## 1 Introduction  
As various IoT services based on big data and deep learning technologies emerge, the importance of cross-service distributed learning techniques for multivariate deep learning models on IoT time-series data collected from diverse sources is increasing. This is because extended IoT services can be developed through training of a multivariate deep learning model that analyzes the combined IoT time-series dataset from existing services. However, sharing raw data of existing services to distributedly train this multivariate deep learning model is vulnerable in terms of security. Therefore, it is important to develop techniques for distributed learning of multivariate deep learning models for existing services without sharing the raw data of them. Using vertical federated deep learning (VFDL) methods, we can train a deep learning model for multivariate IoT time-series data distributed across services. VFDL methods are techniques for distributed learning of deep learning models based on vertically partitioned data architectures, where features are distributed [1]. We classified various existing VFDL methods into two categories from the design approach perspective. Existing VFDL methods are based on training loop parallelization approaches, typically Split Learning [2], or data-driven transfer approaches, typically [3], that utilize a transfer learning mechanism which transfers data-driven features trained by unsupervised representation learning. The mechanism of the latest VFDL methods [4, 5], which is generally applicable to vertically partitioned multivariate IoT time-series data distributed across services, rather than targeting only security vulnerabilities [6] or specific neural network structures [7], is based on one of the two design approaches we classified. However, existing VFDL methods still have limitations when applied to multivariate IoT time-series data distributed by service. The design strategy of the training loop parallelization approach is to train task-driven features by parallelizing forward and back propagation. Because existing VFDL methods of the training loop parallelization approach parallelize forward and back propagation, a large communication amount is required, but because they train task-driven features, it shows similar performance, that is accuracy or MSE, to centralized training. On the other hand, the design strategies of the data-driven transfer approach are to train data-driven features using unsupervised representation learning and design a distributed learning mechanism based on the transfer learning mechanism to transfer the data-driven features. The existing VFDL methods of the data-driven transfer approach are very communication-efficient. This is because they use a transfer learning mechanism to design their distributed learning mechanism where each parallelization unit has a separate training loop. But because they train data-driven features, it shows relatively low performance, that is accuracy or MSE, in centralized training, especially in the IoT domain. The purpose of this study is to propose a new design approach for vertical federated deep learning mechanisms suitable to the characteristics of the IoT domain. The limitations of existing VFDL methods are because the design strategies for the mechanism of each VFDL method do not sufficiently reflect the characteristics of IoT time-series data. Vertically partitioned IoT time-series data are typically big data distributed across services or data silos. In other words, because the design of a communication-efficient vertical federated deep learning mechanism is necessary, we design a distributed learning mechanism based on transfer learning, similar to the data-driven transfer approach. Meanwhile, even if it is the same type of sensor data, the characteristics that need to be focused on are different depending on the target task. That is, because the target task is more important than data characteristics in the IoT domain, we utilize the task-driven transfer approach rather than the data-driven approach.