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Theoretical Limits of Language Model Alignment $f$-Divergence Regularized RLHF: Two Tales of Sampling and Unified Analyses A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models When Can Voting Help, Hurt, or Change Course? 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Homogeneous Weights and Möbius Functions on Finite Rings
Yun Fan, Hongwei Liu · 2013-04-18 · via cs.IT updates on arXiv.org

The homogeneous weights and the Möbius functions and Euler phi-functions on finite rings are discussed; some computational formulas for these functions on finite principal ideal rings are characterized; for the residue rings of integers, they are reduced to the classical number-theoretical Möbius functions and the classical number-theoretical Euler phi-functions.

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