## 3 Network Sliced Distributed Learning
### End-to-End Functional Decomposition of DL  
As described in the previous section, different DL methods can be characterized by different sets of functions that must be implemented in distributed networks to have the proper benefits. Thus, each DL approach can be implemented as a set of functions coordinated through a chain characterized by functional dependencies. For this, an adequate functional decomposition providing a set of typical DL functions is needed. After having discussed the different learning techniques in distributed environments, here we propose a set of possible learning functions that are needed for implementing various DL methods:  
* **Data Acquisition Function (DAF):** Generally, distributed training operations involve several learning devices collaboratively performing the learning process. In the case of vehicular scenarios, this can be geographically distributed sets of vehicles moving across road networks. For the case of DL, learning devices need their own datasets to perform the training process, which can be collected through a data acquisition mechanism that involves a set of sensory nodes, processing devices, and data collection devices. The process that allows the composition of the learning dataset can be defined through a typical data acquisition function. Note that such functions can only be implemented on nodes/devices with typical hardware settings. With new vehicular nodes equipped with several sensory nodes, they can collect large amounts of data samples over time through DAF that can be exploited for a successful implementation of DL. * **Data Preprocessing Function (DPFr):** In general, the learning data acquired through DAF can be in different formats, e.g., texts, images, videos, etc. Based on the learning tasks, the selected learning method, and their requirements, these data need to be pre-processed in a typical form. This can be achieved through learning data preprocessing methods implemented through a Data Preprocessing Function (DPrF). This function can have methods for data cleaning, data dimensionality reduction, data normalization, etc. DPrF function can help reduce the overall size of the original datasets, and thus reduce the communication overhead for some typical DL methods where data parallelization techniques involving learning data transfer are needed. Thus, preferably, this function needs to be implemented alongside the DAF function to avoid possible communication overheads. * **Distributed Learning Function (DLF):** In DL frameworks, the learning process can be performed on different nodes, e.g., end devices or edge nodes, according to the learning frameworks adopted. The end devices can do the learning process themselves for some simplified learning tasks. In some cases, collaborative learning frameworks can be adopted for complex learning models such as DNN, allowing different devices to collaboratively train the models (e.g., through different model split techniques). In another case, a data parallelism approach can be adopted, allowing struggling end devices with limited computational resources to send their data to the nearby devices/edge nodes to complete the training process in time. Therefore, a distributed learning function (DLF) is needed that adopts the selected learning strategy for the successful implementation of DL. Typical learning steps, such as learning model selection, hyperparameter settings, stochastic gradient descent (SGD), and backpropagation, can be part of a holistic DLF that can be implemented on distributed nodes. * **Data Post Processing function (DPsF):** In a typical DL process, after performing the learning steps through DLF, the parameter updates must be sent to the parameter server or other learning nodes based on the adopted learning strategy. Often, data processing is needed to avoid communication overhead, limit data security risks, and add the appropriate weighting coefficients to the learning process results.