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…
Yau's Affine-Normal Descent for Large-Scale Unrestricted Higher-Moment Portfolio Optimization
Ya-Juan Wang, Yi-Shuai Niu, Artan Sheshmani +1
Unrestricted mean-variance-skewness-kurtosis portfolio optimization can capture asymmetry and tail risk, but sample-moment formulations become computationally impractical when the…
Polylab: A MATLAB Toolbox for Multivariate Polynomial Modeling
Yi-Shuai Niu, Shing-Tung Yau
Polylab is a MATLAB toolbox for multivariate polynomial scalars and polynomial matrices with a unified symbolic-numeric interface across CPU and GPU-oriented backends. The software…
Yau's Affine Normal Descent: Algorithmic Framework and Convergence Analysis
Yi-Shuai Niu, Artan Sheshmani, Shing-Tung Yau
We propose Yau's Affine Normal Descent (YAND), a geometric framework for smooth unconstrained optimization in which search directions are defined by the equi-affine normal of level…