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Geometric Factorization of Sufficient Harmonic Representations

arXiv CS Monday 08 June 2026, 04:00 UTC By Kennon Stewart 1 min read
Key Points

arXiv:2606.07346v1 Announce Type: cross Abstract: For tasks of likelihood families invariant under the action of a lie group, the quotient is the minimal sufficient invariant representation. On compact homogeneous spaces, this quotient representation admits a harmonic realization through spherical Fourier coefficients; for finite-band harmonic exponential families, the empirical harmonic coefficients are minimal sufficient statistics. The partition function can be expressed algebraically by...

arXiv:2606.07346v1 Announce Type: cross Abstract: For tasks of likelihood families invariant under the action of a lie group, the quotient is the minimal sufficient invariant representation. On compact homogeneous spaces, this quotient representation admits a harmonic realization through spherical Fourier coefficients; for finite-band harmonic exponential families, the empirical harmonic coefficients are minimal sufficient statistics. The partition function can be expressed algebraically by extracting the trivial representation component through Clebsch-Gordan decomposition.
Clebsch-Gordan (ORG)
Originally published by arXiv CS Read original →

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