Self-expressiveness is a mathematical property that aims at characterizing the relationship between instances in a dataset. This property has been applied widely and successfully in computer-vision tasks, time-series analysis, and to infer underlying network structures in domains including protein signaling interactions and social-networks activity. Nevertheless, despite its potential, self-expressiveness has not been explicitly used to infer gene networks. In this article, we present Generalizable Gene Self-Expressive Networks, a new, interpretable, and generalization-aware formalism to model gene networks, and we propose two methods: GXN•EN and GXN•OMP, based respectively on ElasticNet and OMP (Orthogonal Matching Pursuit), to infer and assess Generalizable Gene Self-Expressive Networks. We evaluate these methods on four Microarray datasets from the DREAM5 benchmark, using both internal and external metrics. The results obtained by both methods are comparable to those obtained by state-of-the-art tools, but are fast to train and exhibit high levels of sparsity, which make them easier to interpret. Moreover we applied these methods to three complex datasets containing RNA-seq informations from different mammalian tissues/cell-types. Lastly, we applied our methodology to compare a normal vs. a disease condition (Alzheimer), which allowed us to detect differential expression of genes' sub-networks between these two biological conditions. Globally, the gene networks obtained exhibit a sparse and modular structure, with inner communities of genes presenting statistically significant over/under-expression on specific cell types, as well as significant enrichment for some anatomical GO terms, suggesting that such communities may also drive important functional roles.