8 papers
The SMG-Yau-Yau Filter and Lossless Data Assimilation: Resolving Infinite Lie Algebras via Statistical Fiber Theory
Bing Cheng, Yi-Shuai Niu, Howell Tong +1
Classical continuous-time non-linear filtering fails in generic non-linear state spaces due to an infinite Lie algebraic derivative explosion (), leadin…
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…
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…
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…
On foundation of generative statistics with G-entropy: a gradient-based approach
Bing Cheng, Howell Tong
This paper explores the interplay between statistics and generative artificial intelligence. Generative statistics, an integral part of the latter, aims to construct models that ca…