Haobo Wang

Shenzhi Yang, Guangcheng Zhu, Xing Zheng et al.

Reinforcement learning with verifiable rewards (RLVR) has proven effective in training large reasoning models (LRMs) by leveraging answer-verifiable signals to guide policy optimization, which, however, suffers from high annotation costs. To alleviate this problem, recent work has explored unsupervised RLVR methods that derive rewards solely from the model's internal consistency, such as through entropy and majority voting. While seemingly promising, these methods often suffer from model collapse in the later stages of training, which may arise from the reinforcement of incorrect reasoning patterns in the absence of external supervision. In this work, we investigate a novel semi-supervised RLVR paradigm that utilizes a small labeled set to guide RLVR training on unlabeled samples. Our key insight is that supervised rewards are essential for stabilizing consistency-based training on unlabeled samples, ensuring that only reasoning patterns verified on labeled instances are incorporated into RL training. Technically, we propose an effective policy optimization algorithm, TraPO, that identifies reliable unlabeled samples by matching their learning trajectory similarity to labeled ones. Building on this, TraPO achieves remarkable data efficiency and strong generalization on six widely used mathematical reasoning benchmarks (AIME24/25, AMC, MATH-500, Minerva, and Olympiad) and three out-of-distribution tasks (ARC-c, GPQA-diamond, and MMLU-pro). With only 1K labeled and 3K unlabeled samples, TraPO reaches 42.6% average accuracy, surpassing the best unsupervised method trained on 45K unlabeled samples (38.3%). Notably, when using 4K labeled and 12K unlabeled samples, TraPO even outperforms the fully supervised model trained on the full 45K labeled samples on all benchmarks, while using only 10% of the labeled data. The code is available via https://github.com/ShenzhiYang2000/TRAPO.

Beibei Li, Yiyuan Zheng, Beihong Jin et al.

Partial-Label Learning (PLL) is a typical problem of weakly supervised learning, where each training instance is annotated with a set of candidate labels. Self-training PLL models achieve state-of-the-art performance but suffer from error accumulation problem caused by mistakenly disambiguated instances. Although co-training can alleviate this issue by training two networks simultaneously and allowing them to interact with each other, most existing co-training methods train two structurally identical networks with the same task, i.e., are symmetric, rendering it insufficient for them to correct each other due to their similar limitations. Therefore, in this paper, we propose an asymmetric dual-task co-training PLL model called AsyCo, which forces its two networks, i.e., a disambiguation network and an auxiliary network, to learn from different views explicitly by optimizing distinct tasks. Specifically, the disambiguation network is trained with self-training PLL task to learn label confidence, while the auxiliary network is trained in a supervised learning paradigm to learn from the noisy pairwise similarity labels that are constructed according to the learned label confidence. Finally, the error accumulation problem is mitigated via information distillation and confidence refinement. Extensive experiments on both uniform and instance-dependent partially labeled datasets demonstrate the effectiveness of AsyCo. The code is available at https://github.com/libeibeics/AsyCo.