A complex-analytic proof of square-restricted stable phase retrieval in Fock space

What the math gives to ML

The paper proves a coercivity statement for holomorphic Fock-space functions: deviation of the intensity |F|^2 from its best constant baseline controls deviation of the squared analytic representation F^2 from the phase-invariant anchor F(0)^2. This gives a nontrivial stability certificate for models whose observations discard phase, rather than merely supplying another reconstruction loss. The most plausible neural transfer is a complex-valued, analytically parameterized feature module for phase retrieval or magnitude-only sensing, using a Gaussian-weighted intensity residual as a stability regularizer. The result is specialized and likely moderate-impact, but it suggests a concrete way to prevent magnitude-only training from producing unstable complex features.