Linear Distillation Learning

Deep Linear Networks do not have expressive power but they are mathematically tractable. In our work, we found an architecture in which they are expressive. This paper presents a Linear Distillation Learning (LDL) a simple remedy to improve the performance of linear networks through distillation. In deep learning models, distillation often allows the smaller/shallow network to mimic the larger models in a much more accurate way, while a network of the same size trained on the one-hot targets can't achieve comparable results to the cumbersome model. In our method, we train students to distill teacher separately for each class in dataset. The most striking result to emerge from the data is that neural networks without activation functions can achieve high classification score on a small amount of data on MNIST and Omniglot datasets. Due to tractability, linear networks can be used to explain some phenomena observed experimentally in deep non-linear networks. The suggested approach could become a simple and practical instrument while further studies in the field of linear networks and distillation are yet to be undertaken.