Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an effective approach for improving the reasoning abilities of large language models (LLMs). The Group Relative Policy Optimization (GRPO) family has demonstrated strong performance in training LLMs with RLVR. However, as models train longer and scale larger, more training prompts become residual prompts, those with zero variance rewards that provide no training signal. Consequently, fewer prompts contribute to training, reducing diversity and hindering effectiveness. To fully exploit these residual prompts, we propose the Explore Residual Prompts in Policy Optimization (ERPO) framework, which encourages exploration on residual prompts and reactivates their training signals. ERPO maintains a history tracker for each prompt and adaptively increases the sampling temperature for residual prompts that previously produced all correct responses. This encourages the model to generate more diverse reasoning traces, introducing incorrect responses that revive training signals. Empirical results on the Qwen2.5 series demonstrate that ERPO consistently surpasses strong baselines across multiple mathematical reasoning benchmarks.

Soft prompt tuning techniques have recently gained traction as an effective strategy for the parameter-efficient tuning of pretrained language models, particularly minimizing the required adjustment of model parameters. Despite their growing use, achieving optimal tuning with soft prompts, especially for smaller datasets, remains a substantial challenge. This study makes two contributions in this domain: (i) we introduce SuperPos-Prompt, a new reparameterization technique employing the superposition of multiple pretrained vocabulary embeddings to improve the learning of soft prompts. Our experiments across several GLUE and SuperGLUE benchmarks consistently highlight SuperPos-Prompt's superiority over Residual Prompt tuning, exhibiting an average score increase of $+6.4$ in T5-Small and $+5.0$ in T5-Base along with a faster convergence. Remarkably, SuperPos-Prompt occasionally outperforms even full fine-tuning methods. (ii) Additionally, we demonstrate enhanced performance and rapid convergence by omitting dropouts from the frozen network, yielding consistent improvements across various scenarios and tuning methods.

While prompt tuning approaches have achieved competitive performance with high efficiency, we observe that they invariably employ the same initialization process, wherein the soft prompt is either randomly initialized or derived from an existing embedding vocabulary. In contrast to these conventional methods, this study aims to investigate an alternative way to derive soft prompt. Our empirical studies show that the soft prompt typically exhibits a low intrinsic rank characteristic. With such observations, we propose decomposed prompt tuning, a novel approach that utilizes low-rank matrices to initialize the soft prompt. Through the low-rank reparameterization, our method significantly reduces the number of trainable parameters while maintaining effectiveness. Experimental results on the SuperGLUE benchmark in both high-resource and low-resource scenarios demonstrate the effectiveness of the proposed method.