## 2 Backgrounds
### Existing Vertical Federated Deep Learning (VFDL) Methods
#### 2.4.1 Training Loop Parallelization Approach  
Most of the existing VFDL methods based on the training loop parallelization approach split the target task model and parallelize forward propagation and back propagation based on the split submodels [2; 11; 12; 13; 14; 15]. On the other hand, [14; 15] defines a final loss that aggregates the training results of each party and parallelizes forward propagation and back propagation based on this. However, in all VFDL methods based on the training loop parallelization approach, communication occurs at every step of the training loop. As a  
Figure 2: Training mechanism of proposed TT-VFDL-SIM and other comparison methods: CNTR is a centralized training mechanism. TT-VFDL-SIM and other comparison methods perform VFDL on a deep learning model with the same structure as CNTR. P-VFDL-SL is a Split Learning mechanism, one of the representative VFDL methods using the training loop parallelization approach. P-VFDL-SLG is Split Learning with a local gradient update mechanism added. DT-VFDL-AE is based on a data-driven transfer approach using unsupervised representation learning. TT-VFDL-SIM is based on our task-driven transfer approach. The blue arrows are the communication from each guest party to the host party, and the red arrows are the communication from the host party to each guest party.  
result, the amount of communication required for distributed learning is very large, and research is also being conducted to reduce the amount of communication, such as in [26].  
Most VFDL methods based on the training loop parallelization approach leverage Split Learning [2]. In Split Learning, the target task model is split based on the set cut layer. Then, forward propagation and back propagation are parallelized based on this cut layer. Communication required for distributed learning also occurs at the cut layer. Several existing VFDL methods are based on Split Learning [11; 12; 13]. Some methods applied Split Learning to a federated healthcare service scenario based on a completely distributed architecture [11]. There are some methods that applied Split Learning to a VFDL scenario based on an active/passive party architecture [12; 13]. In addition to vertical federated learning scenarios, Split Learning can also be applied to horizontal federated learning scenarios [16; 27] or hybrid architectures [28; 29].  
P-VFDL-SL in Figure 2 applies Split Learning [2] to the vertical federated learning scenario for multivariate IoT time-series analysis. First, each guest party forward propagates its own submodel (FE part) consisting of all layers from the input layer to the cut layer. Then, the features of each cut layer are sent to the host party. The host party completes forward propagation for its submodel (FM part) based on the received features and calculates the loss at the output layer. The host party starts back propagation based on this loss. To complete parallelized back propagation, the host party transmits the gradient calculated at the cut layer to each guest party. P-VFDL-SLG is an implementation of [16] that added a local gradient update mechanism to improve the performance of Split Learning. It was originally a technique for horizontal federated learning scenarios but was implemented as P-VFDL-SLG to fit the VFDL scenario for multivariate IoT time-series data.