Integrating side information in recommendation systems to address user feedback sparsity has gained significant research interest. However, existing models face challenges in generalization across different domains and types of side information. Specifically, two unresolved challenges are (1) the diverse formats of side information, including text sequences and numerical features, and (2) the challenge of measuring diverse correlations in side information beyond pairwise relationships. In this paper, we introduce \(\texttt {GENET} \) (Generalized hypErgraph pretraiNing on sidE informaTion), that pre-trains user and item representations on feedback-irrelevant side information and fine-tunes the representations on user feedback data. GENET utilizes pre-training to prevent side information from overshadowing critical feedback signals. It employs a hypergraph framework to accommodate various types of diverse side information. During pre-training, GENET integrates the task for hyperlink prediction by a unique strategy to enhance pre-training robustness by perturbing positive samples while maintaining high-order relations. Extensive experiments demonstrate that GENET exhibits strong generalization capabilities, outperforming the SOTA method by up to \(38\%\) in TOP-N recommendation on various datasets.