Transforming Neural Networks on Manifold and Renormalization

This paper presents an enhanced Fully Connected Neural Network (FCNN) framework that incorporates manifold learning and Renormalization Group (RG) methods. By integrating Christoffel symbols, the model adapts to the curvature and topology of the data manifold, improving learning from geometrically complex data. Additionally, RG methods enable effective multi-scale data processing. We demonstrate the enhanced model’s performance on synthetic and real-world datasets, showing improved accuracy compared to standard FCNNs, particularly in complex systems simulation.