7 papers
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…
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…
Statistically Meaningful Geometry and Gauge Symmetry Breaking: A Geometric Foundation for Scientific Discovery and Intelligence Emergence
Bing Cheng, Yi-Shuai Niu, Howell Tong +1
The rapid scaling of over-parameterized machine learning architectures, particularly LLMs, raises a profound crisis: do these systems exhibit genuine intelligence, or are they mere…
Statistically Meaningful Geometry (SMG) Beyond the Euclidean Paradigm, with Application to Generative AI
Bing Cheng, Yi-Shuai Niu, Howell Tong +1
Conventional uniform convergence bounds and empirical risk minimization break down in massive over-parameterized models, such as large language transformers and biological sequence…
On a fast consistent selection of nested models with possibly unnormalized probability densities
Rong Bian, Kung-Sik Chan, Bing Cheng +1
Models with unnormalized probability density functions are ubiquitous in statistics, artificial intelligence and many other fields. However, they face significant challenges in mod…
An approach to Fisher-Rao metric for infinite dimensional non-parametric information geometry
Bing Cheng, Howell Tong
Being infinite dimensional, non-parametric information geometry has long faced an "intractability barrier" due to the fact that the Fisher-Rao metric is now a functional incurring…