Hierarchical multi-label classification is a challenging task implying the encoding of a high level constraint in the neural network model. Before the rise of this field, the classification was done without paying attention to the hierarchical links existing between data. Nevertheless, information relating the classes and subclasses may be very useful for improving the network performances. Recently, some works have integrated the hierarchy information by proposing new neural network architectures (called B-CNN or H-CNN), achieving promising results. However with these architectures, the network is separated into blocks where each block is responsible for predicting only the classes of a given level in the hierarchy. In this paper, we propose a novel architecture such that the whole network layers are involved in the prediction of the entire labels of a sample, i.e., from its class in the top level of the hierarchy to its class in the bottom level. The proposed solution is based on a Bayesian adjustment encoding the hierarchy in terms of conditional probabilities, together with a customized semantic loss function that penalizes drastically the hierarchy violation. A teacher forcing strategy learning is used to enhance the learning quality. Thanks to this approach, we could outperform the state of the art results in terms of accuracy (improved for all levels) and also in terms of hierarchy coherence.