Turning Failures into Value: Negative Experience Replay for RLVR via Confidence Gating and Boundary Failure Sampling

Reinforcement Learning with Verifiable Re-wards (RLVR) has become the standard paradigm for enhancing reasoning capabilities in Large Language Models, yet on-policy algorithms like GRPO suffer from sample inefficiency. Current experience replay methods for RLVR typically replay correct trajectories to consolidate learned reasoning patterns and accelerate convergence, but overlook the vast failure space. This work investigates how to effectively replay failure trajectories. We find that the high heterogeneity of failures renders random replay ineffective, and that high-value negatives should be both gradient-efficient and structurally proximal to correct solutions. To this end, we propose NexGRPO, which employs mid-confidence gating to filter invalid noise and saturated errors, and utilizes boundary failure sampling to retrieve boundary errors semantically similar to correct solutions for targeted refinement. Extensive experiments on mathematical and general reasoning benchmarks demonstrate that NexGRPO outperforms strong baselines and achieves improved out-of-distribution generalization.