# Sample Smart, Not Hard: Correctness-First Decoding for Better Reasoning in LLMs

arXiv: https://arxiv.org/abs/2510.05987 · HTML: https://mlsanity.com/paper/2510.05987/

## Key facts

- Cited by 5 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 31 of its 37 references that are in the map.
- First posted on arXiv 7 Oct 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 31)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Scalable Best-of-N Selection for Large Language Models via Self-Certainty](https://mlsanity.com/paper/2502.18581/) (2025)
- [Turning Up the Heat: Min-p Sampling for Creative and Coherent LLM Outputs](https://mlsanity.com/paper/2407.01082/) (2024)
- [Truncation Sampling as Language Model Desmoothing](https://mlsanity.com/paper/2210.15191/) (2022)
- [To Believe or Not to Believe Your LLM](https://mlsanity.com/paper/2406.02543/) (2024)
- [A Thorough Examination of Decoding Methods in the Era of LLMs](https://mlsanity.com/paper/2402.06925/) (2024)
- [Locally Typical Sampling](https://mlsanity.com/paper/2202.00666/) (2022)
- [Why Exposure Bias Matters: An Imitation Learning Perspective of Error Accumulation in Language Generation](https://mlsanity.com/paper/2204.01171/) (2022)
- [EDT: Improving Large Language Models' Generation by Entropy-based Dynamic Temperature Sampling](https://mlsanity.com/paper/2403.14541/) (2024)
- [LitBench: A Benchmark and Dataset for Reliable Evaluation of Creative Writing](https://mlsanity.com/paper/2507.00769/) (2025)
- [Hot or Cold? Adaptive Temperature Sampling for Code Generation with Large Language Models](https://mlsanity.com/paper/2309.02772/) (2023)
- [Calibrated Interpretation: Confidence Estimation in Semantic Parsing](https://mlsanity.com/paper/2211.07443/) (2022)
- [Calibrating Long-form Generations from Large Language Models](https://mlsanity.com/paper/2402.06544/) (2024)
- [Just Ask One More Time! Self-Agreement Improves Reasoning of Language Models in (Almost) All Scenarios](https://mlsanity.com/paper/2311.08154/) (2023)
- [On the Efficacy of Sampling Adapters](https://mlsanity.com/paper/2307.03749/) (2023)
- [Model-Based Minimum Bayes Risk Decoding for Text Generation](https://mlsanity.com/paper/2311.05263/) (2023)
- [REAL Sampling: Boosting Factuality and Diversity of Open-Ended Generation via Asymptotic Entropy](https://mlsanity.com/paper/2406.07735/) (2024)
- [Min-p, Max Exaggeration: A Critical Analysis of Min-p Sampling in Language Models](https://mlsanity.com/paper/2506.13681/) (2025)

## Built on by (most cited first, 5 of 5)

- [From Efficiency to Adaptivity: A Deeper Look at Adaptive Reasoning in Large Language Models](https://mlsanity.com/paper/2511.10788/) (2025)
- [When are likely answers right? On Sequence Probability and Correctness in LLMs](https://mlsanity.com/paper/2606.27359/) (2026)
- [Efficient Test-Time Inference via Deterministic Exploration of Truncated Decoding Trees](https://mlsanity.com/paper/2604.20500/) (2026)
- [Revisiting Greedy Decoding for Visual Question Answering: A Calibration Perspective](https://mlsanity.com/paper/2604.23443/) (2026)
- [Attention-Aware Routing: Coupling Routing and Attention in MoEs](https://mlsanity.com/paper/2609.20974/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) are increasingly applied to complex tasks that require extended reasoning. In such settings, models often benefit from diverse chains-of-thought to arrive at multiple candidate solutions. This requires two competing objectives: to inject enough stochasticity to explore multiple reasoning chains, and to ensure sufficient accuracy and quality in each path. Existing works pursue the first objective by increasing exploration at highly uncertain steps with higher temperature or larger candidate token sets, while others improve reliability by rejecting samples with low confidence post-generation, implying that low confidence correlates with low answer quality. These two lines of thought are in conflict, as they conflate different sources of uncertainty. To resolve this, we argue that the decoding rule should be calibrated by correctness, not confidence alone. We should sample from tokens with higher estimated correctness, and reduce sampling where expected correctness is low. We propose simple strategies that achieve this goal: Greedy-Threshold makes sampling greedy at very low confidence steps. Calibrated-TopK and Calibrated-epsilon set truncation threshold based on estimated rank-wise correctness. Together, our findings challenge prevailing heuristics about decoding under uncertainty and show gains across math and general reasoning benchmarks.