# Deep Learning-based Method for Expressing Knowledge Boundary of Black-Box LLM

arXiv: https://arxiv.org/abs/2602.10801 · HTML: https://mlsanity.com/paper/2602.10801/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 25 references that are in the map.
- First posted on arXiv 11 Feb 2026.

## Builds on (most cited first, 21 of 21)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [Active Retrieval Augmented Generation](https://mlsanity.com/paper/2305.06983/) (2023)
- [Prompting GPT-3 To Be Reliable](https://mlsanity.com/paper/2210.09150/) (2022)
- [Don't Hallucinate, Abstain: Identifying LLM Knowledge Gaps via Multi-LLM Collaboration](https://mlsanity.com/paper/2402.00367/) (2024)
- [Investigating the Factual Knowledge Boundary of Large Language Models with Retrieval Augmentation](https://mlsanity.com/paper/2307.11019/) (2023)
- [Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthiness](https://mlsanity.com/paper/2308.16175/) (2023)
- [R-Tuning: Instructing Large Language Models to Say `I Don't Know'](https://mlsanity.com/paper/2311.09677/) (2023)
- [Towards Building Multilingual Language Model for Medicine](https://mlsanity.com/paper/2402.13963/) (2024)
- [Unfamiliar Finetuning Examples Control How Language Models Hallucinate](https://mlsanity.com/paper/2403.05612/) (2024)
- [Calibrating the Confidence of Large Language Models by Eliciting Fidelity](https://mlsanity.com/paper/2404.02655/) (2024)
- [From Code to Correctness: Closing the Last Mile of Code Generation with Hierarchical Debugging](https://mlsanity.com/paper/2410.01215/) (2024)
- [Think Twice Before Trusting: Self-Detection for Large Language Models through Comprehensive Answer Reflection](https://mlsanity.com/paper/2403.09972/) (2024)
- [Knowledge Boundary of Large Language Models: A Survey](https://mlsanity.com/paper/2412.12472/) (2024)
- [Teaching Large Language Models to Express Knowledge Boundary from Their Own Signals](https://mlsanity.com/paper/2406.10881/) (2024)
- [Pruning the Unsurprising: Efficient LLM Reasoning via First-Token Surprisal](https://mlsanity.com/paper/2508.05988/) (2025)
- [MedBench: A Large-Scale Chinese Benchmark for Evaluating Medical Large Language Models](https://mlsanity.com/paper/2312.12806/) (2023)
- [Fact-and-Reflection (FaR) Improves Confidence Calibration of Large Language Models](https://mlsanity.com/paper/2402.17124/) (2024)
- [Benchmarking Large Language Models on CFLUE -- A Chinese Financial Language Understanding Evaluation Dataset](https://mlsanity.com/paper/2405.10542/) (2024)

## Abstract (arXiv)

Large Language Models (LLMs) have achieved remarkable success, however, the emergence of content generation distortion (hallucination) limits their practical applications. The core cause of hallucination lies in LLMs' lack of awareness regarding their stored internal knowledge, preventing them from expressing their knowledge state on questions beyond their internal knowledge boundaries, as humans do. However, existing research on knowledge boundary expression primarily focuses on white-box LLMs, leaving methods suitable for black-box LLMs which offer only API access without revealing internal parameters-largely unexplored. Against this backdrop, this paper proposes LSCL (LLM-Supervised Confidence Learning), a deep learning-based method for expressing the knowledge boundaries of black-box LLMs. Based on the knowledge distillation framework, this method designs a deep learning model. Taking the input question, output answer, and token probability from a black-box LLM as inputs, it constructs a mapping between the inputs and the model' internal knowledge state, enabling the quantification and expression of the black-box LLM' knowledge boundaries. Experiments conducted on diverse public datasets and with multiple prominent black-box LLMs demonstrate that LSCL effectively assists black-box LLMs in accurately expressing their knowledge boundaries. It significantly outperforms existing baseline models on metrics such as accuracy and recall rate. Furthermore, considering scenarios where some black-box LLMs do not support access to token probability, an adaptive alternative method is proposed. The performance of this alternative approach is close to that of LSCL and surpasses baseline models.