• Abductive Learning (ABL) Package
• • Installation
  • Examples
  • Quick Start
  • • Working with Data
    • Building the Learning Part
    • Building the Reasoning Part
    • Building Evaluation Metrics
    • Bridging Learning and Reasoning
  • References

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Abductive Learning (ABL) Package

ABL-Package is an open source library for Abductive Learning (ABL).
ABL is a novel paradigm that integrates machine learning and
logical reasoning in a unified framework. It is suitable for tasks
where both data and (logical) domain knowledge are available.

Key Features of ABL-Package:

• Great Flexibility: Adaptable to various machine learning modules and logical reasoning components.
• User-Friendly: Provide data, model, and KB, and get started with just a few lines of code.
• High-Performance: Optimization for high accuracy and fast training speed.

ABL-Package encapsulates advanced ABL techniques, providing users with
an efficient and convenient package to develop dual-driven ABL systems,
which leverage the power of both data and knowledge.

To learn how to use it, please refer to - document.

Installation

The easiest way to install ABL-Package is using pip:

# (TODO)
$ pip install abl

For testing purposes, you can install it using:

$ pip install -i https://test.pypi.org/simple/ --extra-index-url https://mirrors.nju.edu.cn/pypi/web/simple/ abl

Alternatively, to install by source code, sequentially run following commands in your terminal/command line.

$ git clone https://github.com/AbductiveLearning/ABL-Package.git
$ cd ABL-Package
$ pip install -v -e .

(Optional) If the use of a Prolog-based knowledge base is necessary, the installation of Swi-Prolog is also required:

For Linux users:

$ sudo apt-get install swi-prolog

For Windows and Mac users, please refer to the Swi-Prolog Install Guide.

Examples

We provide several examples in examples/. Each example is stored in a separate folder containing a README file.

• MNIST Addition
• Handwritten Formula
• Handwritten Equation Decipherment
• Zoo

Quick Start

We use the MNIST Addition task as a quick start example. In this task, pairs of MNIST handwritten images and their sums are given, alongwith a domain knowledge base which contains information on how to perform addition operations. Our objective is to input a pair of handwritten images and accurately determine their sum.

Working with Data

ABL-Package requires data in the format of (X, gt_pseudo_label, Y) where X is a list of input examples containing instances, gt_pseudo_label is the ground-truth label of each example in X and Y is the ground-truth reasoning result of each example in X. Note that gt_pseudo_label is only used to evaluate the machine learning model's performance but not to train it.

In the MNIST Addition task, the data loading looks like:

# The 'datasets' module below is located in 'examples/mnist_add/'
from datasets import get_dataset
    
# train_data and test_data are tuples in the format of (X, gt_pseudo_label, Y)
train_data = get_dataset(train=True)
test_data = get_dataset(train=False)

Building the Learning Part

Learning part is constructed by first defining a base model for machine learning. The ABL-Package offers considerable flexibility, supporting any base model that conforms to the scikit-learn style (which requires the implementation of fit and predict methods), or a PyTorch-based neural network (which has defined the architecture and implemented forward method). In this example, we build a simple LeNet5 network as the base model.

# The 'models' module below is located in 'examples/mnist_add/'
from models.nn import LeNet5

cls = LeNet5(num_classes=10)

To facilitate uniform processing, ABL-Package provides the BasicNN class to convert a PyTorch-based neural network into a format compatible with scikit-learn models. To construct a BasicNN instance, aside from the network itself, we also need to define a loss function, an optimizer, and the computing device.

​import torch
​from abl.learning import BasicNN
​    
​loss_fn = torch.nn.CrossEntropyLoss()
​optimizer = torch.optim.RMSprop(cls.parameters(), lr=0.001, alpha=0.9)
​device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
​base_model = BasicNN(model=cls, loss_fn=loss_fn, optimizer=optimizer, device=device)

The base model built above is trained to make predictions on instance-level data (e.g., a single image), while ABL deals with example-level data. To bridge this gap, we wrap the base_model into an instance of ABLModel. This class serves as a unified wrapper for base models, facilitating the learning part to train, test, and predict on example-level data, (e.g., images that comprise an equation).

from abl.learning import ABLModel
​    
​model = ABLModel(base_model)

Building the Reasoning Part

To build the reasoning part, we first define a knowledge base by creating a subclass of KBBase. In the subclass, we initialize the pseudo_label_list parameter and override the logic_forward method, which specifies how to perform (deductive) reasoning that processes pseudo-labels of an example to the corresponding reasoning result. Specifically, for the MNIST Addition task, this logic_forward method is tailored to execute the sum operation.

from abl.reasoning import KBBase
​    
class AddKB(KBBase):
    def __init__(self, pseudo_label_list=list(range(10))):
        super().__init__(pseudo_label_list)

​    def logic_forward(self, nums):
        return sum(nums)
​    
kb = AddKB()

Next, we create a reasoner by instantiating the class Reasoner, passing the knowledge base as a parameter. Due to the indeterminism of abductive reasoning, there could be multiple candidate pseudo-labels compatible to the knowledge base. In such scenarios, the reasoner can minimize inconsistency and return the pseudo-label with the highest consistency.

from abl.reasoning import Reasoner
​    
reasoner = Reasoner(kb)

Building Evaluation Metrics

ABL-Package provides two basic metrics, namely SymbolAccuracy and ReasoningMetric, which are used to evaluate the accuracy of the machine learning model's predictions and the accuracy of the logic_forward results, respectively.

from abl.data.evaluation import ReasoningMetric, SymbolAccuracy
​    
metric_list = [SymbolAccuracy(), ReasoningMetric(kb=kb)]

Bridging Learning and Reasoning

Now, we use SimpleBridge to combine learning and reasoning in a
unified ABL framework.

from abl.bridge import SimpleBridge
​    
bridge = SimpleBridge(model, reasoner, metric_list)

Finally, we proceed with training and testing.

​bridge.train(train_data, loops=1, segment_size=0.01)
bridge.test(test_data)

References

For more information about ABL, please refer to: Zhou, 2019 and Zhou and Huang, 2022.

@article{zhou2019abductive,
  title     = {Abductive learning: towards bridging machine learning and logical reasoning},
  author    = {Zhou, Zhi-Hua},
  journal   = {Science China Information Sciences},
  volume    = {62},
  number    = {7},
  pages     = {76101},
  year      = {2019}
}

@incollection{zhou2022abductive,
  title     = {Abductive Learning},
  author    = {Zhou, Zhi-Hua and Huang, Yu-Xuan},
  booktitle = {Neuro-Symbolic Artificial Intelligence: The State of the Art},
  editor    = {Pascal Hitzler and Md. Kamruzzaman Sarker},
  publisher = {{IOS} Press},
  pages     = {353--369},
  address   = {Amsterdam},
  year      = {2022}
}