Learning order-parameter expectations from labels via surrogate losses

Establish whether sufficiently accurate approximations of order-parameter expectations can be learned from phase labels alone—which are thresholded transforms of the expectations—by leveraging relationships between 0–1 losses and convex surrogate losses, thereby enabling shadow-based learning of order parameters in the LUQPI setting.

Background

The authors note prior work showing order parameters can be learned from shadows when expectations are available. In their LUQPI setting, only phase labels (thresholded versions of the expectations) may be available, creating a gap.

They conjecture that known relationships between 0–1 losses and convex surrogates could enable learning sufficiently accurate order-parameter approximations from labels alone, which would permit combining shadow-based learning with LUQPI without accessing expectation values directly.

References

Given the known relationships between 0-1 losses (here corresponding to the thresholded values) and convex surrogates (actual expectations) (see [https://statistics.berkeley.edu/sites/default/files/tech-reports/638.pdf)]) we conjecture sufficiently good approximations of order parameters could be learned.

— Machine learning with minimal use of quantum computers: Provable advantages in Learning Under Quantum Privileged Information (LUQPI)  (2601.22006 - Bokov et al., 29 Jan 2026) in Section 7, Limitations and future directions (footnote after item (iii))