The brain has to solve inverse problems to correctly interpret sensory data and infer the set of causes that generated the sensory inputs. When imposing sparse prior and hierarchical structure this problem is called Hierarchical Sparse Coding (HSC). Predictive Coding (PC) is a computational neuroscience framework suggesting that each layer predicts the activity of the lower layer via feedback connections. The error between predicted and actual response is then sent back to the next higher level via feed-forward connections to correct the estimation of the representation. While computer scientists often solved HSC using a stacking of Lasso sub-problems that we will call Hierarchical Lasso (Hi-La), we propose to leverage PC into a hierarchical and sparse model called Sparse Deep Predictive Coding (SDPC) network. This poster shows computational differences between SDPC and Hi-La.