  Modern solutions to the single image super-resolution (SISR) problem using
deep neural networks aim not only at better performance accuracy but also at a
lighter and computationally efficient model. To that end, recently, neural
architecture search (NAS) approaches have shown some tremendous potential.
Following the same underlying, in this paper, we suggest a novel trilevel NAS
method that provides a better balance between different efficiency metrics and
performance to solve SISR. Unlike available NAS, our search is more complete,
and therefore it leads to an efficient, optimized, and compressed architecture.
We innovatively introduce a trilevel search space modeling, i.e., hierarchical
modeling on network-, cell-, and kernel-level structures. To make the search on
trilevel spaces differentiable and efficient, we exploit a new sparsestmax
technique that is excellent at generating sparse distributions of individual
neural architecture candidates so that they can be better disentangled for the
final selection from the enlarged search space. We further introduce the
sorting technique to the sparsestmax relaxation for better network-level
compression. The proposed NAS optimization additionally facilitates
simultaneous search and training in a single phase, reducing search time and
train time. Comprehensive evaluations on the benchmark datasets show our
method's clear superiority over the state-of-the-art NAS in terms of a good
trade-off between model size, performance, and efficiency.
