  We study solutions to Einstein-Maxwell-dilaton gravity with a constant
magnetic flux which describe, in the holographic AdS/CFT framework, field
theories characterized by a dynamical critical exponent and a hyperscaling
violation exponent. Such solutions are known to be IR-incomplete due to the
presence of a running dilaton, which drives the theory towards strong coupling
in the IR, where quantum corrections become important. After introducing
generic corrections, in this note we examine the conditions for the emergence
of an AdS_2 x R^2 region close to the horizon, which provides an IR-completion
for the hyperscaling violating solutions. In the presence of these corrections,
we construct explicit numerical solutions where the geometry flows from AdS_4
in the UV to AdS_2 x R^2 in the deep IR, with an intermediate region which
exhbits both hyperscaling violation and Lifshitz scaling.We also provide
constraints on the structure of Einstein-Maxwell-dilaton theories that admit
such solutions, as well as an emergent AdS_2 x R^2 region in the infrared.
