Transversal Pooling Neural Networks

2026-09-28

AI Summary

This study addresses the inherent difficulty of existing learning methods in simultaneously achieving stability to small transformations and sensitivity to large ones. To this end, we propose transverse pooling neural networks, which generalize spatial max-pooling to affine group actions, thereby enforcing subgroup equivariance and deriving rigorous stability bounds. Furthermore, this work establishes the first explicit stability theory for wavelet coefficients under affine perturbations, overcoming the limitations of conventional pooling operations. By integrating wavelet analysis with equivariant architectures, the proposed approach significantly enhances model performance in low-data regimes. The exceptional utility of this method is empirically validated on the task of tropical cyclone intensity forecasting.

Abstract

Many learning tasks require stability to small transformations while retaining sensitivity to larger ones. We introduce \emph{transversal pooling neural networks}, which generalize spatial max pooling to affine group actions. We establish equivariance to a chosen subgroup and derive explicit stability bounds for individual pooled wavelet coefficients under affine perturbations of the input. Experimentally, we demonstrate the utility of our networks in low-data environments and for predicting tropical cyclone intensification.

Problem

• transversal pooling
• affine group actions
• stability
• equivariance
• low-data environments

Innovation

• Transversal Pooling Neural Networks
• Affine Group Actions
• Equivariance
• Stability Bounds
• Wavelet Coefficients