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R\'enyi-Induced Information Geometry and Hartigan's Prior Family
Rebecca Maria Kuntz, Heinrich von Campe, Bj\"orn Malte Sch\"afer
https://arxiv.org/abs/2506.12028

Rényi-Induced Information Geometry and Hartigan's Prior Family
We derive the information geometry induced by the statistical Rényi divergence, namely its metric tensor, its dual parametrized connections, as well as its dual Laplacians. Based on these results, we demonstrate that the Rényi-geometry, though closely related, differs in structure from Amari's well-known $α$-geometry. Subsequently, we derive the canonical uniform prior distributions for a statistical manifold endowed with a Rényi-geometry, namely the dual Rényi-covolumes. We find that the …

Each week, Metacurity offers our free and paid subscribers a weekly digest of the best long-form (and longish) infosec-related pieces we couldn't properly fit into our daily news crush.
This week's selection covers
--Satellite jamming and spoofing set back global shipping,
--AI is inherently janky,
--Salvadoran gender freedom advocates fight oppression with digital training,
--A new sector arises to fight AI false positives in Chinese universities,

Best infosec-related long reads for the weeks of 6/28/25 and 7/5/25
Satellite jamming and spoofing sets back global shipping, AI is inherently janky, Salvadoran gender freedom advocates fight oppression with digital training, Sector arises to fight AI false positives in Chinese universities, Uncovering the venality of a nudify app, so much more

Stochastic Krasnosel skii-Mann Iterations in Banach Spaces with Bregman Distances
Saeed Hashemi Sababe, Ehsan Lotfali Ghasab
https://arxiv.org/abs/2506.08031

Stochastic Krasnosel skii-Mann Iterations in Banach Spaces with Bregman Distances
We propose a generalization of the stochastic Krasnoselskil-Mann $(SKM)$ algorithm to reflexive Banach spaces endowed with Bregman distances. Under standard martingale-difference noise assumptions in the dual space and mild conditions on the distance-generating function, we establish almost-sure convergence to a fixed point and derive non-asymptotic residual bounds that depend on the uniform convexity modulus of the generating function. Extensions to adaptive Bregman geometries and robust noise…

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🎵 Geometria del Universo
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