# Calibrated Reasoning: An Explanatory Verifier for Dynamic and Efficient Problem-Solving

arXiv: https://arxiv.org/abs/2509.19681 · HTML: https://mlsanity.com/paper/2509.19681/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 26 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 20 of 20)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [Inference-Time Scaling for Generalist Reward Modeling](https://mlsanity.com/paper/2504.02495/) (2025)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [TACO: Topics in Algorithmic COde generation dataset](https://mlsanity.com/paper/2312.14852/) (2023)
- [RLEF: Grounding Code LLMs in Execution Feedback with Reinforcement Learning](https://mlsanity.com/paper/2410.02089/) (2024)
- [AceReason-Nemotron: Advancing Math and Code Reasoning through Reinforcement Learning](https://mlsanity.com/paper/2505.16400/) (2025)
- [LeetCodeDataset: A Temporal Dataset for Robust Evaluation and Efficient Training of Code LLMs](https://mlsanity.com/paper/2504.14655/) (2025)
- [xVerify: Efficient Answer Verifier for Reasoning Model Evaluations](https://mlsanity.com/paper/2504.10481/) (2025)
- [VerifyBench: A Systematic Benchmark for Evaluating Reasoning Verifiers Across Domains](https://mlsanity.com/paper/2507.09884/) (2025)
- [TinyV: Reducing False Negatives in Verification Improves RL for LLM Reasoning](https://mlsanity.com/paper/2505.14625/) (2025)
- [Search, Verify and Feedback: Towards Next Generation Post-training Paradigm of Foundation Models via Verifier Engineering](https://mlsanity.com/paper/2411.11504/) (2024)
- [Putting the Value Back in RL: Better Test-Time Scaling by Unifying LLM Reasoners With Verifiers](https://mlsanity.com/paper/2505.04842/) (2025)
- [Scaling Flaws of Verifier-Guided Search in Mathematical Reasoning](https://mlsanity.com/paper/2502.00271/) (2025)

## Built on by (most cited first, 1 of 1)

- [C-Instrument: Automating RL Data Generation and Hillclimbing with a Constitution-Grid Instrument](https://mlsanity.com/paper/2608.00180/) (2026)

## Abstract (arXiv)

Advanced test-time computing strategies are essential for scaling reasoning models, but their effectiveness is capped by the models' poor self-evaluation. We propose a pairwise Explanatory Verifier, trained via reinforcement learning (GRPO), that produces calibrated confidence scores and associated natural language reasoning for generated solutions. Our verifier improves the accuracy and efficiency of test-time strategies like best-of-n and self-reflection. Crucially, it excels at identifying challenging failure modes, such as when both candidate solutions are identically incorrect, succeeding where standard methods like majority voting fail.