Federated learning (FL) achieves collaborative learning without the need for data sharing, thus preventing privacy leakage. To extend FL into a fully decentralized algorithm, researchers have applied distributed optimization algorithms to FL by considering machine learning (ML) tasks as parameter optimization problems. Conversely, the consensus-based multi-hop federated distillation (CMFD) proposed in the authors' previous work makes neural network (NN) models get close with others in a function space rather than in a parameter space. Hence, this study solves two unresolved challenges of CMFD: (1) communication cost reduction and (2) visualization of model convergence. Based on a proposed dynamic communication cost reduction method (DCCR), the amount of data transferred in a network is reduced; however, with a slight degradation in the prediction accuracy. In addition, a technique for visualizing the distance between the NN models in a function space is also proposed. The technique applies a dimensionality reduction technique by approximating infinite-dimensional functions as numerical vectors to visualize the trajectory of how the models change by the distributed learning algorithm.