Ordering-based approaches to causal discovery identify topological orders of causal graphs, providing scalable alternatives to combinatorial search methods. Under the Additive Noise Models (ANMs) assumption, recent causal ordering methods based on score matching require an accurate estimation of the Hessian diagonal of the log-densities. However, previous approaches mainly use Stein gradient estimators, which are computationally expensive and memory-intensive. Although DiffAN addresses these limitations by substituting kernel-based estimates with diffusion models, it remains numerically unstable due to the second-order derivatives of score models. To alleviate these problems, we propose Score-informed Neural Operator (SciNO), a probabilistic generative model in smooth function spaces designed to stably approximate the Hessian diagonal and to preserve structural information during the score modeling. Empirical results show that SciNO reduces order divergence by 42.7% on synthetic graphs and by 31.5% in real-world datasets on average compared to DiffAN, while maintaining memory efficiency and scalability. Furthermore, we propose a probabilistic control algorithm for causal reasoning with autoregressive models that integrates SciNO's probability estimates with autoregressive model priors, enabling reliable data-driven causal ordering informed by semantic information. Consequently, the proposed method enhances causal reasoning abilities of LLMs without additional fine-tuning or prompt engineering.

Large language models (LLMs) trained on massive corpora demonstrate impressive capabilities in a wide range of tasks. While there are ongoing efforts to adapt these models to languages beyond English, the attention given to their evaluation methodologies remains limited. Current multilingual benchmarks often rely on back translations or re-implementations of English tests, limiting their capacity to capture unique cultural and linguistic nuances. To bridge this gap for the Korean language, we introduce the HAE-RAE Bench, a dataset curated to challenge models lacking Korean cultural and contextual depth. The dataset encompasses six downstream tasks across four domains: vocabulary, history, general knowledge, and reading comprehension. Unlike traditional evaluation suites focused on token and sequence classification or mathematical and logical reasoning, the HAE-RAE Bench emphasizes a model’s aptitude for recalling Korean-specific knowledge and cultural contexts. Comparative analysis with prior Korean benchmarks indicates that the HAE-RAE Bench presents a greater challenge to non-Korean models by disturbing abilities and knowledge learned from English being transferred.