  Can deep neural networks learn to solve any task, and in particular problems
of high complexity? This question attracts a lot of interest, with recent works
tackling computationally hard tasks such as the traveling salesman problem and
satisfiability. In this work we offer a different perspective on this question.
Given the common assumption that $\textit{NP} \neq \textit{coNP}$ we prove that
any polynomial-time sample generator for an $\textit{NP}$-hard problem samples,
in fact, from an easier sub-problem. We empirically explore a case study,
Conjunctive Query Containment, and show how common data generation techniques
generate biased datasets that lead practitioners to over-estimate model
accuracy. Our results suggest that machine learning approaches that require
training on a dense uniform sampling from the target distribution cannot be
used to solve computationally hard problems, the reason being the difficulty of
generating sufficiently large and unbiased training sets.
