This article proposes a communication-efficient decentralized deep learning algorithm, coined layer-wise federated group ADMM (L-FGADMM). To minimize an empirical risk, every worker in L-FGADMM periodically communicates with two neighbors, in which the periods are separately adjusted for different layers of its deep neural network. A constrained optimization problem for this setting is formulated and solved using the stochastic version of GADMM proposed in our prior work. Numerical evaluations show that by less frequently exchanging the largest layer, L-FGADMM can significantly reduce the communication cost, without compromising the convergence speed. Surprisingly, despite less exchanged information and decentralized operations, intermittently skipping the largest layer consensus in L-FGADMM creates a regularizing effect, thereby achieving the test accuracy as high as federated learning (FL), a baseline method with the entire layer consensus by the aid of a central entity.