# KCluster: An LLM-based Clustering Approach to Knowledge Component Discovery

arXiv: https://arxiv.org/abs/2505.06469 · HTML: https://mlsanity.com/paper/2505.06469/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 52 references that are in the map.
- First posted on arXiv 9 May 2025.

## Builds on (most cited first, 8 of 8)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [Tag-Aware Ordinal Sparse Factor Analysis for Learning and Content Analytics](https://mlsanity.com/paper/1412.5967/) (2014)
- [Automated Generation and Tagging of Knowledge Components from Multiple-Choice Questions](https://mlsanity.com/paper/2405.20526/) (2024)

## Built on by (most cited first, 5 of 5)

- [Small but Significant: On the Promise of Small Language Models for Accessible AIED](https://mlsanity.com/paper/2505.08588/) (2025)
- [Generate-Then-Validate: A Novel Question Generation Approach Using Small Language Models](https://mlsanity.com/paper/2512.10110/) (2025)
- [RoMathExam: A Longitudinal Dataset of Romanian Math Exams (1895-2025) with a Seven-Decade Core (1957-2025)](https://mlsanity.com/paper/2604.16392/) (2026)
- [Capturing LLM Capabilities via Evidence-Calibrated Query Clustering](https://mlsanity.com/paper/2605.17110/) (2026)
- [Atom Learning Model (ALM): how a real classroom got tokenised](https://mlsanity.com/paper/2608.21106/) (2026)

## Abstract (arXiv)

Educators evaluate student knowledge using knowledge component (KC) models that map assessment questions to KCs. Still, designing KC models for large question banks remains an insurmountable challenge for instructors who need to analyze each question by hand. The growing use of Generative AI in education is expected only to aggravate this chronic deficiency of expert-designed KC models, as course engineers designing KCs struggle to keep up with the pace at which questions are generated. In this work, we propose KCluster, a novel KC discovery algorithm based on identifying clusters of congruent questions according to a new similarity metric induced by a large language model (LLM). We demonstrate in three datasets that an LLM can create an effective metric of question similarity, which a clustering algorithm can use to create KC models from questions with minimal human effort. Combining the strengths of LLM and clustering, KCluster generates descriptive KC labels and discovers KC models that predict student performance better than the best expert-designed models available. In anticipation of future work, we illustrate how KCluster can reveal insights into difficult KCs and suggest improvements to instruction.