Publications (252)
PostLie algebra structures on the Lie algebra sl(2,C)
Yu Pan, Qing Liu, Chengming Bai +1
The PostLie algebra is an enriched structure of the Lie algebra that has recently arisen from operadic study. It is closely related to pre-Lie algebra, Rota-Baxter algebra, dendrif…
Integrable Renormalization II: the general case
Kurusch Ebrahimi-Fard, Li Guo, Dirk Kreimer
We extend the results we obtained in an earlier work. The cocommutative case of rooted ladder trees is generalized to a full Hopf algebra of (decorated) rooted trees. For Hopf alge…
Cross Entropy versus Label Smoothing: A Neural Collapse Perspective
Li Guo, George Andriopoulos, Zifan Zhao +3
Label smoothing loss is a widely adopted technique to mitigate overfitting in deep neural networks. This paper studies label smoothing from the perspective of Neural Collapse (NC),…
An Algebraic Study of Multivariable Integration and Linear Substitution
Markus Rosenkranz, Xing Gao, Li Guo
We set up an algebraic theory of multivariable integration, based on a hierarchy of Rota-Baxter operators and an action of the matrix monoid as linear substitutions. Given a suitab…
Advances in Embodied Navigation Using Large Language Models: A Survey
Jinzhou Lin, Han Gao, Xuxiang Feng +5
In recent years, the rapid advancement of Large Language Models (LLMs) such as the Generative Pre-trained Transformer (GPT) has attracted increasing attention due to their potentia…
Characteristics of Rota-Baxter Algebras
Li Guo, Houyi Yu
The characteristic is a simple yet important invariant of an algebra. In this paper, we study the characteristic of a Rota-Baxter algebra, called the Rota-Baxter characteristic. We…