Cervical cancer is a major global health challenge, with disease burden falling disproportionately on low- and middle-income countries (LMICs) due to a shortage of trained specialists and the subjective nature of colposcopy-based screening. To address this challenge, we propose a novel deep learning framework for the automated grading of Cervical Intraepithelial Neoplasia (CIN) and the prediction of clinical Swede scores. We also introduce the BUET Multi-Center Colposcopy Dataset, a novel, multi-center cohort designed and annotated for Swede score prediction and CIN grading. Our proposed dual-stream cross-attention architecture mimics the visual reasoning of an expert colposcopist by explicitly fusing paired multimodal cervigrams to evaluate comparative tissue responses. Furthermore, we introduce a custom composite loss function to address severe class imbalances and scoring inconsistencies across the five Swede score components. The proposed framework achieved 71.85% accuracy and an 86.23% AUC-ROC for three-class CIN grading, outperforming existing methods. For Swede score component prediction, the architecture achieved AUC-ROC values ranging from 75.7% to 88.4%, with the composite loss function yielding consistent F1-score improvements. Finally, the total predicted Swede Score, which ranges between 0 and 10, shows a Mean Absolute Error (MAE) of 1.489. The results show that the proposed method can pave the way towards developing AI-assisted colposcopy screening tools to support risk-based triage in resource-limited healthcare settings. The dataset and source code are publicly available(url: https://github.com/mHealthBuet/BUET-colposcopy)

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