Stealthy point processes and lattice induction

What the math gives to ML

The paper gives a constructive way to create translation-invariant point configurations whose Bartlett spectrum has an actual spectral gap around zero: sufficiently smooth large-scale counting statistics have zero variance, not merely reduced asymptotic variance. This suggests a neural regularizer for spatial activations, sparse token layouts, or MoE routing masks that suppresses low-frequency fluctuations while preserving higher-frequency structure. The transferable asset is the exact variance–spectral-measure identity, which turns a global stability objective into a computable Fourier-domain penalty; the paper's lattice-induced construction is less directly transferable because its detailed algorithm is not present in the extracted text.