arXiv — cs.AI preprintsInternational5 October 2026
Beyond Global Divergences: A Local-Mass Perspective on Bayesian Inference
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arXiv:2606.27090v2 Announce Type: replace-cross Abstract: Global objectives, such as KL divergence and ELBO, are widely used in Bayesian inference for measuring distributional discrepancy. This paper studies distributional ``local-mass behaviours'' that are not directly captured by such global objectives. We introduce and use two mathematical tools: (1) Mass Index for recording the polynomial and logarithmic decay scales of local mass, and (2) regularised extended KL (RE-KL), a set-localised divergence that can be formulated in the presence of singular components. Mass Indices help characteris
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