ABLkit/docs/Examples/MNISTAdd.rst

MNIST Addition
==============

Below shows an implementation of `MNIST
Addition <https://arxiv.org/abs/1805.10872>`__. In this task, pairs of
MNIST handwritten images and their sums are given, alongwith a domain
knowledge base containing information on how to perform addition
operations. The task is to recognize the digits of handwritten images
and accurately determine their sum.

Intuitively, we first use a machine learning model (learning part) to
convert the input images to digits (we call them pseudo-labels), and
then use the knowledge base (reasoning part) to calculate the sum of
these digits. Since we do not have ground-truth of the digits, in
Abductive Learning, the reasoning part will leverage domain knowledge
and revise the initial digits yielded by the learning part through
abductive reasoning. This process enables us to further update the
machine learning model.

.. code:: ipython3

    # Import necessary libraries and modules
    import os.path as osp
    import torch
    import torch.nn as nn
    import matplotlib.pyplot as plt
    from examples.mnist_add.datasets import get_dataset
    from examples.models.nn import LeNet5
    from abl.learning import ABLModel, BasicNN
    from abl.reasoning import KBBase, Reasoner
    from abl.evaluation import ReasoningMetric, SymbolMetric
    from abl.utils import ABLLogger, print_log
    from abl.bridge import SimpleBridge

Working with Data
-----------------

First, we get the training and testing datasets:

.. code:: ipython3

    train_data = get_dataset(train=True, get_pseudo_label=True)
    test_data = get_dataset(train=False, get_pseudo_label=True)

``train_data`` and ``test_data`` share identical structures: 
tuples with three components: X (list where each element is a 
list of two images), gt_pseudo_label (list where each element 
is a list of two digits, i.e., pseudo-labels) and Y (list where 
each element is the sum of the two digits). The length and structures 
of datasets are illustrated as follows.

.. note::

    ``gt_pseudo_label`` is only used to evaluate the performance of
    the learning part but not to train the model.

.. code:: ipython3

    print(f"Both train_data and test_data consist of 3 components: X, gt_pseudo_label, Y")
    print("\n")
    train_X, train_gt_pseudo_label, train_Y = train_data
    print(f"Length of X, gt_pseudo_label, Y in train_data: " +
          f"{len(train_X)}, {len(train_gt_pseudo_label)}, {len(train_Y)}")
    test_X, test_gt_pseudo_label, test_Y = test_data
    print(f"Length of X, gt_pseudo_label, Y in test_data: " +
          f"{len(test_X)}, {len(test_gt_pseudo_label)}, {len(test_Y)}")
    print("\n")

    X_0, gt_pseudo_label_0, Y_0 = train_X[0], train_gt_pseudo_label[0], train_Y[0]
    print(f"X is a {type(train_X).__name__}, " +
          f"with each element being a {type(X_0).__name__} " +
          f"of {len(X_0)} {type(X_0[0]).__name__}.")
    print(f"gt_pseudo_label is a {type(train_gt_pseudo_label).__name__}, " +
          f"with each element being a {type(gt_pseudo_label_0).__name__} " +
          f"of {len(gt_pseudo_label_0)} {type(gt_pseudo_label_0[0]).__name__}.")
    print(f"Y is a {type(train_Y).__name__}, " +
          f"with each element being a {type(Y_0).__name__}.")


Out:
    .. code:: none
        :class: code-out

        Both train_data and test_data consist of 3 components: X, gt_pseudo_label, Y

        Length of X, gt_pseudo_label, Y in train_data: 30000, 30000, 30000
        Length of X, gt_pseudo_label, Y in test_data: 5000, 5000, 5000

        X is a list, with each element being a list of 2 Tensor.
        gt_pseudo_label is a list, with each element being a list of 2 int.
        Y is a list, with each element being a int.
    

The ith element of X, gt_pseudo_label, and Y together constitute the ith
data example. As an illustration, in the first data example of the
training set, we have:

.. code:: ipython3

    X_0, gt_pseudo_label_0, Y_0 = train_X[0], train_gt_pseudo_label[0], train_Y[0]
    print(f"X in the first data example (a list of two images):")
    plt.subplot(1,2,1)
    plt.axis('off') 
    plt.imshow(X_0[0].numpy().transpose(1, 2, 0))
    plt.subplot(1,2,2)
    plt.axis('off') 
    plt.imshow(X_0[1].numpy().transpose(1, 2, 0))
    plt.show()
    print(f"gt_pseudo_label in the first data example (a list of two ground truth pseudo-labels): {gt_pseudo_label_0}")
    print(f"Y in the first data example (their sum result): {Y_0}")


Out:
    .. code:: none
        :class: code-out

        X in the first data example (a list of two images):
    
    .. image:: ../img/mnist_add_datasets.png
        :width: 400px


    .. parsed-literal::

        gt_pseudo_label in the first data example (a list of two ground truth pseudo-labels): [7, 5]
        Y in the first data example (their sum result): 12
    

Building the Learning Part
--------------------------

To build the learning part, we need to first build a machine learning
base model. We use a simple `LeNet-5 neural
network <https://en.wikipedia.org/wiki/LeNet>`__, and encapsulate it
within a ``BasicNN`` object to create the base model. ``BasicNN`` is a
class that encapsulates a PyTorch model, transforming it into a base
model with an sklearn-style interface.

.. code:: ipython3

    cls = LeNet5(num_classes=10)
    loss_fn = nn.CrossEntropyLoss()
    optimizer = torch.optim.RMSprop(cls.parameters(), lr=0.001, alpha=0.9)
    device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
    
    base_model = BasicNN(
        cls,
        loss_fn,
        optimizer,
        device,
        batch_size=32,
        num_epochs=1,
    )

``BasicNN`` offers methods like ``predict`` and ``predict_prob``, which
are used to predict the class index and the probabilities of each class
for images. As shown below:

.. code:: ipython3

    data_instances = [torch.randn(1, 28, 28).to(device) for _ in range(32)]
    pred_idx = base_model.predict(X=data_instances)
    print(f"Predicted class index for a batch of 32 instances: np.ndarray with shape {pred_idx.shape}")
    pred_prob = base_model.predict_proba(X=data_instances)
    print(f"Predicted class probabilities for a batch of 32 instances: np.ndarray with shape {pred_prob.shape}")


Out:
    .. code:: none
        :class: code-out

        Predicted class index for a batch of 32 instances: np.ndarray with shape (32,)
        Predicted class probabilities for a batch of 32 instances: np.ndarray with shape (32, 10)
    

However, the base model built above deals with instance-level data
(i.e., individual images), and can not directly deal with example-level
data (i.e., a pair of images). Therefore, we wrap the base model into
``ABLModel``, which enables the learning part to train, test, and
predict on example-level data.

.. code:: ipython3

    model = ABLModel(base_model)

As an illustration, consider this example of training on example-level
data using the ``predict`` method in ``ABLModel``. In this process, the
method accepts data examples as input and outputs the class labels and
the probabilities of each class for all instances within these data
examples.

.. code:: ipython3

    from abl.structures import ListData
    # ListData is a data structure provided by ABL-Package that can be used to organize data examples
    data_examples = ListData()
    # We use the first 100 data examples in the training set as an illustration
    data_examples.X = train_X[:100]
    data_examples.gt_pseudo_label = train_gt_pseudo_label[:100]
    data_examples.Y = train_Y[:100]

    # Perform prediction on the 100 data examples
    pred_label, pred_prob = model.predict(data_examples)['label'], model.predict(data_examples)['prob']
    print(f"Predicted class labels for the 100 data examples: \n" +
          f"a list of length {len(pred_label)}, and each element is " +
          f"a {type(pred_label[0]).__name__} of shape {pred_label[0].shape}.\n")
    print(f"Predicted class probabilities for the 100 data examples: \n" +
          f"a list of length {len(pred_prob)}, and each element is " +
          f"a {type(pred_prob[0]).__name__} of shape {pred_prob[0].shape}.")


Out:
    .. code:: none
        :class: code-out

        Predicted class labels for the 100 data examples: 
        a list of length 100, and each element is a ndarray of shape (2,).

        Predicted class probabilities for the 100 data examples: 
        a list of length 100, and each element is a ndarray of shape (2, 10).


Building the Reasoning Part
---------------------------

In the reasoning part, we first build a knowledge base which contain
information on how to perform addition operations. We build it by
creating a subclass of ``KBBase``. In the derived subclass, we
initialize the ``pseudo_label_list`` parameter specifying list of
possible pseudo-labels, and override the ``logic_forward`` function
defining how to perform (deductive) reasoning.

.. code:: ipython3

    class AddKB(KBBase):
        def __init__(self, pseudo_label_list=list(range(10))):
            super().__init__(pseudo_label_list)
    
        # Implement the deduction function
        def logic_forward(self, nums):
            return sum(nums)
    
    kb = AddKB()

The knowledge base can perform logical reasoning (both deductive
reasoning and abductive reasoning). Below is an example of performing
(deductive) reasoning, and users can refer to :ref:`Performing abductive 
reasoning in the knowledge base <kb-abd>` for details of abductive reasoning.

.. code:: ipython3

    pseudo_label_example = [1, 2]
    reasoning_result = kb.logic_forward(pseudo_label_example)
    print(f"Reasoning result of pseudo-label example {pseudo_label_example} is {reasoning_result}.")


Out:
    .. code:: none
        :class: code-out

        Reasoning result of pseudo-label example [1, 2] is 3.
    

.. note::

    In addition to building a knowledge base based on ``KBBase``, we
    can also establish a knowledge base with a ground KB using ``GroundKB``,
    or a knowledge base implemented based on Prolog files using
    ``PrologKB``. The corresponding code for these implementations can be
    found in the ``main.py`` file. Those interested are encouraged to
    examine it for further insights.

Then, we create a reasoner by instantiating the class ``Reasoner``. Due
to the indeterminism of abductive reasoning, there could be multiple
candidates compatible to the knowledge base. When this happens, reasoner
can minimize inconsistencies between the knowledge base and
pseudo-labels predicted by the learning part, and then return only one
candidate that has the highest consistency.

.. code:: ipython3

    reasoner = Reasoner(kb)

.. note::

    During creating reasoner, the definition of “consistency” can be
    customized within the ``dist_func`` parameter. In the code above, we
    employ a consistency measurement based on confidence, which calculates
    the consistency between the data example and candidates based on the
    confidence derived from the predicted probability. In ``examples/mnist_add/main.py``, we
    provide options for utilizing other forms of consistency measurement.

    Also, during process of inconsistency minimization, we can leverage
    `ZOOpt library <https://github.com/polixir/ZOOpt>`__ for acceleration.
    Options for this are also available in ``examples/mnist_add/main.py``. Those interested are
    encouraged to explore these features.

Building Evaluation Metrics
---------------------------

Next, we set up evaluation metrics. These metrics will be used to
evaluate the model performance during training and testing.
Specifically, we use ``SymbolMetric`` and ``ReasoningMetric``, which are
used to evaluate the accuracy of the machine learning model’s
predictions and the accuracy of the final reasoning results,
respectively.

.. code:: ipython3

    metric_list = [SymbolMetric(prefix="mnist_add"), ReasoningMetric(kb=kb, prefix="mnist_add")]

Bridge Learning and Reasoning
-----------------------------

Now, the last step is to bridge the learning and reasoning part. We
proceed this step by creating an instance of ``SimpleBridge``.

.. code:: ipython3

    bridge = SimpleBridge(model, reasoner, metric_list)

Perform training and testing by invoking the ``train`` and ``test``
methods of ``SimpleBridge``.

.. code:: ipython3

    # Build logger
    print_log("Abductive Learning on the MNIST Addition example.", logger="current")
    log_dir = ABLLogger.get_current_instance().log_dir
    weights_dir = osp.join(log_dir, "weights")
    
    bridge.train(train_data, loops=5, segment_size=1/3, save_interval=1, save_dir=weights_dir)
    bridge.test(test_data)

Out:
    .. code:: none
        :class: code-out

        abl - INFO - Abductive Learning on the MNIST Addition example.
        abl - INFO - loop(train) [1/5] segment(train) [1/3] 
        abl - INFO - model loss: 1.49104
        abl - INFO - loop(train) [1/5] segment(train) [2/3] 
        abl - INFO - model loss: 1.24945
        abl - INFO - loop(train) [1/5] segment(train) [3/3] 
        abl - INFO - model loss: 0.87861
        abl - INFO - Evaluation start: loop(val) [1]
        abl - INFO - Evaluation ended, mnist_add/character_accuracy: 0.818 mnist_add/reasoning_accuracy: 0.672 
        abl - INFO - Saving model: loop(save) [1]
        abl - INFO - Checkpoints will be saved to weights_dir/model_checkpoint_loop_1.pth
        abl - INFO - loop(train) [2/5] segment(train) [1/3] 
        abl - INFO - model loss: 0.31148
        abl - INFO - loop(train) [2/5] segment(train) [2/3] 
        abl - INFO - model loss: 0.09520
        abl - INFO - loop(train) [2/5] segment(train) [3/3] 
        abl - INFO - model loss: 0.07402
        abl - INFO - Evaluation start: loop(val) [2]
        abl - INFO - Evaluation ended, mnist_add/character_accuracy: 0.982 mnist_add/reasoning_accuracy: 0.964 
        abl - INFO - Saving model: loop(save) [2]
        abl - INFO - Checkpoints will be saved to weights_dir/model_checkpoint_loop_2.pth
        abl - INFO - loop(train) [3/5] segment(train) [1/3] 
        abl - INFO - model loss: 0.06027
        abl - INFO - loop(train) [3/5] segment(train) [2/3] 
        abl - INFO - model loss: 0.05341
        abl - INFO - loop(train) [3/5] segment(train) [3/3] 
        abl - INFO - model loss: 0.04915
        abl - INFO - Evaluation start: loop(val) [3]
        abl - INFO - Evaluation ended, mnist_add/character_accuracy: 0.987 mnist_add/reasoning_accuracy: 0.975 
        abl - INFO - Saving model: loop(save) [3]
        abl - INFO - Checkpoints will be saved to weights_dir/model_checkpoint_loop_3.pth
        abl - INFO - loop(train) [4/5] segment(train) [1/3] 
        abl - INFO - model loss: 0.04413
        abl - INFO - loop(train) [4/5] segment(train) [2/3] 
        abl - INFO - model loss: 0.04181
        abl - INFO - loop(train) [4/5] segment(train) [3/3] 
        abl - INFO - model loss: 0.04127
        abl - INFO - Evaluation start: loop(val) [4]
        abl - INFO - Evaluation ended, mnist_add/character_accuracy: 0.990 mnist_add/reasoning_accuracy: 0.980 
        abl - INFO - Saving model: loop(save) [4]
        abl - INFO - Checkpoints will be saved to weights_dir/model_checkpoint_loop_4.pth
        abl - INFO - loop(train) [5/5] segment(train) [1/3] 
        abl - INFO - model loss: 0.03544
        abl - INFO - loop(train) [5/5] segment(train) [2/3] 
        abl - INFO - model loss: 0.03092
        abl - INFO - loop(train) [5/5] segment(train) [3/3] 
        abl - INFO - model loss: 0.03663
        abl - INFO - Evaluation start: loop(val) [5]
        abl - INFO - Evaluation ended, mnist_add/character_accuracy: 0.991 mnist_add/reasoning_accuracy: 0.982 
        abl - INFO - Saving model: loop(save) [5]
        abl - INFO - Checkpoints will be saved to weights_dir/model_checkpoint_loop_5.pth
        abl - INFO - Evaluation ended, mnist_add/character_accuracy: 0.987 mnist_add/reasoning_accuracy: 0.974 

More concrete examples are available in ``examples/mnist_add/main.py`` and ``examples/mnist_add/mnist_add.ipynb``.