In this paper, we study the learned iterative shrinkage thresholding algorithm (LISTA) for solving sparse coding problems.   Following assumptions made by prior works, we first discover that the code components in its estimations may be lower than expected, i.e., require gains, and to address this problem, a gated mechanism amenable to theoretical analysis is then introduced. Specific design of the gates is inspired by convergence analyses of the mechanism and hence its effectiveness can be formally guaranteed. In addition to the gain gates, we further introduce overshoot gates for compensating insufficient step size in LISTA. Extensive empirical results confirm our theoretical findings and verify the effectiveness of our method.
We propose gated mechanisms to enhance learned ISTA for sparse coding, with theoretical guarantees on the superiority of the method.  Proposes extensions to LISTA which address underestimation by introducing "gain gates" and including momentum with "overshoot gates", showing improved convergence rates. This paper is focused on solving sparse coding problems using LISTA-type networks by proposing a "gain gating function" to mitigate the weakness of the "no false positive" assumption.