4 papers
Beyond Positive Scaling: How Negation Impacts Scaling Trends of Language Models
Yuhui Zhang, Michihiro Yasunaga, Zhengping Zhou +4
Language models have been shown to exhibit positive scaling, where performance improves as models are scaled up in terms of size, compute, or data. In this work, we introduce NeQA,…
Mixed Eigenvalues of {\LARGE \,}-Laplacian
Mu-Fa Chen, Ling-Di Wang, Yu-Hui Zhang
The mixed principal eigenvalue of -Laplacian (equivalently, the optimal constant of weighted Hardy inequality in space) is studied in this paper. Several variational for…
Mixed Eigenvalues of Discrete {\LARGE \,}-Laplacian
Mu-Fa Chen, Ling-Di Wang, Yu-Hui Zhang
This paper deals with the principal eigenvalue of discrete -Laplacian on the set of nonnegative integers. Alternatively, it is studying the optimal constant of a class of weight…
Mixed principal eigenvalues in dimension one
Mu-Fa Chen, Ling-Di Wang, Yu-Hui Zhang
This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic opera…