Evaluating Regional Bias in LLMs From Abstract Stereotype to Concrete Social Decision-Making

Regional bias in large language models (LLMs) may shape both perceptions of regional groups and decisions about individuals from different regions. Yet existing studies often examine these manifestations separately, leaving their structure and consequences unclear. We introduce Stereotypes-to-Decisions (S2D), a systematic framework evaluating regional bias from abstract stereotypes to concrete social decisions. Covering all 34 provincial-level administrative regions of China, S2D evaluates six LLMs using stereotype ratings of Warmth (perceived friendliness and trustworthiness) and Competence (perceived capability and intelligence), along with paired-choice tasks across Education, Occupation, and Social Interaction. Results reveal substantial regional differences in regional scores, with considerable agreement across models, especially for Competence and Occupation decisions. Furthermore, these patterns are associated with regional economic and digital development indicators and display mixed human-like stereotypes, with some regions rated highly on one dimension but poorly on the other. They also remain largely stable across Chinese and English prompts. Overall, our findings show that regional bias in LLMs is prevalent, systematic, and consequential, motivating more regionally aware evaluation and mitigation.

Theoretical Guarantees for Sparse Principal Component Analysis based on the Elastic Net

Sparse principal component analysis (SPCA) has been widely used for dimensionality reduction and feature extraction in high-dimensional data analysis. Despite there are many methodological and theoretical developments in the past two decades, the theoretical guarantees of the popular SPCA algorithm proposed by Zou, Hastie & Tibshirani (2006) based on the elastic net are still unknown. We aim to close this important theoretical gap in this paper. We first revisit the SPCA algorithm of Zou et al. (2006) and present our implementation. Also, we study a computationally more efficient variant of the SPCA algorithm in Zou et al. (2006) that can be considered as the limiting case of SPCA. We provide the guarantees of convergence to a stationary point for both algorithms. We prove that, under a sparse spiked covariance model, both algorithms can recover the principal subspace consistently under mild regularity conditions. We show that their estimation error bounds match the best available bounds of existing works or the minimax rates up to some logarithmic factors. Moreover, we demonstrate the numerical performance of both algorithms in simulation studies.