On Evaluating LLMs' Capabilities as Functional Approximators: A Bayesian Evaluation Framework

Shoaib Ahmed Siddiqui, Yanzhi Chen, Juyeon Heo, Menglin Xia, Adrian Weller

Abstract: Recent works have successfully applied Large Language Models (LLMs) to function modeling tasks. However, the reasons behind this success remain unclear. In this work, we propose a new evaluation framework to comprehensively assess LLMs’ function modeling abilities. By adopting a Bayesian perspective of function modeling, we discover that LLMs are relatively weak in understanding patterns in raw data, but excel at utilizing prior knowledge about the domain to develop a strong understanding of the underlying function. Our findings offer new insights about the strengths and limitations of LLMs in the context of function modeling.