AI4BayesCode: From Natural Language Descriptions to Validated Modular Stateful Bayesian Samplers

Coding and computation remain major bottlenecks in Markov chain Monte Carlo (MCMC) workflows, especially as modern sampling algorithms have become increasingly complex and existing probabilistic programming systems remain limited in model support, extensibility, and composability. We introduce \textbf{AI4BayesCode}, an extensible LLM-driven system that translates natural-language Bayesian model descriptions into runnable, validated MCMC samplers. To improve reliability, AI4BayesCode adopts a modular design that decomposes models into modular sampling blocks and maps each block to a built-in sampling component, reducing the need to implement complex sampling algorithms from scratch. Reliability is further improved through pre-generation validation of model specifications and post-generation validation of generated sampler code. AI4BayesCode also introduces a novel recursively stateful coding paradigm for MCMC, allowing modular sampling components, potentially developed by different contributors, to be composed coherently within larger MCMC procedures. We develop a benchmark suite to evaluate AI4BayesCode for sampler-generation. Experiments show that AI4BayesCode can implement a wide range of Bayesian models from natural-language descriptions alone. As an open-ended system, its capability can continue to expand with improvements in the underlying AI agent and the addition of new built-in blocks.

Fairness or Fluency? An Investigation into Language Bias of Pairwise LLM-as-a-Judge

Recent advances in Large Language Models (LLMs) have incentivized the development of LLM-as-a-judge, an application of LLMs where they are used as judges to decide the quality of a certain piece of text given a certain context. However, previous studies have demonstrated that LLM-as-a-judge can be biased towards different aspects of the judged texts, which often do not align with human preference. One of the identified biases is language bias, which indicates that the decision of LLM-as-a-judge can differ based on the language of the judged texts. In this paper, we study two types of language bias in pairwise LLM-as-a-judge: (1) performance disparity between languages when the judge is prompted to compare options from the same language, and (2) bias towards options written in major languages when the judge is prompted to compare options of two different languages. We find that for same-language judging, there exist significant performance disparities across language families, with European languages consistently outperforming African languages, and this bias is more pronounced in culturally-related subjects. For inter-language judging, we observe that most models favor English answers, and that this preference is influenced more by answer language than question language. Finally, we investigate whether language bias is in fact caused by low-perplexity bias, a previously identified bias of LLM-as-a-judge, and we find that while perplexity is slightly correlated with language bias, language bias cannot be fully explained by perplexity only.