PATCH -- Psychometrics-AssisTed benCHmarking of Large Language Models: A Case Study of Mathematics Proficiency

Many existing benchmarks of large (multimodal) language models (LLMs) focus on measuring LLMs' academic proficiency, often with also an interest in comparing model performance with human test takers. While these benchmarks have proven key to the development of LLMs, they suffer from several limitations, including questionable measurement quality (e.g., Do they measure what they are supposed to in a reliable way?), lack of quality assessment on the item level (e.g., Are some items more important or difficult than others?) and unclear human population reference (e.g., To whom can the model be compared?). In response to these challenges, we propose leveraging knowledge from psychometrics - a field dedicated to the measurement of latent variables like academic proficiency - into LLM benchmarking. We make three primary contributions. First, we introduce PATCH: a novel framework for Psychometrics-AssisTed benCHmarking of LLMs. PATCH addresses the aforementioned limitations, presenting a new direction for LLM benchmark research. Second, we implement PATCH by measuring GPT-4 and Gemini-Pro-Vision's proficiency in 8th grade mathematics against 56 human populations. We show that adopting a psychometrics-based approach yields evaluation outcomes that diverge from those based on existing benchmarking practices. Third, we release 4 datasets to support measuring and comparing LLM proficiency in grade school mathematics and science against human populations.