This paper introduces the concept of Spherical Convolutional Neural Networks (CNNs) for analyzing spherical signals, which are essential in applications such as omnidirectional vision, molecular regression, and global weather modeling. The authors address the challenge of applying traditional planar CNNs to spherical data, which introduces distortions due to the projection from the sphere to a plane. They propose a rotation-equivariant definition of spherical cross-correlation, which is both expressive and efficient. This definition satisfies a generalized Fourier theorem, allowing for efficient computation using a generalized Fast Fourier Transform (FFT) algorithm. The paper evaluates the effectiveness of spherical CNNs through experiments on 3D model recognition and atomization energy regression, demonstrating superior performance compared to planar CNNs in rotation-invariant tasks. The main contributions include the theoretical foundation of spherical CNNs, the first differentiable implementation of the generalized Fourier transform for spherical and rotation group signals, and empirical evidence of the utility of spherical CNNs in rotation-invariant learning problems.This paper introduces the concept of Spherical Convolutional Neural Networks (CNNs) for analyzing spherical signals, which are essential in applications such as omnidirectional vision, molecular regression, and global weather modeling. The authors address the challenge of applying traditional planar CNNs to spherical data, which introduces distortions due to the projection from the sphere to a plane. They propose a rotation-equivariant definition of spherical cross-correlation, which is both expressive and efficient. This definition satisfies a generalized Fourier theorem, allowing for efficient computation using a generalized Fast Fourier Transform (FFT) algorithm. The paper evaluates the effectiveness of spherical CNNs through experiments on 3D model recognition and atomization energy regression, demonstrating superior performance compared to planar CNNs in rotation-invariant tasks. The main contributions include the theoretical foundation of spherical CNNs, the first differentiable implementation of the generalized Fourier transform for spherical and rotation group signals, and empirical evidence of the utility of spherical CNNs in rotation-invariant learning problems.