Matrix neural networks

![CDATA[Traditional neural networks assume vectorial inputs as the network is arranged as layers of single line of computing units called neurons. This special structure requires the non-vectorial inputs such as matrices to be converted into vectors. This process can be problematic for loss of spatial information and huge solution space. To address these issues, we propose matrix neural networks (MatNet), which takes matrices directly as inputs. Each layer summarises and passes information through bilinear mapping. Under this structure, back prorogation and gradient descent combination can be utilised to obtain network parameters efficiently. Furthermore, it can be conveniently extended for multi-modal inputs. We apply MatNet to MNIST handwritten digits classification and image super resolution tasks to show its effectiveness. Without too much tweaking MatNet achieves comparable performance as the state-of-the-art methods in both tasks with considerably reduced complexity.]]