Additive-error PAC-verification for AC^0[2]

Develop PAC-verification protocols for agnostic learning of AC^0[2] under the uniform distribution that achieve additive error guarantees of the form opt(f, AC^0[2]) + ε, potentially by exploiting the algebraic structure arising from Razborov–Smolensky lower bounds.

Background

The paper gives quasi-polynomial-time, doubly efficient PAC-verification protocols for AC^0[2] with polylogarithmic multiplicative approximation factors. Achieving additive-error guarantees would be a qualitative improvement, aligning verification error with the optimal distance rather than a multiplicative factor.

The authors suggest leveraging the algebraic structure that underlies AC^0[2] lower bounds (Razborov and Smolensky) as a potential pathway to additive-error verification.