Optimal concentration in the Paley-Wiener space

What the math gives to ML

The paper proves a sharp rearrangement principle for time-frequency concentration: among measurable time sets of fixed measure, an interval captures the largest possible fraction of the energy of any function whose Fourier support lies in a bounded interval. The transferable object is the concentration operator P_Omega M_E P_Omega, whose top eigenfunctions provide optimally localized bandlimited features. A practical neural-network use is to replace random Fourier features or generic localized basis functions with discretized concentration eigenfunctions. This may improve parameter efficiency and sample efficiency for coordinate networks and signal models with localized structure.