MNIST Addition ============== Below shows an implementation of `MNIST Addition `__. 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.data.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 `__, 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.data.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 ` 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 `__ 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``.