Mid Sweden University

Convolutional Neural Networks (CNNs) have been instrumental in the recent advances in machine learning, with applications to media applications. Multi-Layered Convolutional Sparse Coding (ML-CSC) based on a cascade of convolutional layers in which each layer can be approximately explained by the following layer can be seen as a biologically inspired framework. However, both CNNs and ML-CSC networks lack top-down information flows that are studied in neuroscience for understanding the mechanisms of the mammal cortex. A successful implementation of such top-down connections could lead to another leap in machine learning and media applications.%This study analyses the effects of a feedback connection on an ML-CSC network, considering trade-off between sparsity and reconstruction error, support recovery rate, and mutual coherence in trained dictionaries. We find that using the feedback connection during training impacts the mutual coherence of the dictionary in a way that the equivalence between the $l_0$- and $l_1$-norm is verified for a smaller range of sparsity values. Experimental results show that the use of feedback during training does not favour inference with feedback, in terms of sparse support recovery rates. However, when the sparsity constraints are given a lower weight, the use of feedback at inference time is beneficial, in terms of support recovery rates.