# Beyond Token-level Supervision: Unlocking the Potential of Decoding-based Regression via Reinforcement Learning

arXiv: https://arxiv.org/abs/2512.06533 · HTML: https://mlsanity.com/paper/2512.06533/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Interpretable and logic-guided RL, one of 15 directions in Deep reinforcement learning methods.
- Builds on 77 of its 107 references that are in the map.
- First posted on arXiv 6 Dec 2025.

## Placed in

- Deep reinforcement learning methods / [Interpretable and logic-guided RL](https://mlsanity.com/deeprl/interpretable-and-logic-guided-rl/)

## Builds on (most cited first, 30 of 77)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Transformers Can Do Bayesian Inference](https://mlsanity.com/paper/2112.10510/) (2021)
- [Inference-Time Scaling for Generalist Reward Modeling](https://mlsanity.com/paper/2504.02495/) (2025)
- [CodeNet: A Large-Scale AI for Code Dataset for Learning a Diversity of Coding Tasks](https://mlsanity.com/paper/2105.12655/) (2021)
- [ReMax: A Simple, Effective, and Efficient Reinforcement Learning Method for Aligning Large Language Models](https://mlsanity.com/paper/2310.10505/) (2023)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [Generative Reward Models](https://mlsanity.com/paper/2410.12832/) (2024)
- [Stop Regressing: Training Value Functions via Classification for Scalable Deep RL](https://mlsanity.com/paper/2403.03950/) (2024)

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

- [Reinforcement Learning over Predictive Distributions for LLM Regression](https://mlsanity.com/paper/2605.20740/) (2026)

## Abstract (arXiv)

Decoding-based regression, which reformulates regression as a sequence generation task, has emerged as a promising paradigm of applying large language models for numerical prediction. However, its progress is hindered by the misalignment between discrete token-level objectives (e.g., cross-entropy) and continuous numerical values. Existing approaches relying on token-level constraints often fail to capture the global magnitude of the target value, limiting their precision and generalization. In this paper, we propose to unlock the potential of decoding-based regression via Reinforcement Learning (RL). We formulate the generation process as a Markov Decision Process, utilizing sequence-level rewards to enforce global numerical coherence. Extensive experiments on tabular regression and code metric regression demonstrate that our method (specifically with ReMax and GRPO) consistently outperforms both state-of-the-art token-level baselines and traditional regression heads, showing the superiority of introducing sequence-level signals. Our analysis further reveals that RL significantly enhances sampling efficiency and predictive precision, establishing decoding-based regression as a robust and accurate paradigm for general-purpose numerical prediction.