# When are likely answers right? On Sequence Probability and Correctness in LLMs

arXiv: https://arxiv.org/abs/2606.27359 · HTML: https://mlsanity.com/paper/2606.27359/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 59 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 30 of 43)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Be Your Own Teacher: Improve the Performance of Convolutional Neural Networks via Self Distillation](https://mlsanity.com/paper/1905.08094/) (2019)
- [Six Challenges for Neural Machine Translation](https://mlsanity.com/paper/1706.03872/) (2017)
- [Diverse Beam Search: Decoding Diverse Solutions from Neural Sequence Models](https://mlsanity.com/paper/1610.02424/) (2016)
- [A Contrastive Framework for Neural Text Generation](https://mlsanity.com/paper/2202.06417/) (2022)
- [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)
- [Truncation Sampling as Language Model Desmoothing](https://mlsanity.com/paper/2210.15191/) (2022)
- [Confidence Improves Self-Consistency in LLMs](https://mlsanity.com/paper/2502.06233/) (2025)
- [Probabilistic Inference in Language Models via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2404.17546/) (2024)
- [Reasoning with Sampling: Your Base Model is Smarter Than You Think](https://mlsanity.com/paper/2510.14901/) (2025)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)
- [Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening](https://mlsanity.com/paper/2506.02355/) (2025)

## Built on by (most cited first, 4 of 4)

- [Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loops](https://mlsanity.com/paper/2607.07663/) (2026)
- [The Calibration Floor: Format Repair Can Masquerade as Self-Correction at Small-to-Mid Scale](https://mlsanity.com/paper/2608.04355/) (2026)
- [GRPODropout: Less is More for Online Reinforcement Learning Rollouts](https://mlsanity.com/paper/2610.11854/) (2026)
- [Decoupled Marginal Sharpening for Training-Free Inference-Time Scaling](https://mlsanity.com/paper/2610.20483/) (2026)

## Abstract (arXiv)

Many decoding methods for large language models can be understood as shifting probability mass toward outputs that are more likely under the model, either locally at the token level or globally at the sequence level. Therefore, their success depends on a fundamental question: when does sequence probability, that is, the conditional probability of a continuation given a prompt, actually align with correctness? In this paper, we set out to quantify this relationship across decoding methods, models, and benchmarks at four levels: across decoding methods, across hyperparameters within a method, across prompt-answer pairs within a dataset, and across repeated responses to the same prompt. We find that higher sequence probability is often predictive of correctness across prompt-answer pairs within a fixed dataset. However, this relationship does not generally transfer to decoding decisions: increasing sequence probability by changing hyperparameters or methods does not reliably improve accuracy. Further, sequence probability is not a good indicator of correctness for responses to the same prompt. These findings clarify when decoding can and cannot be expected to improve correctness, and provide practical guidance for decoding, self-consistency, and verifier-free self-improvement.