Brief Summary
We propose a novel and interpretable data augmentation method based on energy-based modeling and principles from information geometry. Unlike black-box generative models, which rely on deep neural networks, our approach replaces these non-interpretable transformations with explicit, theoretically grounded ones, ensuring interpretability and strong guarantees such as energy minimization. Central to our method is the introduction of the backward projection* algorithm, which reverses dimension reduction to generate new data. Empirical results demonstrate that our method achieves competitive performance with black-box generative models while offering greater transparency and interpretability.