# Step Guided Reasoning: Improving Mathematical Reasoning using Guidance Generation and Step Reasoning

arXiv: https://arxiv.org/abs/2410.19817 · HTML: https://mlsanity.com/paper/2410.19817/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 17 of its 43 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Placed in

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

## Builds on (most cited first, 17 of 17)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2312.10997/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [A Systematic Survey of Prompt Engineering in Large Language Models: Techniques and Applications](https://mlsanity.com/paper/2402.07927/) (2024)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [Cumulative Reasoning with Large Language Models](https://mlsanity.com/paper/2308.04371/) (2023)
- [Interpretable Contrastive Monte Carlo Tree Search Reasoning](https://mlsanity.com/paper/2410.01707/) (2024)
- [SLCNN: Sentence-Level Convolutional Neural Network for Text Classification](https://mlsanity.com/paper/2301.11696/) (2023)

## Built on by (most cited first, 9 of 9)

- [RAIN-Merging: A Gradient-Free Method to Enhance Instruction Following in Large Reasoning Models with Preserved Thinking Format](https://mlsanity.com/paper/2602.22538/) (2026)
- [Where to Spend Rollouts: Hit-Utility Optimal Rollout Allocation for Group-Based RLVR](https://mlsanity.com/paper/2605.07114/) (2026)
- [Persona Switch: Mixing Distinct Perspectives in Decoding Time](https://mlsanity.com/paper/2601.15708/) (2026)
- [Strategy Executability in Mathematical Reasoning: Leveraging Human-Model Differences for Effective Guidance](https://mlsanity.com/paper/2602.22583/) (2026)
- [Value-Aware Numerical Representations for Transformer Language Models](https://mlsanity.com/paper/2601.09706/) (2026)
- [TRACES: Tagging Reasoning Steps for Adaptive Cost-Efficient Early-Stopping](https://mlsanity.com/paper/2604.21057/) (2026)
- [When Tokenization is Secretly Output Supervision](https://mlsanity.com/paper/2609.01386/) (2026)
- [Understanding and Exploiting Anisotropy in Post-Training](https://mlsanity.com/paper/2609.32792/) (2026)
- [MetaCtrl: Your Large Language Models Can Reason Better and More Concisely with a Metacognitive Controller](https://mlsanity.com/paper/2609.37304/) (2026)

## Abstract (arXiv)

Mathematical reasoning has been challenging for large language models (LLMs), and the introduction of step-by-step Chain-of-Thought (CoT) inference has significantly advanced the mathematical capabilities of LLMs. However, current approaches either necessitate extensive inference datasets for training or depend on few-shot methods that frequently compromise computational accuracy. To address these fundamental limitations, we propose Step Guided Reasoning, a novel training-free adaptation framework that efficiently equips general-purpose pre-trained language models with enhanced mathematical reasoning capabilities. In this approach, LLMs reflect on small reasoning steps, similar to how humans deliberate and focus attention on what to do next. By incorporating this reflective process into the inference stage, LLMs can effectively guide their reasoning from one step to the next. Through extensive experiments, we demonstrate the significant effect of Step Guided Reasoning in enhancing mathematical performance in state-of-the-art language models -- Qwen2-72B-Instruct outperforms its math-specific counterpart, Qwen2.5-72B-Math-Instruct, on MMLU-STEM with a score of 90.9%, compared to 87.3%. The average scores of Qwen2-7B-Instruct and Qwen2-72B-Instruct increase from 27.1% to 36. 3% and from 36. 5% to 47.4% in the math domain, respectively.