Emerging cross-device artificial intelligence (AI) applications require a transition from conventional centralized learning systems toward large-scale distributed AI systems that can collaboratively perform complex learning tasks. In this regard, democratized learning (Dem-AI) lays out a holistic philosophy with underlying principles for building large-scale distributed and democratized machine learning systems. The outlined principles are meant to study a generalization in distributed learning systems that go beyond existing mechanisms such as federated learning (FL). Moreover, such learning systems rely on hierarchical self-organization of well-connected distributed learning agents who have limited and highly personalized data and can evolve and regulate themselves based on the underlying duality of specialized and generalized processes. Inspired by Dem-AI philosophy, a novel distributed learning approach is proposed in this article. The approach consists of a self-organizing hierarchical structuring mechanism based on agglomerative clustering, hierarchical generalization, and corresponding learning mechanism. Subsequently, hierarchical generalized learning problems in recursive forms are formulated and shown to be approximately solved using the solutions of distributed personalized learning problems and hierarchical update mechanisms. To that end, a distributed learning algorithm, namely DemLearn, is proposed. Extensive experiments on benchmark MNIST, Fashion-MNIST, FE-MNIST, and CIFAR-10 datasets show that the proposed algorithm demonstrates better results in the generalization performance of learning models in agents compared to the conventional FL algorithms. The detailed analysis provides useful observations to further handle both the generalization and specialization performance of the learning models in Dem-AI systems.