Learning threshold functions of sparse polynomials using only queries

Establish whether threshold functions of sparse polynomials over {0,1}^n, specifically f(x) = sign(∑_{i=1}^d a_i χ_{S_i}(x) + a) with at most d nonzero terms, can be efficiently learned using only query access to f, with polynomial-time and polynomial-query complexity.

Background

The authors connect conditional-sampling-only learning of low logit rank models to classical query learning of Boolean functions. They argue that a positive resolution to learning low logit rank models from conditional samples would imply efficient query-learning of threshold functions of sparse polynomials.

They note that this implication targets a longstanding challenge in learning theory, and explicitly state that this appears to be an open question in the literature.