Lie Group Equivariant Convolutional Neural Network Based on Laplace Distribution

Traditional convolutional neural networks (CNNs) lack equivariance for transformations such as rotation and scaling. Consequently, they typically exhibit weak robustness when an input image undergoes generic transformations. Moreover, the complex model structure complicates the interpretation of learned low- and mid-level features. To address these issues, we introduce a Lie group equivariant convolutional neural network predicated on the Laplace distribution. This model's Lie group characteristics blend multiple mid- and low-level features in image representation, unveiling the Lie group geometry and spatial structure of the Laplace distribution function space. It efficiently computes and resists noise while capturing pertinent information between image regions and features. Additionally, it refines and formulates an equivariant convolutional network appropriate for the Lie group feature map, maximizing the utilization of the equivariant feature at each level and boosting data efficiency. Experimental validation of our methodology using three remote sensing datasets confirms its feasibility and superiority. By ensuring a high accuracy rate, it enhances data utility and interpretability, proving to be an innovative and effective approach.