  Hardness magnification reduces major complexity separations (such as
$\mathsf{\mathsf{EXP}} \nsubseteq \mathsf{NC}^1$) to proving lower bounds for
some natural problem $Q$ against weak circuit models. Several recent works
[OS18, MMW19, CT19, OPS19, CMMW19, Oli19, CJW19a] have established results of
this form. In the most intriguing cases, the required lower bound is known for
problems that appear to be significantly easier than $Q$, while $Q$ itself is
susceptible to lower bounds but these are not yet sufficient for magnification.
  In this work, we provide more examples of this phenomenon, and investigate
the prospects of proving new lower bounds using this approach. In particular,
we consider the following essential questions associated with the hardness
magnification program:
  Does hardness magnification avoid the natural proofs barrier of Razborov and
Rudich [RR97]?
  Can we adapt known lower bound techniques to establish the desired lower
bound for $Q$?
