Xinhao Qu

Hao Zeng, Huipeng Huang, Xinhao Qu et al.

Data annotation often involves multiple sources with different cost-quality trade-offs, such as fast large language models (LLMs), slow reasoning models, and human experts. In this work, we study the problem of routing inputs to the most cost-efficient annotation source while controlling the labeling error on test instances. We propose \textbf{HyPAC}, a method that adaptively labels inputs to the most cost-efficient annotation source while providing distribution-free guarantees on annotation error. HyPAC calibrates two decision thresholds using importance sampling and upper confidence bounds, partitioning inputs into three regions based on uncertainty and routing each to the appropriate annotation source. We prove that HyPAC achieves the minimum expected cost with a probably approximately correct (PAC) guarantee on the annotation error, free of data distribution and pre-trained models. Experiments on common benchmarks demonstrate the effectiveness of our method, reducing the annotation cost by 78.51\% while tightly controlling the annotation error.

Xinhao Qu, Qiang Heng, Hao Zeng et al.

Evaluation of large language models (LLMs) is increasingly critical, yet standard benchmarking methods rely on average accuracy, overlooking both the inherent stochasticity of LLM outputs and the heterogeneity of benchmark items. Item Response Theory (IRT) offers a principled framework for modeling latent model abilities and item characteristics, but conventional methods are computationally expensive and numerically unstable, limiting large-scale implementations. To address these challenges, we propose an interpretable and scalable framework for LLM evaluation based on the majorization-minimization principle. Our approach reformulates the problem as a sequence of constrained matrix factorization subproblems, enabling stable and efficient parameter estimation with theoretical guarantees for identifiability and convergence. Experiments on synthetic and real-world datasets, including MATH-500 and six Open LLM Leaderboard benchmarks, demonstrate that our method achieves superior scalability and interpretability. It delivers orders-of-magnitude speedups over competing methods while maintaining comparable or even higher estimation accuracy. Our results align with established scaling laws and offer insights into item difficulty and discrimination, informing more principled benchmark design.