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An unsolved fundamental problem in biology and ecology is to predict observable traits (phenotypes) from a new genetic constitution (genotype) of an organism under environmental perturbations (e.g., drug treatment). The emergence of multiple omics data provides new opportunities but imposes great challenges in the predictive modeling of genotype-phenotype associations. Firstly, the high-dimensionality of genomics data and the lack of labeled data often make the existing supervised learning techniques less successful. Secondly, it is a challenging task to integrate heterogeneous omics data from different resources. Finally, the information transmission from DNA to phenotype involves multiple intermediate levels of RNA, protein, metabolite, etc. The higher-level features (e.g., gene expression) usually have stronger discriminative power than the lower level features (e.g., somatic mutation). To address above issues, we proposed a novel Cross-LEvel Information Transmission network (CLEIT) framework. CLEIT aims to explicitly model the asymmetrical multi-level organization of the biological system. Inspired by domain adaptation, CLEIT first learns the latent representation of high-level domain then uses it as ground-truth embedding to improve the representation learning of the low-level domain in the form of contrastive loss. In addition, we adopt a pre-training-fine-tuning approach to leveraging the unlabeled heterogeneous omics data to improve the generalizability of CLEIT. We demonstrate the effectiveness and performance boost of CLEIT in predicting anti-cancer drug sensitivity from somatic mutations via the assistance of gene expressions when compared with state-of-the-art methods.