BOW: Training Language Models to Reason Over Plausible Next Words

arXiv:2506.13502 · cs.CL · Submitted 2025-06-16 · Read on arXiv

cs.CL

Submitted: 2025-06-16

Updated: 2026-08-31

Code: https://github.com/huggingface/Math-Verify

Terminology

• Core — 91× in this paper · explained in 2 episodes
• Benchmark — 26× in this paper · explained in 2 episodes
• Ablation — 4× in this paper · explained in 1 episode
• Consistency — 4× in this paper · explained in 3 episodes
• Regularization — 4× in this paper · explained in 3 episodes
• Robustness — 4× in this paper · explained in 5 episodes
• Verification — 4× in this paper · explained in 2 episodes
• Adaptation — 3× in this paper · explained in 1 episode
• Credit assignment — 3× in this paper · explained in 3 episodes
• GRPO — 3× in this paper · explained in 6 episodes
• Self-consistency — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Emergency Department — 2× in this paper
• Reinforcement Pre-Training — 2× in this paper
• Trace — 2× in this paper · explained in 2 episodes
• Transformer — 2× in this paper · explained in 2 episodes
• Abstention — 1× in this paper · explained in 1 episode
• Abstraction — 1× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• BinaryReward RL — 1× in this paper
• Evaluation Dimensions — 1× in this paper · explained in 3 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Generative AI — 1× in this paper · explained in 2 episodes
• Grouped Relative Policy Optimization — 1× in this paper
• Hallucination — 1× in this paper · explained in 3 episodes
• Information-Gain RL — 1× in this paper
• Large Language Models (LLMs) — 1× in this paper · explained in 6 episodes
• Multi-hop Reasoning — 1× in this paper · explained in 3 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes
• Transfer Learning — 1× in this paper · explained in 10 episodes

Sources

• Reinforcement Pre-Training
• Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge
• Proximal Policy Optimization Algorithms
• DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
• Conceptual and Unbiased Reasoning in Language Models
• Qwen2.5 Technical Report
• ReasonAgain: Using Extractable Symbolic Programs to Evaluate Mathematical Reasoning

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