Rank Ordered Autoencoders

A new method for the unsupervised learning of sparse representations using autoencoders is proposed and implemented by ordering the output of the hidden units by their activation value and progressively reconstructing the input in this order. This can be done efficiently in parallel with the use of cumulative sums and sorting only slightly increasing the computational costs. Minimizing the difference of this progressive reconstruction with respect to the input can be seen as minimizing the number of active output units required for the reconstruction of the input. The model thus learns to reconstruct optimally using the least number of active output units. This leads to high sparsity without the need for extra hyperparameters, the amount of sparsity is instead implicitly learned by minimizing this progressive reconstruction error. Results of the trained model are given for patches of the CIFAR10 dataset, showing rapid convergence of features and extremely sparse output activations while maintaining a minimal reconstruction error and showing extreme robustness to overfitting. Additionally the reconstruction as function of number of active units is presented which shows the autoencoder learns a rank order code over the input where the highest ranked units correspond to the highest decrease in reconstruction error.