Matrix-centric Neural Networks

We present a new distributed representation in deep neural nets wherein the information is represented in native form as a matrix. This differs from current neural architectures that rely on vector representations. We consider matrices as central to the architecture and they compose the input, hidden and output layers. The model representation is more compact and elegant - the number of parameters grows only with the largest dimension of the incoming layer rather than the number of hidden units. We derive feed-forward nets that map an input matrix into an output matrix, and recurrent nets which map a sequence of input matrices into a sequence of output matrices. Experiments on handwritten digits recognition, face reconstruction, sequence to sequence learning and EEG classification demonstrate the efficacy and compactness of the matrix-centric architectures.