# Flaming-hot Initiation with Regular Execution Sampling for Large Language Models

arXiv: https://arxiv.org/abs/2410.21236 · HTML: https://mlsanity.com/paper/2410.21236/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 47 references that are in the map.
- First posted on arXiv 28 Oct 2024.

## Builds on (most cited first, 30 of 31)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [The Rise and Potential of Large Language Model Based Agents: A Survey](https://mlsanity.com/paper/2309.07864/) (2023)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [PlanBench: An Extensible Benchmark for Evaluating Large Language Models on Planning and Reasoning about Change](https://mlsanity.com/paper/2206.10498/) (2022)
- [DeepSeek-Coder-V2: Breaking the Barrier of Closed-Source Models in Code Intelligence](https://mlsanity.com/paper/2406.11931/) (2024)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)
- [Chain-of-Thought Reasoning Without Prompting](https://mlsanity.com/paper/2402.10200/) (2024)
- [A Language Agent for Autonomous Driving](https://mlsanity.com/paper/2311.10813/) (2023)
- [RLTF: Reinforcement Learning from Unit Test Feedback](https://mlsanity.com/paper/2307.04349/) (2023)
- [Large Language Models are Diverse Role-Players for Summarization Evaluation](https://mlsanity.com/paper/2303.15078/) (2023)
- [Enhancing Large Language Models in Coding Through Multi-Perspective Self-Consistency](https://mlsanity.com/paper/2309.17272/) (2023)
- [EDT: Improving Large Language Models' Generation by Entropy-based Dynamic Temperature Sampling](https://mlsanity.com/paper/2403.14541/) (2024)
- [Why Solving Multi-agent Path Finding with Large Language Model has not Succeeded Yet](https://mlsanity.com/paper/2401.03630/) (2024)

## Built on by (most cited first, 6 of 6)

- [Harnessing the Reasoning Economy: A Survey of Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.24377/) (2025)
- [LSPO: Length-aware Dynamic Sampling for Policy Optimization in LLM Reasoning](https://mlsanity.com/paper/2510.01459/) (2025)
- [Iterative Deepening Sampling as Efficient Test-Time Scaling](https://mlsanity.com/paper/2502.05449/) (2025)
- [Think Outside the Policy: In-Context Steered Policy Optimization](https://mlsanity.com/paper/2510.26519/) (2025)
- [Partial Reasoning in Language Models: Search and Refinement Guided by Uncertainty](https://mlsanity.com/paper/2601.12040/) (2026)
- [Large Language Models Explore by Latent Distilling](https://mlsanity.com/paper/2604.24927/) (2026)

## Abstract (arXiv)

Since the release of ChatGPT, large language models (LLMs) have demonstrated remarkable capabilities across various domains. A key challenge in developing these general capabilities is efficiently sourcing diverse, high-quality data. This becomes especially critical in reasoning-related tasks with sandbox checkers, such as math or code, where the goal is to generate correct solutions to specific problems with higher probability. In this work, we introduce Flaming-hot Initiation with Regular Execution (FIRE) sampling, a simple yet highly effective method to efficiently find good responses. Our empirical findings show that FIRE sampling enhances inference-time generation quality and also benefits training in the alignment stage. Furthermore, we explore how FIRE sampling improves performance by promoting diversity and analyze the impact of employing FIRE at different positions within a response.