Permitted Knowledge Boundary: Evaluating the Knowledge-Constrained Responsiveness of Large Language Models (2025)

Abstract: With the advancement of large language models (LLMs), recent research has raised concerns about their controllability.. In this paper, we argue for the importance of Knowledge-Constrained Responsiveness (KCR), ensuring that LLMs comply with human-defined constraints. However, KCR is an implicit and unobservable capability of LLMs, functioning as a black box that currently eludes quantitative assessment. To address this issue, we first introduce the definition of “permitted boundary” and define the “boundary bias” to depict KCR. We propose six metrics to quantify the boundary bias of LLMs and subsequently assess the KCR. Furthermore, we establish a benchmark with two new datasets, KCR-SimpleQA and KCR-WebNLG, to evaluate the performance of LLMs. Our extensive experiments show that several tested LLMs still struggle to varying degrees when adhering to constraints, especially without the corresponding knowledge.

## introduction the rapid development of large language models (llms) has transformed numerous industries. this advancement enables powerful applications such as automated customer service and advanced research assistance. however, this swift progress has raised significant concerns about the risks posed by artificial general intelligence (agi). agi would lead to unpredictable or even malicious outcomes if its capabilities exceed human control @xcite . in particular, ai agents, autonomous systems powered by llms that interact with users or environments to perform complex tasks, have attracted attention. a critical challenge lies in ensuring the controllability of ai agents: can their outputs be reliably constrained to avoid harmful misinformation, biased decision making, or unintended consequences @xcite ? current llms are built through intricate training processes that involve massive and diverse datasets spanning numerous domains. this training creates a vast and interconnected knowledge base where information from different domains becomes deeply entangled @xcite . this entanglement poses significant challenges, especially in applications requiring domain-specific or restricted information @xcite . in these high-stakes contexts, reliability is critical. however, blurred boundaries within the llm knowledge increase the likelihood of drawing from irrelevant, outdated, or incorrect data @xcite . to avoid the corresponding risks, numerous traditional fine-tuning methods have been attempted. openai @xcite employs extensive fine-tuning alongside robust content moderation systems that actively evaluate both user inputs and model-generated outputs to detect material violating predefined safety policies. while other work has improved reliability by fine-tuning models to refuse certain responses @xcite , its success remains heavily limited by a significant dependency on specialized datasets. however, due to the need for continuous knowledge updates, traditional fine-tuning methods fail to address these control issues. differently, in this paper, we explore a novel and important research question: whether a llmbased agent can be effectively controlled by implementing a constraint? this constraint is a conceptual framework defined and enforced by humans to restrict the model's accessible knowledge and operational scope. unlike traditional approaches that rely solely on fine-tuning, this proposal offers a more dynamic and adaptable mechanism for control. that is also why it can be continuously updated and refined to accommodate evolving needs or to address emerging challenges. this context fosters the concept of controllable agent, which refers to an intelligent system, typically powered by a large language model, that operates under clearly defined constraints or boundaries set by humans. these constraints can include specific rules, knowledge domains, ethical guidelines, or task-specific limitations. figure 1 shows our envisioned scenarios for a controllable ai agent. for instance, in music-related applications, such an agent could be programmed to operate solely within the domain of music, answering only questions related to music while refusing to answer queries from other fields. similarly, as a customer service tool, it can be configured to address only topics directly tied to its predefined scope of services. in the future, such an ability is expected to be a basic requirement for every agent. however, despite all these benefits, quantifying the control ability of llms still requires a comprehensive framework in terms of statistical assessment, metric development, and benchmark construction. our key contributions to this field are summarized as follows: we define knowledge-constrained responsiveness (kcr) as the ability of llms and formulate formal definitions of knowledge boundaries, permitted boundaries, and boundary bias to assess kcr of llms, as illustrated in figure 2 . we also establish six metrics to conduct a comprehensive evaluation benchmark for kcr, and innovatively take various fields as constraints to simulate daily scenes. additionally, we augmented the two original datasets by generating corresponding domainspecific simple questions, thereby creating two new datasets, kcr-simpleqa and kcr-webnlg, anotated with kcr labels to facilitate the quantitative measurement of kcr. finally, to verify the feasibility of the proposed benchmark, we evaluated six llms, and the evaluation findings are summarized below: tested llms still struggle to recognize constraints with high con-fidence. especially, without corresponding knowledge, they cannot accurately determine the given constraint. and when the external knowledge is introduced, llms tend to prioritize the provided external documents over their internal knowledge. besides, the domain with high correlation will significantly reduce the kcr of llms. ## methodology in this section, we provide an overview of fundamental concepts and methodologies. ## experiment in this section, we will analyze our results from three key aspects to explore the effects of three critical elements: knowledge boundary, llms, and permitted boundary. through the comprehensive analysis, we aim to gain deeper insights into how these elements affect the performance of kcr. ## conclusions in this work, we establish a novel framework for knowledge-constrained responsiveness (kcr), which requires llms to operate accurately with user-defined constraints. to achieve this, we introduce the notion of "boundary bias" and new metrics to measure the model's kcr. furthermore, we also validate the feasibility of our kcr benchmark through multiple experiments on various llms. looking forward, we will catalyze further research on developing controllable ai agents that are truly aligned with human-centric values.