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Robert Gerbicz

Publications and source records attributed to Robert Gerbicz.

5 recordsLinked to original sources

Humanity's Last Exam

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.

cs.LG

Sums and differences of sets (improvement over AlphaEvolve)

On May 14, 2025, DeepMind announced that AlphaEvolve, a large language model applied to a set of mathematical problems, had matched or exceeded the best known bounds on several problems. In the case of the sum and difference of sets problem, AlphaEvolve, using a set of $54265$ integers, improved the known lower bound of $θ=1.14465$ to $θ=1.1584$. In this paper, we present an improved bound $θ=1.173050$ using an explicit construction of a U set that contains more than $10^{43546}$ elements. For fast integer and floating-point arithmetic, we used the (free) GMP library.

math.NT

A search for Wilson primes

A Wilson prime is a prime p such that (p-1)! = -1 mod p^2. We report on a search for Wilson primes up to 2 * 10^13, and describe several new algorithms that were used in the search. In particular we give the first known algorithm that computes (p-1)! mod p^2 in average polynomial time per prime.

math.NT

New lower bounds for two color and multicolor Ramsey numbers

Using cyclic graphs I give new lower bounds for two color and multicolor Ramsey numbers: R(4,16)>163, R(5,11)>170, R(5,12)>190, R(5,13)>212, R(5,14)>238, R(3,3,9)>117, R(3,3,10)>141 and R(3,3,11)>157. Improving the previous best known bounds.

math.CO