Prerequisites

Hardware requirement: The example works on my ultrabook (LG Gram Style 2023 with i7-1360P) under Arch Linux, so theoretically, the codes provided work on any system without requirement of dedicated GPUs (i.e., an Nvidia or AMD GPU).

System requirement: I have only tested under Linux, but with Python 3's virtual environment, it should work on any system, including Mac and Windows by using Anaconda. However, if you are using Windows and unwilling to install Linux or running Linux on virtual machines (such as VMware), I'd recommend you to use Windows Subsystems for Linux, such as the Ubuntu WSL, which is much more convenient than Windows' Anaconda-like environments.

Preparing the Environment

1. Install SWI-Prolog (tested with version 9.1.11-5-gddaf93732), make sure swipl works in your command line shell (命令行解释器，例如 Linux/Mac 下的 terminal 或者 Windows 下的命令行提示符/Windows 终端/Powershell 等等).

2. Install Python (tested with version 3.11.3) and Jupyter Notebook. However, I strongly recommend you to use VS Code.

3. Use your command line shell to initialize your virtual environment and activate it temporarily.

   # Initialize a virtual environment
   python -m venv .venv
   
   # Activate the virtual environment
   source .venv/bin/activate

4. Install Pytorch CPU version by

   pip3 install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cpu

5. Use venv to install other dependencies:

   # Activate the virtual environment
   source .venv/bin/activate
   
   # Install dependencies
   pip3 install -r requirements.txt

6. The PySwip package in PyPI sometimes are out-dated, you may want to install the master branch from its github repo:

   pip install git+https://github.com/yuce/pyswip@master#egg=pyswip

About the Codes

1. data_generator.ipynb explains about the task and how was the MNIST Sum dataset generated.
2. mnist_sum.pl is the prolog file to abduce two digits given the sum. Try it with Prolog: consult('mnist_sum.pl'). and then abduce([X,Y],13). (Don't forget the period symbol "." and type ";" to see more answers).
3. mnist_sum.ipynb is a self-explained notebook for the simple MNIST Sum task.

Task

1. Try to train a pure neural network to learn the MNIST Sum task.
2. Compare your method with the Abductive Learning algorithm, in two aspects:
   1. Mean squared error of the final output, i.e., the sum;
   2. Digit-wise classification accuracy (like what has been done in the notebook).
3. (Optional) Try some advanced tasks and background knowledge by yourself, an example is given in mnist_sum_2. Maybe you can try MNIST product and so on.

Hint: You can try different types of neural networks, even different combinations of neural networks, for example:

1. CNN encoder for perception, MLP to calculate the sum;
2. CNN encoder for perception, LSTM or other types of RNNs, even Transformers to calculate the sum;

Task (simple version)

For students who are not very good at coding, you could try these things:

1. Write a program to generate a big (>10000) dataset of [x1,x2,y], where x1 and x2 are in [0, 1000] and x1+x2=y;
2. Use an MLP to learn from this dataset, in which [x1,x2] is the input and y is the target output.
3. Generate another dataset like step 1, but with x1 and x2 in [50000, 100000].
4. Test your MLP learned from step 2 with the new dataset.