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

.. raw:: html
    
    <p>For detailed code implementation, please view it on <a class="reference external" href="https://github.com/AbductiveLearning/ABLkit/tree/main/examples/mnist_add" target="_blank">GitHub</a>.</p>

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:: python

    # Import necessary libraries and modules
    import os.path as osp

    import matplotlib.pyplot as plt
    import torch
    import torch.nn as nn
    from torch.optim import RMSprop, lr_scheduler

    from ablkit.bridge import SimpleBridge
    from ablkit.data.evaluation import ReasoningMetric, SymbolAccuracy
    from ablkit.learning import ABLModel, BasicNN
    from ablkit.reasoning import KBBase, Reasoner
    from ablkit.utils import ABLLogger, print_log

    from datasets import get_dataset
    from models.nn import LeNet5

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

First, we get the training and testing datasets:

.. code:: python

    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:: python

    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 an {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 an 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:: python

    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].squeeze(), cmap='gray')
    plt.subplot(1,2,2)
    plt.axis('off') 
    plt.imshow(X_0[1].squeeze(), cmap='gray')
    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:: ../_static/img/mnist_add_datasets.png
        :width: 200px


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

        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 a sklearn-style interface.

.. code:: python

    cls = LeNet5(num_classes=10)
    loss_fn = nn.CrossEntropyLoss(label_smoothing=0.1)
    optimizer = RMSprop(cls.parameters(), lr=0.001, alpha=0.9)
    device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
    scheduler = lr_scheduler.OneCycleLR(optimizer, max_lr=0.001, pct_start=0.1, total_steps=100)

    base_model = BasicNN(
        cls,
        loss_fn,
        optimizer,
        scheduler=scheduler,
        device=device,
        batch_size=32,
        num_epochs=1,
    )

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

.. code:: python

    data_instances = [torch.randn(1, 28, 28) 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:: python

    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:: python

    from ablkit.data.structures import ListData
    # ListData is a data structure provided by ABLkit 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 contains
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:: python

    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:: python

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


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

        Reasoning result of pseudo-labels [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 with 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:: python

    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 the 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 ``SymbolAccuracy`` 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:: python

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

Bridging Learning and Reasoning
-------------------------------

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

.. code:: python

    bridge = SimpleBridge(model, reasoner, metric_list)

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

.. code:: python

    # 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=1, segment_size=0.01, save_interval=1, save_dir=weights_dir)
    bridge.test(test_data)

The log will appear similar to the following:

Log:
    .. code:: none
        :class: code-out

        abl - INFO - Abductive Learning on the MNIST Addition example.
        abl - INFO - Working with Data.
        abl - INFO - Building the Learning Part.
        abl - INFO - Building the Reasoning Part.
        abl - INFO - Building Evaluation Metrics.
        abl - INFO - Bridge Learning and Reasoning.
        abl - INFO - loop(train) [1/2] segment(train) [1/100] 
        abl - INFO - model loss: 2.25980
        abl - INFO - loop(train) [1/2] segment(train) [2/100] 
        abl - INFO - model loss: 2.14168
        abl - INFO - loop(train) [1/2] segment(train) [3/100] 
        abl - INFO - model loss: 2.02010
        ...
        abl - INFO - loop(train) [2/2] segment(train) [1/100] 
        abl - INFO - model loss: 0.90260
        ...
        abl - INFO - Eval start: loop(val) [2]
        abl - INFO - Evaluation ended, mnist_add/character_accuracy: 0.993 mnist_add/reasoning_accuracy: 0.986 
        abl - INFO - Test start:
        abl - INFO - Evaluation ended, mnist_add/character_accuracy: 0.991 mnist_add/reasoning_accuracy: 0.980 


Environment
-----------

For all experiments, we used a single linux server. Details on the specifications are listed in the table below.

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    .tg tr:nth-child(odd) {background-color:#ffffff;}
    </style>

    <table class="tg" style="margin-left: auto; margin-right: auto;">
    <thead>
    <tr>
        <th>CPU</th>
        <th>GPU</th>
        <th>Memory</th>
        <th>OS</th>
    </tr>
    </thead>
    <tbody>
    <tr>
        <td>2 * Xeon Platinum 8358, 32 Cores, 2.6 GHz Base Frequency</td>
        <td>A100 80GB</td>
        <td>512GB</td>
        <td>Ubuntu 20.04</td>
    </tr>
    </tbody>
    </table>


Performance
-----------

We present the results of ABL as follows, which include the reasoning accuracy (the proportion of equations that are correctly summed), and the training time used to achieve this accuracy. These results are compared with the following methods:

- `NeurASP <https://github.com/azreasoners/NeurASP>`_: An extension of answer set programs by treating the neural network output as the probability distribution over atomic facts;
- `DeepProbLog <https://github.com/ML-KULeuven/deepproblog>`_: An extension of ProbLog by introducing neural predicates in Probabilistic Logic Programming;
- `LTN <https://github.com/logictensornetworks/logictensornetworks>`_: A neural-symbolic framework that uses differentiable first-order logic language to incorporate data and logic;
- `DeepStochLog <https://github.com/ML-KULeuven/deepstochlog>`_: A neural-symbolic framework based on stochastic logic program.

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    .tg td, .tg th {border:1px solid #ddd;padding:8px 22px;text-align:center;}
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    <table class="tg" style="margin-left: auto; margin-right: auto;">
    <thead>
    <tr>
        <th>Method</th>
        <th>Accuracy</th>
        <th>Time to achieve the Acc. (s)</th>
        <th>Average Memory Usage (MB)</th>
    </tr>
    </thead>
    <tbody>
    <tr>
        <td>NeurASP</td>
        <td>96.2</td>
        <td>966</td>
        <td>3552</td>
    </tr>
    <tr>
        <td>DeepProbLog</td>
        <td>97.1</td>
        <td>2045</td>
        <td>3521</td>
    </tr>
    <tr>
        <td>LTN</td>
        <td>97.4</td>
        <td>251</td>
        <td>3860</td>
    </tr>
    <tr>
        <td>DeepStochLog</td>
        <td>97.5</td>
        <td>257</td>
        <td>3545</td>
    </tr>
    <tr>
        <td>ABL</td>
        <td><span style="font-weight:bold">98.1</span></td>
        <td><span style="font-weight:bold">47</span></td>
        <td><span style="font-weight:bold">2482</span></td>
    </tr>
    </tbody>
    </table>