🧠 Logic Diffusion v0

Logic Diffusion is a neuro-symbolic generative architecture designed to address bias in deep learning distributions.

Unlike standard diffusion models that blindly approximate the training data distribution $p(x)$ (inheriting all its biases), Logic Diffusion learns a conditional distribution $p(x | L)$ subject to a set of differentiable logical constraints $L$. This effectively "steers" the generative process toward a fair manifold, even when trained on biased data.

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📂 Project Structure

logic-diffusion-v0/
│
├── logic_diffusion/        # The Core Framework
│   ├── __init__.py         # Package initialization
│   ├── config.py           # Hyperparameters & Configuration
│   ├── logic.py            # Differentiable Logic (T-Norms) & Constraints
│   ├── modeling.py         # Lightweight U-Net Architecture
│   └── pipeline.py         # Logic-Guided Diffusion Sampling Loop
│
├── train.py                # Main training script (Joint Optimization)
├── app.py                  # Interactive Gradio Web Demo
├── requirements.txt        # Project Dependencies
└── README.md               # Documentation

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🚀 Getting Started

1. Installation

Clone the repository and install the dependencies.

git clone [https://github.com/your-username/logic-diffusion-v0.git](https://github.com/your-username/logic-diffusion-v0.git)
cd logic-diffusion-v0
pip install -r requirements.txt

2. Training the Model

Run the training script to initialize the U-Net and train it on synthetic data. The script uses a joint loss function: $$ \mathcal{L}{total} = \mathcal{L}{MSE} + \lambda \cdot \mathcal{L}_{Logic} $$

python train.py

• Output: The script will print loss metrics to the console and save the trained model weights to logic_diffusion_v0.pt.

3. Interactive Demo (Web UI)

Launch the Gradio interface to generate samples and tweak the "Logic Strictness" parameter in real-time.

python app.py

• Click the local URL (e.g., http://127.0.0.1:7860) to open the app in your browser.

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🧠 How It Works

The Core Innovation: Differentiable Logic

Standard Boolean logic (True/False) has no gradients, making it unusable for deep learning training. Logic Diffusion uses Fuzzy Logic (T-Norms) to relax these rules into continuous functions.

• AND Operator: (Product T-Norm)
• IMPLIES Operator: (Reichenbach Implication)

The Constraint

In logic.py, we define constraints that calculate a "Truth Value" (0 to 1) for a generated batch. The model minimizes the violation of this truth value:

# Pseudo-code example
violation = 1.0 - truth_value(generated_image)
loss.backward()  # Gradients update the image pixels to be "truer"

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🗺 Roadmap

• v0: Core implementation of Differentiable Logic and Simple U-Net.
• v0.1: Integration with Latent Diffusion (Stable Diffusion).
• v0.2: API for defining First-Order Logic rules via natural language.

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🤝 Contributing

Contributions are welcome! We are looking for help with:

1. Implementing new T-Norms (Godel, Lukasiewicz).
2. Optimizing the logical gradient calculation.
3. Adding support for RGB datasets (CIFAR-10, CelebA).

📜 License

This project is licensed under the MIT License - see the LICENSE file for details.