# A Survey on Feedback-based Multi-step Reasoning for Large Language Models on Mathematics

arXiv: https://arxiv.org/abs/2502.14333 · HTML: https://mlsanity.com/paper/2502.14333/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 80 of its 125 references that are in the map.
- First posted on arXiv 20 Feb 2025.

## Placed in

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

## Builds on (most cited first, 30 of 80)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [Humanity's Last Exam](https://mlsanity.com/paper/2501.14249/) (2025)
- [LLMs-as-Judges: A Comprehensive Survey on LLM-based Evaluation Methods](https://mlsanity.com/paper/2412.05579/) (2024)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [From r to Q^*: Your Language Model is Secretly a Q-Function](https://mlsanity.com/paper/2404.12358/) (2024)

## Built on by (most cited first, 11 of 11)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [SIM-CoT: Supervised Implicit Chain-of-Thought](https://mlsanity.com/paper/2509.20317/) (2025)
- [Does Reasoning Introduce Bias? A Study of Social Bias Evaluation and Mitigation in LLM Reasoning](https://mlsanity.com/paper/2502.15361/) (2025)
- [A Survey of Scaling in Large Language Model Reasoning](https://mlsanity.com/paper/2504.02181/) (2025)
- [SeLaR: Selective Latent Reasoning in Large Language Models](https://mlsanity.com/paper/2604.08299/) (2026)
- [SSR: Speculative Parallel Scaling Reasoning in Test-time](https://mlsanity.com/paper/2505.15340/) (2025)
- [Mathematics Isn't Culture-Free: Probing Cultural Gaps via Entity and Scenario Perturbations](https://mlsanity.com/paper/2507.00883/) (2025)
- [Unveiling Instruction-Specific Neurons & Experts: An Analytical Framework for LLM's Instruction-Following Capabilities](https://mlsanity.com/paper/2505.21191/) (2025)
- [PiERN: Token-Level Routing for Integrating High-Precision Computation and Reasoning](https://mlsanity.com/paper/2509.18169/) (2025)
- [Iterative LLM-Based Generation and Refinement of Distracting Conditions in Math Word Problems](https://mlsanity.com/paper/2510.08615/) (2025)
- [Gradually Compacting Large Language Models for Reasoning Like a Boiling Frog](https://mlsanity.com/paper/2602.04919/) (2026)

## Abstract (arXiv)

Recent progress in large language models (LLM) found chain-of-thought prompting strategies to improve the reasoning ability of LLMs by encouraging problem solving through multiple steps. Therefore, subsequent research aimed to integrate the multi-step reasoning process into the LLM itself through process rewards as feedback and achieved improvements over prompting strategies. Due to the cost of step-level annotation, some turn to outcome rewards as feedback. Aside from these training-based approaches, training-free techniques leverage frozen LLMs or external tools for feedback at each step to enhance the reasoning process. With the abundance of work in mathematics due to its logical nature, we present a survey of strategies utilizing feedback at the step and outcome levels to enhance multi-step math reasoning for LLMs. As multi-step reasoning emerges a crucial component in scaling LLMs, we hope to establish its foundation for easier understanding and empower further research.