# Self-Consistency Boosts Calibration for Math Reasoning

arXiv: https://arxiv.org/abs/2403.09849 · HTML: https://mlsanity.com/paper/2403.09849/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 7 of its 25 references that are in the map.
- First posted on arXiv 14 Mar 2024.

## Placed in

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

## Builds on (most cited first, 7 of 7)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)

## Built on by (most cited first, 13 of 13)

- [Efficient Test-Time Scaling via Self-Calibration](https://mlsanity.com/paper/2503.00031/) (2025)
- [LiteSearch: Efficacious Tree Search for LLM](https://mlsanity.com/paper/2407.00320/) (2024)
- [Mirror-Consistency: Harnessing Inconsistency in Majority Voting](https://mlsanity.com/paper/2410.10857/) (2024)
- [Black-box Optimization of LLM Outputs by Asking for Directions](https://mlsanity.com/paper/2510.16794/) (2025)
- [Let the Model Distribute Its Doubt: Confidence Estimation through Verbalized Probability Distribution](https://mlsanity.com/paper/2511.14275/) (2025)
- [Quantifying Consistency in LLM Logical Reasoning via Structural Uncertainty](https://mlsanity.com/paper/2606.17312/) (2026)
- [Direct Confidence Alignment: Aligning Verbalized Confidence with Internal Confidence In Large Language Models](https://mlsanity.com/paper/2512.11998/) (2025)
- [A State-Transition Framework for Efficient LLM Reasoning](https://mlsanity.com/paper/2602.01198/) (2026)
- [AUEB-Archimedes at RIRAG-2025: Is obligation concatenation really all you need?](https://mlsanity.com/paper/2412.11567/) (2024)
- [Better Think Thrice: Learning to Reason Causally with Double Counterfactual Consistency](https://mlsanity.com/paper/2602.16787/) (2026)
- [Gradient-Guided Reward Optimization for Inference-time Alignment](https://mlsanity.com/paper/2606.09635/) (2026)
- [When Tokenization is Secretly Output Supervision](https://mlsanity.com/paper/2609.01386/) (2026)
- [ACED: Reference-Anchored Aggregation of Natural-Language and Executable Evidence for Mathematical Reasoning](https://mlsanity.com/paper/2610.16635/) (2026)

## Abstract (arXiv)

Calibration, which establishes the correlation between accuracy and model confidence, is important for LLM development. We design three off-the-shelf calibration methods based on self-consistency (Wang et al., 2022) for math reasoning tasks. Evaluation on two popular benchmarks (GSM8K and MathQA) using strong open-source LLMs (Mistral and LLaMA2), our methods better bridge model confidence and accuracy than existing methods based on p(True) (Kadavath et al., 2022) or logit (Kadavath et al., 2022).