We measure the performance of in-context learning as a function of task novelty and difficulty for open and closed questions. For that purpose, we created a novel benchmark consisting of hard scientific questions, each paired with a context of various relevancy. We show that counter-intuitively, a context that is more aligned with the topic does not always help more than a less relevant context. This effect is especially visible for open questions and questions of high difficulty or novelty. This result reveals a fundamental difference between the treatment of close-form and open-form questions by large-language models and shows a need for a more robust evaluation of in-context learning on the variety of different types of questions. It also poses a new question of how to optimally select a context for large language models, especially in the context of Retrieval Augmented Generation (RAG) systems. Our results suggest that the answer to this question can be highly application-dependent and might be contingent on factors including the format of the question, the perceived difficulty level of the questions, and the novelty or popularity of the information we seek.

In this paper, we explore the challenges inherent to Large Language Models (LLMs) like GPT-4, particularly their propensity for hallucinations, logic mistakes, and incorrect conclusions when tasked with answering complex questions. The capacity of LLMs to present erroneous answers in a coherent and semantically rigorous manner further complicates the detection of factual inaccuracies. This issue is especially pronounced in fields that require specialized expertise. Our work delves into these challenges, aiming to enhance the understanding and mitigation of such errors, thereby contributing to the improvement of LLM accuracy and reliability in scientific and other specialized domains. Our findings reveal a non-linear relationship between the context's relevancy and the answers' measured quality. In addition, we demonstrate that with the correct calibration, it is possible to automate the grading procedure -- a finding suggesting that, at least to some degree, the LLMs can be used to self-examine the quality of their own performance. Finally, we describe an experimental platform that can be seen as a proof-of-concept of the techniques described in this work.