On-policy distillation (OPD) provides dense token-level supervision by asking a teacher to score student-generated rollouts. However, when the student drifts into an unrecoverable prefix, the teacher may locally agree with the degraded state, producing low reverse KL but little corrective training signal. We identify this persistent regime as a low-KL agreement trap. Further analyses show that tokens during and after such traps produce less useful supervision signals. We propose KAT (KL Agreement Trap Termination), an online OPD termination rule that detects persistent low-KL agreement with a dynamic training-adaptive threshold. By filtering weak supervision from degenerate agreement, KAT improves avg@k accuracy by 2.66% and pass@k by 3.43% across four mathematical benchmarks, while reducing average rollout length by 59.73%.

Though big progress in table-to-text works, effectively leveraging table structure signals, e.g., hierarchical structure, remains challenging. Besides, deliberating generated descriptions proves to be effective for table-to-text. However, determining the appropriate outcome when encountering multi-pass candidates is another challenge. To this end, we propose a novel table-to-text approach on top of Self-evaluated multi-pass Generation and Heterogenous Multidominance Attention, namely SG-HMA. Specifically, we formulate the table structure into a multidominance (MD) structure and devise a heterogenous multidominance attention (HMA) to comprehensively explore the complex interactions encoded in the hierarchical structure, which can further deliver rich signals for text generation with the help of pre-trained language models (PLMs). Afterward, a contrastive loss is introduced to align the generation objective with evaluation metrics, so the more faithful generated descriptions can be guaranteed. We conduct extensive experiments on three public datasets, demonstrating that SG-HMA outperforms several SOTA methods quantitatively and qualitatively.