Pseudo-calibration conjecture: transfer low-degree failure to SoS failure

Establish the pseudo-calibration conjecture asserting that, for the well-defined class of high-dimensional detection problems studied in sos-detect—where the null model is i.i.d. and the planted model obeys suitable symmetry—failure of low-degree polynomials to solve the detection task implies failure of the sum-of-squares hierarchy at corresponding degrees.

Background

Sum-of-squares (SoS) is a powerful semidefinite programming hierarchy used for average-case inference and certification. The pseudo-calibration approach connects SoS lower bounds to properties of low-degree polynomials.

The survey notes that the pseudo-calibration conjecture remains unproven; resolving it would provide a meta-theorem transferring low-degree hardness directly into SoS hardness for a broad class of detection problems.