Reinforcement Learning with Verifiable Rewards (RLVR) frequently suffers from mode collapse due to the inherent sparsity of feedback signals. While strategies such as entropy regularization introduce randomness, they lack directionality. Simply incorporating diversity rewards is overly one-sided and fails to identify potential logical errors or hallucinations. To address these limitations, we propose VANE (Value-Aligned Novelty Exploration), a method that simultaneously quantifies novelty across the outcome space (via reward or solution divergence) and the semantic process space (via semantic process divergence). Moreover, VANE employs a value-alignment mechanism that symmetrically amplifies scarce, high-quality solutions while explicitly penalizing diverse yet erroneous reasoning paths. Extensive experiments on models such as Qwen2.5-Math-7B across eight benchmarks—encompassing both large-scale mathematical reasoning and out-of-distribution (OOD) tasks—demonstrate the effectiveness and generalization of the proposed method.

Reinforcement Learning with Verifiable Rewards (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 baaselines and achieves improved out-of-distribution generalization.