Reinforcement learning with verifiable rewards (RLVR) is a promising approach for improving the complex reasoning abilities of large language models (LLMs). However, current RLVR methods face two significant challenges: the near-miss reward problem, where a small mistake can invalidate an otherwise correct reasoning process, greatly hindering training efficiency; and exploration stagnation, where models tend to focus on solutions within their ”comfort zone”, lacking the motivation to explore potentially more effective alternatives. To address these challenges, we propose StepHint, a novel RLVR algorithm that utilizes multi-level stepwise hints to help models explore the solution space more effectively. StepHint partitions valid reasoning chains into reasoning steps using our proposed adaptive partitioning method. The initial few steps are used as hints, and simultaneously, multiple-level hints (each comprising a different number of steps) are provided to the model. This approach directs the model’s exploration toward a promising solution subspace while preserving its flexibility for independent exploration. By providing hints, StepHint mitigates the near-miss reward problem, thereby improving training efficiency. Additionally, the external reasoning pathways help the model develop better reasoning abilities, enabling it to move beyond its ”comfort zone” and mitigate exploration stagnation. StepHint outperforms competitive RLVR enhancement methods across six mathematical benchmarks and two out-of-domain benchmarks.

On the WikiSQL benchmark, most methods tackle the challenge of text-to-SQL with predefined sketch slots and build sophisticated sub-tasks to fill these slots. Though achieving promising results, these methods suffer from over-complex model structure. In this paper, we present a simple yet effective approach that enables auto-regressive sequence-to-sequence model to robust text-to-SQL generation. Instead of formulating the task of text-to-SQL as slot-filling, we propose to train sequence-to-sequence model with Schema-aware Denoising (SeaD), which consists of two denoising objectives that train model to either recover input or predict output from two novel erosion and shuffle noises. These model-agnostic denoising objectives act as the auxiliary tasks for structural data modeling during sequence-to-sequence generation. In addition, we propose a clause-sensitive execution guided (EG) decoding strategy to overcome the limitation of EG decoding for generative model. The experiments show that the proposed method improves the performance of sequence-to-sequence model in both schema linking and grammar correctness and establishes new state-of-the-art on WikiSQL benchmark. Our work indicates that the capacity of sequence-to-sequence model for text-to-SQL may have been under-estimated and could be enhanced by specialized denoising task.