# MiRAGE: Misconception Detection with Retrieval-Guided Multi-Stage Reasoning and Ensemble Fusion

arXiv: https://arxiv.org/abs/2511.01182 · HTML: https://mlsanity.com/paper/2511.01182/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 21 of its 24 references that are in the map.
- First posted on arXiv 3 Nov 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

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

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [Chain-of-Thought Reasoning Without Prompting](https://mlsanity.com/paper/2402.10200/) (2024)
- [The BiGGen Bench: A Principled Benchmark for Fine-grained Evaluation of Language Models with Language Models](https://mlsanity.com/paper/2406.05761/) (2024)
- [LLM-Ensemble: Optimal Large Language Model Ensemble Method for E-commerce Product Attribute Value Extraction](https://mlsanity.com/paper/2403.00863/) (2024)
- [A Systematic Study of Knowledge Distillation for Natural Language Generation with Pseudo-Target Training](https://mlsanity.com/paper/2305.02031/) (2023)
- [Assessing Student Errors in Experimentation Using Artificial Intelligence and Large Language Models: A Comparative Study with Human Raters](https://mlsanity.com/paper/2308.06088/) (2023)
- [Large Language Models For Text Classification: Case Study And Comprehensive Review](https://mlsanity.com/paper/2501.08457/) (2025)
- [RLAE: Reinforcement Learning-Assisted Ensemble for LLMs](https://mlsanity.com/paper/2506.00439/) (2025)
- [Data-Mining Textual Responses to Uncover Misconception Patterns](https://mlsanity.com/paper/1703.08544/) (2017)
- [Improving Academic Skills Assessment with NLP and Ensemble Learning](https://mlsanity.com/paper/2409.19013/) (2024)
- [Accurate Knowledge Distillation with n-best Reranking](https://mlsanity.com/paper/2305.12057/) (2023)
- [A Review of Hybrid and Ensemble in Deep Learning for Natural Language Processing](https://mlsanity.com/paper/2312.05589/) (2023)
- [Gumbel Reranking: Differentiable End-to-End Reranker Optimization](https://mlsanity.com/paper/2502.11116/) (2025)

## Built on by (most cited first, 1 of 1)

- [Misconception Diagnosis From Student-Tutor Dialogue: Generate, Retrieve, Rerank](https://mlsanity.com/paper/2602.02414/) (2026)

## Abstract (arXiv)

Detecting student misconceptions in open-ended responses is a longstanding challenge, demanding semantic precision and logical reasoning. We propose MiRAGE - Misconception Detection with Retrieval-Guided Multi-Stage Reasoning and Ensemble Fusion, a novel framework for automated misconception detection in mathematics. MiRAGE operates in three stages: (1) a Retrieval module narrows a large candidate pool to a semantically relevant subset; (2) a Reasoning module employs chain-of-thought generation to expose logical inconsistencies in student solutions; and (3) a Reranking module refines predictions by aligning them with the reasoning. These components are unified through an ensemble-fusion strategy that enhances robustness and interpretability. On mathematics datasets, MiRAGE achieves Mean Average Precision scores of 0.82/0.92/0.93 at levels 1/3/5, consistently outperforming individual modules. By coupling retrieval guidance with multi-stage reasoning, MiRAGE reduces dependence on large-scale language models while delivering a scalable and effective solution for educational assessment.