# Optimizing Temperature for Language Models with Multi-Sample Inference

arXiv: https://arxiv.org/abs/2502.05234 · HTML: https://mlsanity.com/paper/2502.05234/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 35 of its 41 references that are in the map.
- First posted on arXiv 7 Feb 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 35)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [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)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Building Cooperative Embodied Agents Modularly with Large Language Models](https://mlsanity.com/paper/2307.02485/) (2023)
- [Stochastic Beams and Where to Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacement](https://mlsanity.com/paper/1903.06059/) (2019)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [The Effect of Sampling Temperature on Problem Solving in Large Language Models](https://mlsanity.com/paper/2402.05201/) (2024)
- [Turning Up the Heat: Min-p Sampling for Creative and Coherent LLM Outputs](https://mlsanity.com/paper/2407.01082/) (2024)
- [From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Models](https://mlsanity.com/paper/2406.16838/) (2024)
- [Locally Typical Sampling](https://mlsanity.com/paper/2202.00666/) (2022)
- [Evaluating Open-Domain Question Answering in the Era of Large Language Models](https://mlsanity.com/paper/2305.06984/) (2023)
- [Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervision](https://mlsanity.com/paper/2403.09472/) (2024)
- [LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discovery](https://mlsanity.com/paper/2405.09783/) (2024)
- [Planning In Natural Language Improves LLM Search For Code Generation](https://mlsanity.com/paper/2409.03733/) (2024)
- [Lean-STaR: Learning to Interleave Thinking and Proving](https://mlsanity.com/paper/2407.10040/) (2024)
- [Calibration of Encoder Decoder Models for Neural Machine Translation](https://mlsanity.com/paper/1903.00802/) (2019)

## Built on by (most cited first, 30 of 34)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [BroRL: Scaling Reinforcement Learning via Broadened Exploration](https://mlsanity.com/paper/2510.01180/) (2025)
- [MedArabiQ: Benchmarking Large Language Models on Arabic Medical Tasks](https://mlsanity.com/paper/2505.03427/) (2025)
- [Analyzable Chain-of-Musical-Thought Prompting for High-Fidelity Music Generation](https://mlsanity.com/paper/2503.19611/) (2025)
- [Optimal Self-Consistency for Efficient Reasoning with Large Language Models](https://mlsanity.com/paper/2511.12309/) (2025)
- [Estimating LLM Consistency: A User Baseline vs Surrogate Metrics](https://mlsanity.com/paper/2505.23799/) (2025)
- [When Life Gives You Samples: The Benefits of Scaling up Inference Compute for Multilingual LLMs](https://mlsanity.com/paper/2506.20544/) (2025)
- [Exploring Multi-Temperature Strategies for Token- and Rollout-Level Control in RLVR](https://mlsanity.com/paper/2510.08892/) (2025)
- [Temperature as a Meta-Policy: Adaptive Temperature in LLM Reinforcement Learning](https://mlsanity.com/paper/2602.11779/) (2026)
- [Why Pass@k Optimization Can Degrade Pass@1: Prompt Interference in LLM Post-training](https://mlsanity.com/paper/2602.21189/) (2026)
- [The Consensus Trap: Rescuing Multi-Agent LLMs from Adversarial Majorities via Token-Level Collaboration](https://mlsanity.com/paper/2604.17139/) (2026)
- [Learning to Explore with Parameter-Space Noise: A Deep Dive into Parameter-Space Noise for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2602.02555/) (2026)
- [FinCoT: Grounding Chain-of-Thought in Expert Financial Reasoning](https://mlsanity.com/paper/2506.16123/) (2025)
- [Autonomous Radiotherapy Treatment Planning Using DOLA: A Privacy-Preserving, LLM-Based Optimization Agent](https://mlsanity.com/paper/2503.17553/) (2025)
- [Demystifying LLM-as-a-Judge: Analytically Tractable Model for Inference-Time Scaling](https://mlsanity.com/paper/2512.19905/) (2025)
- [Security Considerations for Multi-agent Systems](https://mlsanity.com/paper/2603.09002/) (2026)
- [The Necessity of Setting Temperature in LLM-as-a-Judge](https://mlsanity.com/paper/2603.28304/) (2026)
- [Instinct vs. Reflection: Unifying Token and Verbalized Confidence in Multimodal Large Models](https://mlsanity.com/paper/2604.17274/) (2026)
- [Learning Adaptive LLM Decoding](https://mlsanity.com/paper/2603.09065/) (2026)
- [FLIPS: Instance-Fingerprinting for LLMs via Pseudo-random Sequences](https://mlsanity.com/paper/2606.03330/) (2026)
- [Large Language Models Develop Novel Social Biases Through Adaptive Exploration](https://mlsanity.com/paper/2511.06148/) (2025)
- [From Token to Token Pair: Efficient Prompt Compression for Large Language Models in Clinical Prediction](https://mlsanity.com/paper/2605.11774/) (2026)
- [AutoCRAT: Within-trajectory Joint Control of Stochasticity and Compute for LLM Reasoning](https://mlsanity.com/paper/2608.29988/) (2026)
- [UpSkill: Mutual Information Skill Learning for Structured Response Diversity in LLMs](https://mlsanity.com/paper/2602.22296/) (2026)
- [TempPerturb-Eval: On the Joint Effects of Internal Temperature and External Perturbations in RAG Robustness](https://mlsanity.com/paper/2512.01183/) (2025)
- [Temperature-Dependent Performance of Prompting Strategies in Extended Reasoning Large Language Models](https://mlsanity.com/paper/2604.08563/) (2026)
- [Trajectory as the Teacher: Few-Step Discrete Flow Matching via Energy-Navigated Distillation](https://mlsanity.com/paper/2605.07924/) (2026)
- [Towards Trust Calibration in Socially Interactive Agents: Investigating Gendered Multimodal Behaviors Generation with LLMs](https://mlsanity.com/paper/2605.19798/) (2026)
- [SonicSampler: Unified Tile-Aware Kernels for LLM Sampling and Speculative Verification](https://mlsanity.com/paper/2607.20475/) (2026)
- [COMPAS: Difficulty-Aware Joint Search for Optimizing Code Generation](https://mlsanity.com/paper/2608.04336/) (2026)

## Abstract (arXiv)

Multi-sample aggregation strategies, such as majority voting and best-of-N sampling, are widely used in contemporary large language models (LLMs) to enhance predictive accuracy across various tasks. A key challenge in this process is temperature selection, which significantly impacts model performance. Existing approaches either rely on a fixed default temperature or require labeled validation data for tuning, which are often scarce and difficult to obtain. This paper addresses the challenge of automatically identifying the (near)-optimal temperature for different LLMs using multi-sample aggregation strategies, without relying on task-specific validation data. We provide a comprehensive analysis of temperature's role in performance optimization, considering variations in model architectures, datasets, task types, model sizes, and predictive accuracy. Furthermore, we propose a novel entropy-based metric for automated temperature optimization, which consistently outperforms fixed-temperature baselines. Additionally, we incorporate a stochastic process model to enhance interpretability, offering deeper insights into the relationship between temperature and model performance.