# From <Answer> to <Think>: Multidimensional Supervision of Reasoning Process for LLM Optimization

arXiv: https://arxiv.org/abs/2510.11457 · HTML: https://mlsanity.com/paper/2510.11457/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 8 of its 59 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## Placed in

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

## Builds on (most cited first, 8 of 8)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [CRUXEval: A Benchmark for Code Reasoning, Understanding and Execution](https://mlsanity.com/paper/2401.03065/) (2024)
- [QASC: A Dataset for Question Answering via Sentence Composition](https://mlsanity.com/paper/1910.11473/) (2019)
- [FlashRAG: A Modular Toolkit for Efficient Retrieval-Augmented Generation Research](https://mlsanity.com/paper/2405.13576/) (2024)
- [HelpSteer3-Preference: Open Human-Annotated Preference Data across Diverse Tasks and Languages](https://mlsanity.com/paper/2505.11475/) (2025)
- [PiCSAR: Probabilistic Confidence Selection And Ranking for Reasoning Chains](https://mlsanity.com/paper/2508.21787/) (2025)

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

- [Guided by Trajectories: Repairing and Rewarding Tool-Use Trajectories for Tool-Integrated Reasoning](https://mlsanity.com/paper/2601.23032/) (2026)
- [VeriBound: PAC-Bayesian Generalization Bounds for Process Reward Models Trained with Formal Verification Tools](https://mlsanity.com/paper/2606.20740/) (2026)
- [HoloGeo: Mitigating Landmark Bias in Geo-localization via Evidence-Driven Reasoning](https://mlsanity.com/paper/2607.15255/) (2026)

## Abstract (arXiv)

Improving the multi-step reasoning ability of Large Language Models (LLMs) is a critical yet challenging task. The dominant paradigm, outcome-supervised reinforcement learning (RLVR), rewards only correct final answers, often propagating flawed reasoning and suffering from sparse reward signals. While process-level reward models (PRMs) provide denser, step-by-step feedback, they lack generalizability and interpretability, requiring task-specific segmentation of the reasoning process. To this end, we propose the Dimension-level Reward Model (DRM), a new supervision framework that bridges the gap between these two approaches. DRM evaluates the quality of a reasoning process along three fundamental, complementary, and interpretable dimensions: Confidence for uncertainty calibration, Relevance for semantic alignment, and Coherence for logical consistency. Together, these dimensions capture aspects beyond final answer correctness and enable interpretable assessment without requiring ground truth answers. Experimental results show that DRM provides effective supervision signals, guides the optimization of LLMs and enhances their reasoning ability. In particular, DRM-supervised training achieves consistent gains on both in-distribution and out-of-distribution open-domain tasks, including mathematics, question answering, code execution, and puzzles. Our findings demonstrate that multidimensional supervision of the reasoning process can improve the generalized reasoning ability of LLMs beyond the training distribution.