Eric Hallman

h-index45
2papers

2 Papers

LGJan 24, 2025
Humanity's Last Exam

Long Phan, Alice Gatti, Ziwen Han et al. · amazon-science, apple-ml

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 2,500 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai.

54.9NAMay 9
A Variational Equation and Lower Bound for the Linear Least-Squares Backward Error

Eric Hallman

This paper derives a new variational equation for the linear least-squares backward error by expressing the backward error in terms of a generalized eigenvalue problem and using results from indefinite linear algebra. For problems with multiple right-hand sides, the variational equation also shows that the backward error can be decomposed as a sum of smaller backward error problems. Applications to stopping criteria for iterative methods are considered, and a new sketching-based lower bound is proposed which is provably of quality comparable to the sketched Karlson-Waldén estimate.