accuracy: 0.9216 - scaled_graph_loss: 0.2883
Epoch 69/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8987 - accuracy: 0.9267 - scaled_graph_loss: 0.2924
Epoch 70/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9188 - accuracy: 0.9216 - scaled_graph_loss: 0.2970
Epoch 71/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9003 - accuracy: 0.9299 - scaled_graph_loss: 0.2962
Epoch 72/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9086 - accuracy: 0.9206 - scaled_graph_loss: 0.2944
Epoch 73/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9047 - accuracy: 0.9304 - scaled_graph_loss: 0.3174
Epoch 74/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9214 - accuracy: 0.9202 - scaled_graph_loss: 0.2923
Epoch 75/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9081 - accuracy: 0.9276 - scaled_graph_loss: 0.3020
Epoch 76/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9043 - accuracy: 0.9220 - scaled_graph_loss: 0.2892
Epoch 77/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9022 - accuracy: 0.9253 - scaled_graph_loss: 0.2998
Epoch 78/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8871 - accuracy: 0.9332 - scaled_graph_loss: 0.2979
Epoch 79/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8863 - accuracy: 0.9295 - scaled_graph_loss: 0.3021
Epoch 80/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8893 - accuracy: 0.9225 - scaled_graph_loss: 0.2928
Epoch 81/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8850 - accuracy: 0.9258 - scaled_graph_loss: 0.2997
Epoch 82/100
17/17 [==============================] - 0s 3ms/step - loss: 0.9013 - accuracy: 0.9165 - scaled_graph_loss: 0.2961
Epoch 83/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8739 - accuracy: 0.9253 - scaled_graph_loss: 0.2886
Epoch 84/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8840 - accuracy: 0.9318 - scaled_graph_loss: 0.3040
Epoch 85/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8628 - accuracy: 0.9378 - scaled_graph_loss: 0.2886
Epoch 86/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8745 - accuracy: 0.9313 - scaled_graph_loss: 0.3013
Epoch 87/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8678 - accuracy: 0.9327 - scaled_graph_loss: 0.2980
Epoch 88/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8614 - accuracy: 0.9397 - scaled_graph_loss: 0.2947
Epoch 89/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8589 - accuracy: 0.9327 - scaled_graph_loss: 0.2957
Epoch 90/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8688 - accuracy: 0.9346 - scaled_graph_loss: 0.2996
Epoch 91/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8661 - accuracy: 0.9216 - scaled_graph_loss: 0.2881
Epoch 92/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8828 - accuracy: 0.9318 - scaled_graph_loss: 0.3019
Epoch 93/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8701 - accuracy: 0.9374 - scaled_graph_loss: 0.3051
Epoch 94/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8572 - accuracy: 0.9383 - scaled_graph_loss: 0.2998
Epoch 95/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8765 - accuracy: 0.9327 - scaled_graph_loss: 0.2999
Epoch 96/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8685 - accuracy: 0.9336 - scaled_graph_loss: 0.3013
Epoch 97/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8710 - accuracy: 0.9378 - scaled_graph_loss: 0.3023
Epoch 98/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8746 - accuracy: 0.9327 - scaled_graph_loss: 0.2956
Epoch 99/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8642 - accuracy: 0.9341 - scaled_graph_loss: 0.2984
Epoch 100/100
17/17 [==============================] - 0s 3ms/step - loss: 0.8638 - accuracy: 0.9318 - scaled_graph_loss: 0.2965
<keras.src.callbacks.History at 0x7f445862f130>

Evaluate MLP model with graph regularization

eval_results = dict(
    zip(graph_reg_model.metrics_names,
        graph_reg_model.evaluate(test_dataset, steps=HPARAMS.eval_steps)))
print_metrics('MLP + graph regularization', eval_results)
5/5 [==============================] - 0s 5ms/step - loss: 0.8791 - accuracy: 0.7993


Eval accuracy for  MLP + graph regularization :  0.7992766499519348
Eval loss for  MLP + graph regularization :  0.8790676593780518

The graph-regularized model's accuracy is about 2-3% higher than that of the base model (base_model).

Conclusion

We have demonstrated the use of graph regularization for document classification on a natural citation graph (Cora) using the Neural Structured Learning (NSL) framework. Our advanced tutorial involves synthesizing graphs based on sample embeddings before training a neural network with graph regularization. This approach is useful if the input does not contain an explicit graph.

We encourage users to experiment further by varying the amount of supervision as well as trying different neural architectures for graph regularization.