Beyond Variance: Prompt-Efficient RLVR via Rare-Event Amplification and Bidirectional Pairing

Reinforcement learning with verifiable rewards (RLVR) is effective for training large language models on deterministic outcome reasoning tasks. Prior work shows RLVR works with few prompts, but prompt selection is often based only on training-accuracy variance, leading to unstable optimization directions and weaker transfer. We revisit prompt selection from a mechanism-level view and argue that an effective minibatch should provide both (i) a reliable positive anchor and (ii) explicit negative learning signals from rare failures. Based on this principle, we propose \emph{positive--negative pairing}: at each update, we sample a hard-but-solvable $q^{+}$ and an easy-but-brittle prompt $q^{-}$(high success rate but not perfect), characterized by low and high empirical success rates under multiple rollouts. We further introduce Weighted GRPO, which reweights binary outcomes at the pair level and uses group-normalized advantages to amplify rare successes on $q^{+}$ into sharp positive guidance while turning rare failures on $q^{-}$ into strong negative penalties. This bidirectional signal provides informative learning feedback for both successes and failures, improving sample efficiency without suppressing exploration. On Qwen2.5-Math-7B, a single paired minibatch per update consistently outperforms a GRPO baseline that selects two prompts via commonly used variance-based selection heuristics: AIME~2025 Pass@8 improves from 16.8 to 22.2, and AMC23 Pass@64 from 94.0 to 97.0, while remaining competitive with large-scale RLVR trained from a pool of 1209 training prompts. Similar gains are observed on Qwen2.5-Math-7B-Instruct.

A Polarization and Radiomics Feature Fusion Network for the Classification of Hepatocellular Carcinoma and Intrahepatic Cholangiocarcinoma

Classifying hepatocellular carcinoma (HCC) and intrahepatic cholangiocarcinoma (ICC) is a critical step in treatment selection and prognosis evaluation for patients with liver diseases. Traditional histopathological diagnosis poses challenges in this context. In this study, we introduce a novel polarization and radiomics feature fusion network, which combines polarization features obtained from Mueller matrix images of liver pathological samples with radiomics features derived from corresponding pathological images to classify HCC and ICC. Our fusion network integrates a two-tier fusion approach, comprising early feature-level fusion and late classification-level fusion. By harnessing the strengths of polarization imaging techniques and image feature-based machine learning, our proposed fusion network significantly enhances classification accuracy. Notably, even at reduced imaging resolutions, the fusion network maintains robust performance due to the additional information provided by polarization features, which may not align with human visual perception. Our experimental results underscore the potential of this fusion network as a powerful tool for computer-aided diagnosis of HCC and ICC, showcasing the benefits and prospects of integrating polarization imaging techniques into the current image-intensive digital pathological diagnosis. We aim to contribute this innovative approach to top-tier journals, offering fresh insights and valuable tools in the fields of medical imaging and cancer diagnosis. By introducing polarization imaging into liver cancer classification, we demonstrate its interdisciplinary potential in addressing challenges in medical image analysis, promising advancements in medical imaging and cancer diagnosis.