<p>Most existing studies employ attention mechanisms within deep learning models to improve representational capacity, yet few provide systematic and rigorous mathematical analyses of their role in feature extraction and dynamic adaptation. In this study, we present an unsupervised cold-start recommendation method based on an Iterative Attention Mechanism (IAM) and prove its convergence under specific conditions via fixed-point theory. IAM iteratively performs similarity weighting and aggregation between user and item feature spaces, enabling self-organized evolution and progressive consolidation of user preference vectors, thereby capturing the temporal dynamics of user interests. Extensive experiments on multiple sparse datasets show that IAM optimizes feature selection, enhances salient preference representation, and achieves strong generalization, interpretability, and computational efficiency—making it highly suitable for cold-start scenarios.</p>