Cascade processes have been proven useful in modeling such diverse phenomena as epidemic spreading, signaling in biological networks, information propagation in social media, financial systemic risk, and the reorganization of international trade networks. In this talk, we will focus on two specific model classes and abstract them within a deep learning framework. We will leverage the fact that load redistribution models correspond one-to-one to the evaluation of deep neural networks. Based on analytic insights for random graph ensembles, we will derive successful initialization strategies that speed up deep learning and improve the generalization ability of the resulting models. We will further discuss how we can utilize these advancements for the inference of gene regulatory networks.