Type-II Neural Symmetry Detection with Lie Theory

Understanding symmetries within data is crucial for explainability and enhancing model efficiency in artificial intelligence. This work investigates an approach to neural symmetry detection, specifically leveraging the mathematical framework of Lie theory. Our approach projects data into a low-dimensional latent space, where symmetry transformations can be efficiently applied. By leveraging the matrix exponential, we accurately capture both affine and non-affine transformations, allowing for improved data augmentation and model selection as potential applications. Our method also estimates transformation magnitude distributions, providing deeper insights into the geometric structure of data. Experiments conducted on augmented MNIST demonstrate the effectiveness of our approach in detecting complex symmetries with multiple transformations. This work paves the way for more interpretable and parameter efficient AI models by identifying structural priors that align with the inherent symmetries in data.