2 citations · 3 across the 4 of their papers we have counts for
5 papers
Geometric Realizations of Capability Spaces of Large Models and Zigzag Persistent Homology
Yu-Zhe Liu, Shengda Liu, Jianyong Pi +1
We propose a topological model for capability changes during large-model training. The model represents knowledge states and preregistered capability probes as subcomplexes of a fi…
Module-valued ordinary differential equations and structure of solution spaces
Shengda Liu, Yu-Zhe Liu, Keyu Tao
We define and study ordinary differential equations (ODEs) for functions valued in a Banach module over a finite-dimensional -algebra by using the tensor of B…
Normed modules, integral sequences, and integrals with variable upper limits
Miantao Liu, Yu-Zhe Liu, Shengda Liu
This paper provides a new categorification of the Lebesgue integral with variable upper limits by using normed modules over finite-dimensional -algebras and the c…
Normed modules and The Stieltjes integrations of functions defined on finite-dimensional algebras
Hanpeng Gao, Shengda Liu, Yu-Zhe Liu +1
We define integrals for functions on finite-dimensional algebras, adapting methods from Leinster's research. This paper discusses the relationships between the integrals of functio…
Normed modules and the categorification of integrations, series expansions, and differentiations
Yu-Zhe Liu, Shengda Liu, Zhaoyong Huang +1
We explore the assignment of norms to -modules over a finite-dimensional algebra , resulting in the establishment of normed -modules. Our primary cont…