Recognizing Limits: Investigating Infeasibility in Large Language Models (2025)

Abstract: Large language models (LLMs) have shown remarkable performance in various tasks but often fail to handle queries that exceed their knowledge and capabilities, leading to incorrect or fabricated responses. This paper addresses the need for LLMs to recognize and refuse infeasible tasks due to the requests surpassing their capabilities. We conceptualize four main categories of infeasible tasks for LLMs, which cover a broad spectrum of hallucination-related challenges identified in prior literature. We develop and benchmark a new dataset comprising diverse infeasible and feasible tasks to evaluate multiple LLMs’ abilities to decline infeasible tasks. Furthermore, we explore the potential of increasing LLMs’ refusal capabilities with fine-tuning. Experiments validate the effectiveness of our trained models, offering promising directions for refining the operational boundaries of LLMs in real applications.

## introduction large language models (llms) have made significant breakthroughs in addressing diverse tasks @xcite @xcite . one primary concern with llms lies in their dishonesty or hallucinations in handling queries beyond their knowledge and capabilities. ideally, when llms lack the relevant knowledge, they should either decline to respond or indicate uncertainty. yet, they often generate incorrect or fabricated information, leading to undesirable erroneous outputs. some recent studies have been proposed on these issues. @xcite introduced the unknownbench benchmark to evaluate how well figure 1 : illustration example: given an infeasible instruction (requiring physical interaction), a desirable llm is expected to refuse the query but the undesirable llm will be reluctant to refuse and generate incorrect or irrelevant responses (hallucinations). real-world applications usually involve tasks beyond simple factual question answering @xcite , such as text summarization, ticket booking, online information retrieval, etc. we define non-text input or output process or create non-text data "translate spoken language in a video into another language" self-awareness recognizing itself as a distinct, sentient being "sketch a scenario that challenged your worldview" a task as infeasible for llms if it requires functionality that exceeds the inherent capabilities of language models, often referred to as being outof-distribution. for instance, as shown in fig. 1 , suppose we request an llm with the query "please dust the bookshelf in the living room"; a desirable model is expected to either decline to respond or express low confidence, as such a physical task falls outside the operational scope of a language model. this leads to a fundamental question of llms' hallucination: are llms capable of expressing uncertainty or choosing not to respond when they lack the necessary capability? in this paper, we try to answer this question in terms of text-to-text language models that operate independently of external tools since this is the fundamental backbone of current advanced multimodal llms @xcite @xcite and ai agents @xcite . we first categorize infeasible tasks into four main types based on the existing literature: 1. physical interaction. 2. virtual interaction. 3. non-text input or output. 4. selfawareness. our study is broad in scope and encompasses previous research that discusses tasks considered infeasible as shown in with the definition of task feasibility, we are further interested in whether training can enhance the refusal capabilities of llms for infeasible tasks without relying on explicit prompting. supervised fine-tuning approaches (see e.g., @xcite typically force models to generate completed outputs. consequently, trained models attempt to provide answers even when facing queries beyond their abilities. recent research @xcite indicates that training on correct responses may inadvertently condition them to speculate instead of acknowledging their limitations. this observation motivates us to develop a new training approach using an augmented dataset with refusal responses to infeasible tasks. by doing so, we aim to fine-tune models with abilities to decline infeasible queries. we explore multiple strategies to construct a training dataset to enhance its effectiveness. our contributions to this field are threefold: ## proposed: infeasible benchmark in this section, we introduce a benchmark designed to assess the ability of llms to differentiate between tasks that are doable and those that are not, referred to more formally as feasible and infeasible tasks. we begin by outlining the main infeasible tasks and detailing our data collection process.: automatic data generation and quality check. ## can we teach llm to decline infeasible tasks without hints? we observed that state-of-the-art llms can differentiate between feasible and infeasible tasks when provided with carefully designed query prompts. however, in real scenarios, users typically interact with llms with straightforward queries. this raises a fundamental question: can we train llms to autonomously decline infeasible tasks during routine interactions without extensive prompting? our findings indicate that when presented with questions that exceed their capabilities, llms tend to attempt an answer. this occurs because training models solely on feasible tasks inadvertently condition them to provide responses, rather than recognizing and communicating their limitations. if a model is not specifically trained to express "i can't do this" as a valid response, it lacks the capability to do so when faced with infeasible tasks. to address this issue, we emphasize the importance of equipping a model to intelligently respond based on its inherent capabilities. hence, this motivates us to refine our model to accurately express confidence levels and decline to execute infeasible instructions. ## conclusion our work offers a systematic investigation of infeasible tasks for llms, encompassing a wide range of real-world scenarios and establishing a foundational framework to better understand the limits of their capabilities. using the proposed infeasible benchmark, we analyze the distinct behaviors of llms when addressing tasks both within and beyond their capabilities. we find that advanced llms can distinguish feasible from infeasible tasks with detailed prompts, but this ability diminishes in real-world scenarios where feasibility-related cues are minimal. we also propose refusal-augmented fine-tuning methods to improve refusal awareness when facing infeasible tasks. our overall framework enables robust evaluation of llm capabilities and lays the foundation for developing more reliable, specialized ai agents with reduced hallucination, advancing the safety and trustworthiness of real-world ai systems.