Uniformly Stable Minimal Weyl--Heisenberg Measurements Approaching the SIC Benchmark

What the math gives to ML

The paper turns conditioning of a Weyl–Heisenberg measurement frame into an explicit max–min problem over ambiguity intensities: the nonidentity Gram eigenvalues are exactly d times the squared magnitudes of the fiducial's displacement correlations. This gives a concrete method for designing structured neural feature maps whose translated and modulated responses avoid nearly-null directions, rather than relying on random or unconstrained filters. The most transferable construction is an ambiguity-flat cyclic feature layer, implemented as a fixed or lightly trainable Weyl–Heisenberg orbit and optimized with a spectral-floor regularizer. Its likely benefit is improved conditioning of downstream linear probes and gradients, especially when the layer is used as a compact structured embedding.