# Masked Thought: Simply Masking Partial Reasoning Steps Can Improve Mathematical Reasoning Learning of Language Models

arXiv: https://arxiv.org/abs/2403.02178 · HTML: https://mlsanity.com/paper/2403.02178/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 41 of its 82 references that are in the map.
- First posted on arXiv 4 Mar 2024.

## Placed in

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

## Builds on (most cited first, 30 of 41)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (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)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models](https://mlsanity.com/paper/2305.04091/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Complexity-Based Prompting for Multi-Step Reasoning](https://mlsanity.com/paper/2210.00720/) (2022)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)

## Built on by (most cited first, 20 of 20)

- [Large Language Models Meet NLP: A Survey](https://mlsanity.com/paper/2405.12819/) (2024)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [From Skepticism to Acceptance: Simulating the Attitude Dynamics Toward Fake News](https://mlsanity.com/paper/2403.09498/) (2024)
- [RATT: A Thought Structure for Coherent and Correct LLM Reasoning](https://mlsanity.com/paper/2406.02746/) (2024)
- [MathChat: Benchmarking Mathematical Reasoning and Instruction Following in Multi-Turn Interactions](https://mlsanity.com/paper/2405.19444/) (2024)
- [Autonomous Agents for Collaborative Task under Information Asymmetry](https://mlsanity.com/paper/2406.14928/) (2024)
- [CoMAT: Chain of Mathematically Annotated Thought Improves Mathematical Reasoning](https://mlsanity.com/paper/2410.10336/) (2024)
- [Embedding Self-Correction as an Inherent Ability in Large Language Models for Enhanced Mathematical Reasoning](https://mlsanity.com/paper/2410.10735/) (2024)
- [Automatic Reviewers Fail to Detect Faulty Reasoning in Research Papers: A New Counterfactual Evaluation Framework](https://mlsanity.com/paper/2508.21422/) (2025)
- [Bridging Large Language Models and Optimization: A Unified Framework for Text-attributed Combinatorial Optimization](https://mlsanity.com/paper/2408.12214/) (2024)
- [SSL4RL: Revisiting Self-supervised Learning as Intrinsic Reward for Visual-Language Reasoning](https://mlsanity.com/paper/2510.16416/) (2025)
- [Agentic Tool Use in Large Language Models](https://mlsanity.com/paper/2604.00835/) (2026)
- [Language Models, Graph Searching, and Supervision Adulteration: When More Supervision is Less and How to Make More More](https://mlsanity.com/paper/2503.10542/) (2025)
- [Pruning Weights but Not Truth: Safeguarding Truthfulness While Pruning LLMs](https://mlsanity.com/paper/2509.00096/) (2025)
- [ESG Classification by Implicit Rule Learning via GPT-4](https://mlsanity.com/paper/2403.15040/) (2024)
- [Closing the Gap: Data-Centric Fine-Tuning of Vision Language Models for the Standardized Exam Questions](https://mlsanity.com/paper/2512.00042/) (2025)
- [TokenSeek: Memory Efficient Fine Tuning via Instance-Aware Token Ditching](https://mlsanity.com/paper/2601.19739/) (2026)
- [A Survey of Multimodal Mathematical Reasoning: From Perception, Alignment to Reasoning](https://mlsanity.com/paper/2603.08291/) (2026)
- [KItCAT: Knowledge Injection via Input Corruption for Auto-regressive Training](https://mlsanity.com/paper/2609.00082/) (2026)
- [When Tokenization is Secretly Output Supervision](https://mlsanity.com/paper/2609.01386/) (2026)

## Abstract (arXiv)

In reasoning tasks, even a minor error can cascade into inaccurate results, leading to suboptimal performance of large language models in such domains. Earlier fine-tuning approaches sought to mitigate this by leveraging more precise supervisory signals from human labeling, larger models, or self-sampling, although at a high cost. Conversely, we develop a method that avoids external resources, relying instead on introducing perturbations to the input. Our training approach randomly masks certain tokens within the chain of thought, a technique we found to be particularly effective for reasoning tasks. When applied to fine-tuning with GSM8K on Llama-2-7B, this method achieved a 5% improvement in GSM8K accuracy and a 10% improvement in GSM-IC accuracy over standard supervised fine-tuning with a few codes modified. Furthermore, it is complementary to existing methods. When integrated with related explicit data augmentation methods, it leads to improvements across five datasets of various augmentation methods, as well as two different base models. We further investigate the mechanisms behind this improvement through case studies and quantitative analysis, suggesting that our approach may provide superior support for the model in capturing long-distance dependencies, especially those related to questions. This enhancement could deepen understanding of the premises in questions and prior steps. Our code is available at Github.