CONSTRUCTING CONVOLUTIONAL NEURAL NETWORKS WITH 90 DEGREE ROTATIONAL EQUIVARIANCE AND INVARIANCE


It’s a well-known fact that the convolutional layer has the property of translational equivariance. However, it’s non-obvious how to expand the symmetry group associated with the said layer. Employing key definitions adopted in deep geometric learning, we construct the set of filters that induce 90-degree rotational equivariance without modifying the convolutional operator. This work is primarily intended as a theoretical exercise, beginning with a predefined symmetric group in mind and producing a convolutional layer with the desired equivariance.