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    <abstract>Reinforcement Learning with Verifiable Rewards (RLVR) has substantially improved mathematical reasoning, yet progress on hard prompts often stalls: a prompt can remain unsolved for many training steps before abruptly transitioning to solved—a discrete “zero-to-one” jump whose underlying dynamics and steerability remain poorly understood. We investigate two questions: what drives this transition, and can it be steered? Through event-based analysis measuring the time-to-first-positive (TTFP), we find that negative rollouts preceding successful transitions consistently retain higher early-stage generation entropy, distinguishing near-solvable failures from dead ends. This signal motivates NAPO (Negative-Augmented Policy Optimization), a method integrated with Group Relative Policy Optimization (GRPO) that ranks negatives in unsolved groups via an early-branching driver and assigns graded advantages, injecting informative gradients precisely where standard group-relative updates vanish. Under fixed rollout budgets, NAPO accelerates early solution discovery and improves Pass@256 by 10.0 points on AIME24 and 6.6 points on AIME2025, demonstrating that zero-to-one transitions are diagnosable and steerable through driver-guided negative learning. Our code is available at https://github.com/jameszhu-pixel-time/Z2O.</abstract>
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%0 Conference Proceedings
%T What Drives the Zero-to-One Jump? Diagnosing and Steering Hard-Prompt Learning in RLVR
%A Zhu, Rui
%A Liu, Yumou
%A Zheng, Zhenzhe
%A Wu, Fan
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F zhu-etal-2026-drives
%X Reinforcement Learning with Verifiable Rewards (RLVR) has substantially improved mathematical reasoning, yet progress on hard prompts often stalls: a prompt can remain unsolved for many training steps before abruptly transitioning to solved—a discrete “zero-to-one” jump whose underlying dynamics and steerability remain poorly understood. We investigate two questions: what drives this transition, and can it be steered? Through event-based analysis measuring the time-to-first-positive (TTFP), we find that negative rollouts preceding successful transitions consistently retain higher early-stage generation entropy, distinguishing near-solvable failures from dead ends. This signal motivates NAPO (Negative-Augmented Policy Optimization), a method integrated with Group Relative Policy Optimization (GRPO) that ranks negatives in unsolved groups via an early-branching driver and assigns graded advantages, injecting informative gradients precisely where standard group-relative updates vanish. Under fixed rollout budgets, NAPO accelerates early solution discovery and improves Pass@256 by 10.0 points on AIME24 and 6.6 points on AIME2025, demonstrating that zero-to-one transitions are diagnosable and steerable through driver-guided negative learning. Our code is available at https://github.com/jameszhu-pixel-time/Z2O.
%U https://aclanthology.org/2026.emnlp-main.1821/
%P 41504-41520

Markdown (Informal)

[What Drives the Zero-to-One Jump? Diagnosing and Steering Hard-Prompt Learning in RLVR](https://aclanthology.org/2026.emnlp-main.1821/) (Zhu et al., EMNLP 2026)

• What Drives the Zero-to-One Jump? Diagnosing and Steering Hard-Prompt Learning in RLVR (Zhu et al., EMNLP 2026)

ACL

• Rui Zhu, Yumou Liu, Zhenzhe Zheng, and Fan Wu. 2026. What Drives the Zero-to-One Jump? Diagnosing and Steering Hard-Prompt Learning in RLVR. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 41504–41520, Budapest, Hungary. Association for Computational Linguistics.