Knowledge augmentation has significantly enhanced the performance of Large Language Models (LLMs) in knowledge-intensive tasks. However, existing methods typically operate on the simplistic premise that model performance equates with internal knowledge, overlooking the knowledge-confidence gaps that lead to overconfident errors or uncertain truths. To bridge this gap, we propose a novel meta-cognitive framework for reliable knowledge augmentation via differentiated intervention and alignment. Our approach leverages internal cognitive signals to partition the knowledge space into mastered, confused, and missing regions, guiding targeted knowledge expansion. Furthermore, we introduce a cognitive consistency mechanism to synchronize subjective certainty with objective accuracy, ensuring calibrated knowledge boundaries. Extensive experiments demonstrate the our framework consistently outperforms strong baselines, validating its rationality in not only enhancing knowledge capabilities but also fostering cognitive behaviors that better distinguish knowns from unknowns. All codes are available at https://github.com/AI9Stars/Know-More-Know-Clearer.
While large language models (LLMs) demonstrate strong capabilities across diverse user queries, they still suffer from hallucinations, often arising from knowledge misalignment between pre-training and fine-tuning. To address this misalignment, we reliably estimate a fine-grained, instance-level knowledge score via multi-sampled inference. Using the knowledge score, we scale the learning signal according to the model's existing knowledge, while encouraging explicit "I don't know" responses for out-of-scope queries. Experimental results show that this approach allows the model to explicitly express uncertainty when it lacks knowledge, while maintaining accuracy on questions it can answer. Furthermore, we propose evaluation metrics for uncertainty, showing that accurate discrimination between known and unknown instances consistently improves performance.
How do large language models (LLMs) know what they know? Answering this question has been difficult because pre-training data is often a "black box" - unknown or inaccessible. The recent release of nanochat - a family of small LLMs with fully open pre-training data - addresses this as it provides a transparent view into where a model's parametric knowledge comes from. Towards the goal of understanding how knowledge is encoded by LLMs, we release NanoKnow, a benchmark dataset that partitions questions from Natural Questions and SQuAD into splits based on whether their answers are present in nanochat's pre-training corpus. Using these splits, we can now properly disentangle the sources of knowledge that LLMs rely on when producing an output. To demonstrate NanoKnow's utility, we conduct experiments using eight nanochat checkpoints. Our findings show: (1) closed-book accuracy is strongly influenced by answer frequency in the pre-training data, (2) providing external evidence can mitigate this frequency dependence, (3) even with external evidence, models are more accurate when answers were seen during pre-training, demonstrating that parametric and external knowledge are complementary,
Ontological knowledge, which comprises classes and properties and their relationships, is integral to world knowledge. It is significant to explore whether Pretrained Language Models (PLMs) know and understand such knowledge. However, existing PLM-probing studies focus mainly on factual knowledge, lacking a systematic probing of ontological knowledge. In this paper, we focus on probing whether PLMs store ontological knowledge and have a semantic understanding of the knowledge rather than rote memorization of the surface form. To probe whether PLMs know ontological knowledge, we investigate how well PLMs memorize: (1) types of entities; (2) hierarchical relationships among classes and properties, e.g., Person is a subclass of Animal and Member of Sports Team is a subproperty of Member of ; (3) domain and range constraints of properties, e.g., the subject of Member of Sports Team should be a Person and the object should be a Sports Team. To further probe whether PLMs truly understand ontological knowledge beyond memorization, we comprehensively study whether they can reliably perform logical reasoning with given knowledge according to ontological entailment rules. Our probing results
Truly reliable AI requires more than simply scaling up knowledge; it demands the ability to know what it knows and when it does not. Yet recent research shows that even the best LLMs misjudge their own competence in more than one in five cases, making any response born of such internal uncertainty impossible to fully trust. Inspired by self-improvement reinforcement learning techniques that require minimal data, we present a simple but powerful framework KnowRL that strengthens a model's internal understanding of its own feasibility boundaries, enabling safer and more responsible behaviour. Our framework combines two components: (i) introspection, where the model generates and classifies tasks it judges feasible or infeasible, and (ii) consensus-based rewarding, where stability of self-knowledge assessment is reinforced through internal agreement. By using internally generated data, this design strengthens consistency in self-knowledge and entirely avoids costly external supervision. In experiments on LLaMA-3.1-8B and Qwen-2.5-7B, KnowRL steadily improved self-knowledge, validated by both intrinsic self-consistency and extrinsic benchmarking. With nothing more than a small seed set
Recently, AI assistants based on large language models (LLMs) show surprising performance in many tasks, such as dialogue, solving math problems, writing code, and using tools. Although LLMs possess intensive world knowledge, they still make factual errors when facing some knowledge intensive tasks, like open-domain question answering. These untruthful responses from the AI assistant may cause significant risks in practical applications. We believe that an AI assistant's refusal to answer questions it does not know is a crucial method for reducing hallucinations and making the assistant truthful. Therefore, in this paper, we ask the question "Can AI assistants know what they don't know and express them through natural language?" To answer this question, we construct a model-specific "I don't know" (Idk) dataset for an assistant, which contains its known and unknown questions, based on existing open-domain question answering datasets. Then we align the assistant with its corresponding Idk dataset and observe whether it can refuse to answer its unknown questions after alignment. Experimental results show that after alignment with Idk datasets, the assistant can refuse to answer most
It is sometimes assumed that Large Language Models (LLMs) know language, or for example that they know that Paris is the capital of France. But what -- if anything -- do LLMs actually know? In this paper, I argue that LLMs can acquire tacit knowledge as defined by Martin Davies (1990). Whereas Davies himself denies that neural networks can acquire tacit knowledge, I demonstrate that certain architectural features of LLMs satisfy the constraints of semantic description, syntactic structure, and causal systematicity. Thus, tacit knowledge may serve as a conceptual framework for describing, explaining, and intervening on LLMs and their behavior.
Existing large language models (LLMs) occasionally generate plausible yet factually incorrect responses, known as hallucinations. Two main approaches have been proposed to mitigate hallucinations: retrieval-augmented language models (RALMs) and refusal post-training. However, current research predominantly focuses on their individual effectiveness while overlooking the evaluation of the refusal capability of RALMs. Ideally, if RALMs know when they do not know, they should refuse to answer.In this study, we ask the fundamental question: Do RALMs know when they don't know? Specifically, we investigate three questions. First, are RALMs well calibrated with respect to different internal and external knowledge states? We examine the influence of various factors. Contrary to expectations, when all retrieved documents are irrelevant, RALMs still tend to refuse questions they could have answered correctly. Next, given the model's pronounced \textbf{over-refusal} behavior, we raise a second question: How does a RALM's refusal ability align with its calibration quality? Our results show that the over-refusal problem can be mitigated through in-context fine-tuning. However, we observe that im
When a model knows when it does not know, many possibilities emerge. The first question is how to enable a model to recognize that it does not know. A promising approach is to use confidence, computed from the model's internal signals, to reflect its ignorance. Prior work in specific domains has shown that calibration can provide reliable confidence estimates. In this work, we propose a simple, effective, and universal training-free method that applies to both vision and language models, performing model calibration, cascading, and data cleaning to better exploit a model's ability to recognize when it does not know. We first highlight two key empirical observations: higher confidence corresponds to higher accuracy within a single model, and models calibrated on the validation set remain calibrated on a held-out test set. These findings empirically establish the reliability and comparability of calibrated confidence. Building on this, we introduce two applications: (1) model cascading with calibrated advantage routing and (2) data cleaning based on model ensemble. Using the routing signal derived from the comparability of calibrated confidences, we cascade large and small models to
We show that a rational agent with true and refinable knowledge of events cannot know if she knows everything or not. This epistemic limitation is not resolved by introspection about tautologies or by learning about new events.
Standard evaluation of LLM confidence relies on calibration metrics (ECE, Brier score) that conflate two distinct capacities: how much a model knows (Type-1 sensitivity) and how well it knows what it knows (Type-2 metacognitive sensitivity). We introduce an evaluation framework based on Type-2 Signal Detection Theory that decomposes these capacities using meta-d' and the metacognitive efficiency ratio M-ratio. Applied to four LLMs (Llama-3-8B-Instruct, Mistral-7B-Instruct-v0.3, Llama-3-8B-Base, Gemma-2-9B-Instruct) across 224,000 factual QA trials, we find: (1) metacognitive efficiency varies substantially across models even when Type-1 sensitivity is similar -- Mistral achieves the highest d' but the lowest M-ratio; (2) metacognitive efficiency is domain-specific, with different models showing different weakest domains, invisible to aggregate metrics; (3) temperature manipulation shifts Type-2 criterion while meta-d' remains stable for two of four models, dissociating confidence policy from metacognitive capacity; (4) AUROC_2 and M-ratio produce fully inverted model rankings, demonstrating these metrics answer fundamentally different evaluation questions. The meta-d' framework rev
Large vision-language models (LVLMs) demonstrate strong visual question answering (VQA) capabilities but are shown to hallucinate. A reliable model should perceive its knowledge boundaries-knowing what it knows and what it does not. This paper investigates LVLMs' perception of their knowledge boundaries by evaluating three types of confidence signals: probabilistic confidence, answer consistency-based confidence, and verbalized confidence. Experiments on three LVLMs across three VQA datasets show that, although LVLMs possess a reasonable perception level, there is substantial room for improvement. Among the three confidences, probabilistic and consistency-based signals are more reliable indicators, while verbalized confidence often leads to overconfidence. To enhance LVLMs' perception, we adapt several established confidence calibration methods from Large Language Models (LLMs) and propose three effective methods. Additionally, we compare LVLMs with their LLM counterparts, finding that jointly processing visual and textual inputs decreases question-answering performance but reduces confidence, resulting in an improved perception level compared to LLMs.
Large Language Models (LLMs) have emerged as highly capable systems and are increasingly being integrated into various uses. However, the rapid pace of their deployment has outpaced a comprehensive understanding of their internal mechanisms and a delineation of their capabilities and limitations. A desired attribute of an intelligent system is its ability to recognize the scope of its own knowledge. To investigate whether LLMs embody this characteristic, we develop a benchmark designed to challenge these models to enumerate all information they possess on specific topics. This benchmark evaluates whether the models recall excessive, insufficient, or the precise amount of information, thereby indicating their awareness of their own knowledge. Our findings reveal that all tested LLMs, given sufficient scale, demonstrate an understanding of how much they know about specific topics. While different architectures exhibit varying rates of this capability's emergence, the results suggest that awareness of knowledge may be a generalizable attribute of LLMs. Further research is needed to confirm this potential and fully elucidate the underlying mechanisms.
Epistemic logic has become a major field of philosophical logic ever since the groundbreaking work by Hintikka (1962). Despite its various successful applications in theoretical computer science, AI, and game theory, the technical development of the field has been mainly focusing on the propositional part, i.e., the propositional modal logics of "knowing that". However, knowledge is expressed in everyday life by using various other locutions such as "knowing whether", "knowing what", "knowing how" and so on (knowing-wh hereafter). Such knowledge expressions are better captured in quantified epistemic logic, as was already discussed by Hintikka (1962) and his sequel works at length. This paper aims to draw the attention back again to such a fascinating but largely neglected topic. We first survey what Hintikka and others did in the literature of quantified epistemic logic, and then advocate a new quantifier-free approach to study the epistemic logics of knowing-wh, which we believe can balance expressivity and complexity, and capture the essential reasoning patterns about knowing-wh. We survey our recent line of work on the epistemic logics of "knowing whether", "knowing what" and "
Conventional methods for PAN-sharpening often struggle to restore fine details due to limitations in leveraging high-frequency information. Moreover, diffusion-based approaches lack sufficient conditioning to fully utilize Panchromatic (PAN) images and low-resolution multispectral (LRMS) inputs effectively. To address these challenges, we propose an uncertainty-aware knowledge distillation diffusion framework with details enhancement for PAN-sharpening, called U-Know-DiffPAN. The U-Know-DiffPAN incorporates uncertainty-aware knowledge distillation for effective transfer of feature details from our teacher model to a student one. The teacher model in our U-Know-DiffPAN captures frequency details through freqeuncy selective attention, facilitating accurate reverse process learning. By conditioning the encoder on compact vector representations of PAN and LRMS and the decoder on Wavelet transforms, we enable rich frequency utilization. So, the high-capacity teacher model distills frequency-rich features into a lightweight student model aided by an uncertainty map. From this, the teacher model can guide the student model to focus on difficult image regions for PAN-sharpening via the usa
Given a predictor and a loss function, how well can we predict the loss that the predictor will incur on an input? This is the problem of loss prediction, a key computational task associated with uncertainty estimation for a predictor. In a classification setting, a predictor will typically predict a distribution over labels and hence have its own estimate of the loss that it will incur, given by the entropy of the predicted distribution. Should we trust this estimate? In other words, when does the predictor know what it knows and what it does not know? In this work we study the theoretical foundations of loss prediction. Our main contribution is to establish tight connections between nontrivial loss prediction and certain forms of multicalibration, a multigroup fairness notion that asks for calibrated predictions across computationally identifiable subgroups. Formally, we show that a loss predictor that is able to improve on the self-estimate of a predictor yields a witness to a failure of multicalibration, and vice versa. This has the implication that nontrivial loss prediction is in effect no easier or harder than auditing for multicalibration. We support our theoretical results
To provide an explanation of the evolution of scientific knowledge, I start from the assumption that knowledge is based on concepts, and propose that each concept about reality is affected by vagueness. This entails a paradox, which I term Knowledge Paradox (KP): i.e. we need concepts to acquire knowledge about the real world but each concept is a step away from reality. The KP provides a unifying context for the sorites and the liar paradoxes. Any concept is viewed as a sorites, i.e. it is impossible to set a boundary between what is, and what is not, the entity to which the concept refers. Hence, any statement about reality can be reduced to a liar, wherefrom the KP follows in its most general form: -If I know, then I do not know-. The KP is self-referential but not contradictory, as it can be referred to two levels of knowledge: -if I know(epistemic), then I do not know(ontic)-, where the ontic level is made unachievable by concept vagueness. Such an interpretation of scientific knowledge provides an understanding of its dynamics. Concept proliferation within theories produces periods of knowledge decay that are episodically reversed by the formulation of new theories based on a
Machine learning has achieved remarkable successes, yet its deployment in safety-critical domains remains hindered by an inherent inability to manage uncertainty, resulting in overconfident and unreliable predictions when models encounter out-of-distribution data, adversarial perturbations, or naturally fluctuating environments. This thesis, titled Epistemic Deep Learning: Enabling Machine Learning Models to 'Know When They Do Not Know', addresses these critical challenges by advancing the paradigm of Epistemic Artificial Intelligence, which explicitly models and quantifies epistemic uncertainty: the uncertainty arising from limited, biased, or incomplete training data, as opposed to the irreducible randomness of aleatoric uncertainty, thereby empowering models to acknowledge their limitations and refrain from overconfident decisions when uncertainty is high. Central to this work is the development of the Random-Set Neural Network (RS-NN), a novel methodology that leverages random set theory to predict belief functions over sets of classes, capturing the extent of epistemic uncertainty through the width of associated credal sets, applications of RS-NN, including its adaptation to L
The Mixture-of-Experts (MoE) architecture has enabled the creation of massive yet efficient Large Language Models (LLMs). However, the standard deterministic routing mechanism presents a significant limitation: its inherent brittleness is a key contributor to model miscalibration and overconfidence, resulting in systems that often do not know what they don't know. This thesis confronts this challenge by proposing a structured \textbf{Bayesian MoE routing framework}. Instead of forcing a single, deterministic expert selection, our approach models a probability distribution over the routing decision itself. We systematically investigate three families of methods that introduce this principled uncertainty at different stages of the routing pipeline: in the \textbf{weight-space}, the \textbf{logit-space}, and the final \textbf{selection-space}. Through a series of controlled experiments on a 3-billion parameter MoE model, we demonstrate that this framework significantly improves routing stability, in-distribution calibration, and out-of-distribution (OoD) detection. The results show that by targeting this core architectural component, we can create a more reliable internal uncertainty
In this paper, we propose a single-agent logic of goal-directed knowing how extending the standard epistemic logic of knowing that with a new knowing how operator. The semantics of the new operator is based on the idea that knowing how to achieve $φ$ means that there exists a (uniform) strategy such that the agent knows that it can make sure $φ$. We give an intuitive axiomatization of our logic and prove the soundness, completeness, and decidability of the logic. The crucial axioms relating knowing that and knowing how illustrate our understanding of knowing how in this setting. This logic can be used in representing both knowledge-that and knowledge-how.