Instruction Boundary: Quantifying Biases in LLM Reasoning under Various Coverage

Abstract: Large-language-model (LLM) reasoning has long been regarded as a powerful tool for problem solving across domains, providing non-experts with valuable advice. However, their limitations - especially those stemming from prompt design - remain underexplored. Because users may supply biased or incomplete prompts - often unintentionally - LLMs can be misled, undermining reliability and creating risks. We refer to this vulnerability as the Instruction Boundary. To investigate the phenomenon, we distill it into eight concrete facets and introduce BiasDetector, a framework that measures biases arising from three instruction types: complete, redundant, and insufficient. We evaluate several mainstream LLMs and find that, despite high headline accuracy, substantial biases persist in many downstream tasks as a direct consequence of prompt coverage. Our empirical study confirms that LLM reasoning reliability can still be significantly improved. We analyze the practical impact of these biases and outline mitigation strategies. Our findings underscore the need for developers to tackle biases and for users to craft options carefully.