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math.GM2026
Information Geometry (IG) Lives at Edge or Boundary of SMG (statistically meaningful geometry): - the First Edge Theorem and Applications
Bing Cheng, Yi-Shuai Niu, Howell Tong +1
Statistically Meaningful Geometry (SMG) is a differential-geometric and information-theoretic framework that lifts over-parameterized models into infinite-dimensional non-parametri…
math.GM2026
The Second Edge Theorem: The Asymptotic Collapse of Sample-Dependent Information Geometry to the Canonical Flat Canvas of Conventional Statistics in Large Sample Limits
Bing Cheng, Yi-Shuai Niu, Howell Tong +1
This paper establishes the global proof of the Second Edge Theorem: as sample size tends to infinity, sample-dependent information-geometric manifolds---formed by the parameter spa…