# BOW: Training Language Models to Reason Over Plausible Next Words

arXiv: https://arxiv.org/abs/2506.13502 · HTML: https://mlsanity.com/paper/2506.13502/

## Key facts

- Cited by 2 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 7 of its 44 references that are in the map.
- First posted on arXiv 16 Jun 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, 7 of 7)

- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Reinforcement Pre-Training](https://mlsanity.com/paper/2506.08007/) (2025)
- [Conceptual and Unbiased Reasoning in Language Models](https://mlsanity.com/paper/2404.00205/) (2024)
- [ReasonAgain: Using Extractable Symbolic Programs to Evaluate Mathematical Reasoning](https://mlsanity.com/paper/2410.19056/) (2024)

## Built on by (most cited first, 2 of 2)

- [Evaluating Medical LLMs by Levels of Autonomy: A Survey Moving from Benchmarks to Applications](https://mlsanity.com/paper/2510.17764/) (2025)
- [Likelihood scoring for continuations of mathematical text: a self-supervised benchmark with tests for shortcut vulnerabilities](https://mlsanity.com/paper/2605.10810/) (2026)

## Abstract (arXiv)

Next-word prediction (NWP) trains language models against a single observed continuation, even though many contexts admit multiple plausible next words. Recent RL-based next-word reasoning methods make this tension explicit: they reward a model for producing a rationale that supports one context-conditioned continuation, which can turn a pre-existing preference into a confident, self-justifying trajectory. We introduce BOW, an RL framework that instead trains models to produce self-contained, neutral, and comprehensive descriptions of the plausible next-word space. The policy generates a next-word reasoning trajectory from the full context, but a frozen scorer computes the core reward from that trajectory alone, without separately receiving the context. BOW-Reg adds a lightweight breadth regularizer to this core reward to discourage premature collapse. On two model backbones, BOW remains competitive with the original models and often outperforms trained baselines across ten general reasoning benchmarks. On benchmarks testing ambiguous references and word meanings, BOW-Reg achieves the highest SharedRef correctness and the lowest HoWN-Simple single-sense collapse on both backbones. Human evaluation further shows that BOW-Reg produces broader next-word reasoning trajectories, while direct next-word-prediction evaluation shows that these trajectories remain predictive.