# Certainty-Guided Reasoning in Large Language Models: A Dynamic Thinking Budget Approach

arXiv: https://arxiv.org/abs/2509.07820 · HTML: https://mlsanity.com/paper/2509.07820/

## Key facts

- Cited by 3 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 13 of its 15 references that are in the map.
- First posted on arXiv 9 Sep 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, 13 of 13)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Gorilla: Large Language Model Connected with Massive APIs](https://mlsanity.com/paper/2305.15334/) (2023)
- [DeeBERT: Dynamic Early Exiting for Accelerating BERT Inference](https://mlsanity.com/paper/2004.12993/) (2020)
- [LayerSkip: Enabling Early Exit Inference and Self-Speculative Decoding](https://mlsanity.com/paper/2404.16710/) (2024)
- [Dynamic Early Exit in Reasoning Models](https://mlsanity.com/paper/2504.15895/) (2025)
- [Phi-4-reasoning Technical Report](https://mlsanity.com/paper/2504.21318/) (2025)
- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [Escape Sky-high Cost: Early-stopping Self-Consistency for Multi-step Reasoning](https://mlsanity.com/paper/2401.10480/) (2024)
- [Maximizing Confidence Alone Improves Reasoning](https://mlsanity.com/paper/2505.22660/) (2025)
- [Inverse Scaling in Test-Time Compute](https://mlsanity.com/paper/2507.14417/) (2025)
- [Steering LLM Thinking with Budget Guidance](https://mlsanity.com/paper/2506.13752/) (2025)

## Built on by (most cited first, 3 of 3)

- [Limited Reasoning Space: The cage of long-horizon reasoning in LLMs](https://mlsanity.com/paper/2602.19281/) (2026)
- [AdaTurn: Budget-Aware Test-Time Scaling for Active Visual Perception Agents](https://mlsanity.com/paper/2607.14547/) (2026)
- [Certainty Is Not Just Correctness: Rethinking Token-Level Certainty in LLM Reasoning](https://mlsanity.com/paper/2610.00296/) (2026)

## Abstract (arXiv)

Large reasoning language models are typically run with fixed inference budgets, which can waste computation or terminate reasoning prematurely. We introduce Certainty-Guided Reasoning (CGR), a model-agnostic adaptive inference procedure that periodically probes whether the current reasoning supports a confident final answer and terminates early once a target certainty threshold is reached, otherwise continuing until the end-of-thinking token or the budget limit. Certainty is estimated from the model's predicted probabilities over the answer tokens, yielding a lightweight stopping criterion. On AIME2025, CGR preserves baseline accuracy while reducing token usage, providing a tunable certainty-efficiency trade-off that can eliminate millions of tokens in aggregate. Across 64 random seeds, CGR exhibits consistent behavior. We also introduce a Grade metric that penalizes incorrect answers and permits abstention, capturing risk-sensitive performance. Results show that CGR improves Grade by abstaining when certainty remains low.