# MinT: Boosting Generalization in Mathematical Reasoning via Multi-View Fine-Tuning

arXiv: https://arxiv.org/abs/2307.07951 · HTML: https://mlsanity.com/paper/2307.07951/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 37 of its 58 references that are in the map.
- First posted on arXiv 16 Jul 2023.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 30 of 37)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Large Language Models Are Reasoning Teachers](https://mlsanity.com/paper/2212.10071/) (2022)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning](https://mlsanity.com/paper/2012.09816/) (2020)
- [Teaching Small Language Models to Reason](https://mlsanity.com/paper/2212.08410/) (2022)
- [Specializing Smaller Language Models towards Multi-Step Reasoning](https://mlsanity.com/paper/2301.12726/) (2023)
- [The AI Teacher Test: Measuring the Pedagogical Ability of Blender and GPT-3 in Educational Dialogues](https://mlsanity.com/paper/2205.07540/) (2022)
- [Ape210K: A Large-Scale and Template-Rich Dataset of Math Word Problems](https://mlsanity.com/paper/2009.11506/) (2020)
- [Translating a Math Word Problem to an Expression Tree](https://mlsanity.com/paper/1811.05632/) (2018)
- [Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction](https://mlsanity.com/paper/2203.10316/) (2022)
- [Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks](https://mlsanity.com/paper/2107.01431/) (2021)
- [MWP-BERT: Numeracy-Augmented Pre-training for Math Word Problem Solving](https://mlsanity.com/paper/2107.13435/) (2021)
- [Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problems](https://mlsanity.com/paper/2110.08464/) (2021)
- [Let GPT be a Math Tutor: Teaching Math Word Problem Solvers with Customized Exercise Generation](https://mlsanity.com/paper/2305.14386/) (2023)
- [Learning by Fixing: Solving Math Word Problems with Weak Supervision](https://mlsanity.com/paper/2012.10582/) (2020)

## Built on by (most cited first, 16 of 16)

- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers](https://mlsanity.com/paper/2402.19255/) (2024)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [SceMQA: A Scientific College Entrance Level Multimodal Question Answering Benchmark](https://mlsanity.com/paper/2402.05138/) (2024)
- [MathChat: Benchmarking Mathematical Reasoning and Instruction Following in Multi-Turn Interactions](https://mlsanity.com/paper/2405.19444/) (2024)
- [Auto-Instruct: Automatic Instruction Generation and Ranking for Black-Box Language Models](https://mlsanity.com/paper/2310.13127/) (2023)
- [cAST: Enhancing Code Retrieval-Augmented Generation with Structural Chunking via Abstract Syntax Tree](https://mlsanity.com/paper/2506.15655/) (2025)
- [Distilling Reasoning Ability from Large Language Models with Adaptive Thinking](https://mlsanity.com/paper/2404.09170/) (2024)
- [Teaching-Assistant-in-the-Loop: Improving Knowledge Distillation from Imperfect Teacher Models in Low-Budget Scenarios](https://mlsanity.com/paper/2406.05322/) (2024)
- [FineMath: A Fine-Grained Mathematical Evaluation Benchmark for Chinese Large Language Models](https://mlsanity.com/paper/2403.07747/) (2024)
- [Enhancing Large Language Model Reasoning with Reward Models: An Analytical Survey](https://mlsanity.com/paper/2510.01925/) (2025)
- [SIaM: Self-Improving Code-Assisted Mathematical Reasoning of Large Language Models](https://mlsanity.com/paper/2408.15565/) (2024)
- [Putting on the Thinking Hats: A Survey on Chain of Thought Fine-tuning from the Perspective of Human Reasoning Mechanism](https://mlsanity.com/paper/2510.13170/) (2025)
- [Template-Driven LLM-Paraphrased Framework for Tabular Math Word Problem Generation](https://mlsanity.com/paper/2412.15594/) (2024)
- [Improving Attributed Long-form Question Answering with Intent Awareness](https://mlsanity.com/paper/2603.27435/) (2026)
- [SAAS: Solving Ability Amplification Strategy for Enhanced Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2404.03887/) (2024)

## Abstract (arXiv)

Reasoning in mathematical domains remains a significant challenge for relatively small language models (LMs). Many current methods focus on specializing LMs in mathematical reasoning and rely heavily on knowledge distillation from powerful but inefficient large LMs (LLMs). In this work, we explore a new direction that avoids over-reliance on LLM teachers, introducing a multi-view fine-tuning method that efficiently exploits existing mathematical problem datasets with diverse annotation styles. Our approach uniquely considers the various annotation formats as different "views" and leverages them in training the model. By postpending distinct instructions to input questions, models can learn to generate solutions in diverse formats in a flexible manner. Experimental results show that our strategy enables a LLaMA-7B model to outperform prior approaches that utilize knowledge distillation, as well as carefully established baselines. Additionally, the proposed method grants the models promising generalization ability across various views and datasets, and the capability to learn from inaccurate or incomplete noisy data. We hope our multi-view training paradigm could inspire future studies in other machine reasoning domains.