Optimization of group equivariant convolutional networks
The explosion of popularity of deep learning owes a lot to the success of convolutional neural networks, widely used in diverse fields including computer vision and natural language processing. Recently, the group equivariant convolutional neural network (G-CNN) was introduced, where equivariance of symmetries inherent in the data set is built in the architecture of the networks. While the G-CNNs has proven to exploit inherent symmetries more effectively than traditional CNNs, their architectural design and implementation require a deeper understanding of the mathematical concept of symmetries. We propose to develop better mathematical tools suitable for deep learning on G-CNNs, with two main goals: (1) improving the optimization methods of G-CNNs by exploiting the geometry underlying the inherent symmetry of the data set; (2) generalizing the architecture of G-CNNs to adapt to other practical learning problems, such as speech recognition and image processing.