Lattice Gaussian distributions: closed-form KL divergence via Riemann theta functions
FrnkNlsn · x · 2026-10-18
Frank Nielsen shares his work on lattice (discrete normal) distributions — the max-entropy distributions on integer lattices whose exponential family ties to the Riemann theta function. The paper (arXiv:2109.14920, J. Indian Inst. Sci.) derives closed-form formulas for common statistical divergences, notably the KL divergence between two discrete normals, plus efficient approximations via Rényi α- and projective γ-divergences. Slides and tech report included; relevant to lattice cryptography and discrete information geometry.
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