  Learned Iterative Shrinkage-Thresholding Algorithm (LISTA) introduces the
concept of unrolling an iterative algorithm and training it like a neural
network. It has had great success on sparse recovery. In this paper, we show
that adding momentum to intermediate variables in the LISTA network achieves a
better convergence rate and, in particular, the network with instance-optimal
parameters is superlinearly convergent. Moreover, our new theoretical results
lead to a practical approach of automatically and adaptively calculating the
parameters of a LISTA network layer based on its previous layers. Perhaps most
surprisingly, such an adaptive-parameter procedure reduces the training of
LISTA to tuning only three hyperparameters from data: a new record set in the
context of the recent advances on trimming down LISTA complexity. We call this
new ultra-light weight network HyperLISTA. Compared to state-of-the-art LISTA
models, HyperLISTA achieves almost the same performance on seen data
distributions and performs better when tested on unseen distributions
(specifically, those with different sparsity levels and nonzero magnitudes).
Code is available: https://github.com/VITA-Group/HyperLISTA.
