## 2 Related Works
### Previous Work
#### 2.4.2 The Previous Method
In TT-VFDL-ST, the target task model has a separate input regarding each guest party and also a separate feature extraction part (FE part) according to each input. Each FE part is completely independent of FE parts for other inputs. Therefore, each guest party could design each FE part structure using their own strategies regardless of other guest parties. The generalized form of the target task model has a feature merging part (FM part) after each FE part. The FM part consists of dense layers only, merging multivariate features extracted from each input using each FE part. FM part structures could be generalized into three types as described in Figure 2 and Section 2.1, which are MFCMLFM, MLFM, and SLFM. FM part design might be solely handled by the host party. The host party only needs to design a submodel consisting of dense layers with strategies of combining multiple features from each guest party. The designed FM part structure inevitably falls into one of the three types we generalized in Figure 2 and Section 2.1. Ultimately, to design the target task model structure of the proposed TT-VFDL-ST, each guest party and the host party only need to concentrate on the design of each substructure of the target task model, which is each FE part for each guest party and the FM part for the host party. To design each substructure, each party could utilize knowledge cumulated during the operation of each existing service or leverage existing studies of deep learning model design for multivariate time-series analysis. If there is an existing model for multivariate time-series analysis that performs well on a single machine, that model could be set as the target task model and distributed to each party. #### 3.4.2 Distribution of the Target Task Model

To distribute the target task model to each party, we only need to concentrate on the way of the distribution of the FM part of the host party to each guest party since each FE part is designed in the independent responsibility of each guest party and not distributed to other parties. For the distribution of the FM part, the host party only needs to send the weight matrices of the FM part, which is initialized with dummy or random values, to each guest party. The purpose of sending the weight matrices of the FM part is for each guest party to be aware of the dense layer structures by parsing the shapes of the weight matrices. After parsing the shapes of the weight matrices of the FM part, each guest party could derive the Split FM structure for itself. If the host party designs the FM part as the type of MFCMLFM, the host party should send an extra flag to the guest party who is not involved in the combination input of the first layer of the FM part. With this extra information and the shape of the weight matrices of the FM part, each guest party could derive its own Split FM part and finally complete the design of the local model for the partial task training. With these distribution strategies, target task model distribution is not much affected by the volume of data held in each party or the computing capacity of each service existing in each party. The only sent data for the target task model distribution are the weight matrices of the FM part in the host party and flags for some guest parties. Also, only the shape is needed for the FM part distribution, not specific values of weight matrices. Thus, even before the merging task training stage, the host party can send the weight matrices of the FM part initialized with dummy or random values. Therefore, it is not vulnerable in terms of privacy. However, if you want to preserve even the shape of the weight matrices securely, you can encrypt the weight matrices with traditional data encryption methods. This is enough since in the proposed TT-VFDL-ST the sent weight matrices or features are not directly used in the calculation during the training loop.