Structure-Preserving Spectral Dynamic Programming on Compact Lie Groups

What the math gives to ML

The transferable asset is a finite-rank spectral operator that preserves the order and sup-norm stability of a Markov transition, unlike ordinary orthogonal Fourier truncation. On a compact Lie group, the proposed Fejér-type filter is simultaneously positivity preserving, non-expansive, and spectrally truncated, so it can stabilize equivariant spectral layers or recurrent group-valued networks without sacrificing finite computational cost. The direct neural implementation is to replace a signed truncated group convolution or Fourier projection by a normalized positive spectral multiplier whose spatial kernel is nonnegative. The coupling between spectral resolution and update step also provides a principled smoothing schedule.