## 1 Introduction  
After entering the 21 st century, the issue of \(PM_{2.5}\) has become increasingly severe and garnered significant attention [1]. Especially in urban regions, \(PM_{2.5}\) significantly affects human health, economic development, and social progress [2]. The prediction of \(PM_{2.5}\) concentrations can assist in better tackling urban air quality issues. Following the production of accurate urban \(PM_{2.5}\) estimations, the relevant authorities can implement more powerful strategies, such as regulating industrial production and issuing travel warnings [3, 4]. Currently, many urban \(PM_{2.5}\) forecasting methods are being developed, and some of them, relying on deep learning technologies, can accomplish high-precision prediction. Unfortunately, most researchers train their models on a central cloud [5, 6]. For instance, [PERSON] et al. [6] deployed a deep-learning-based method DAQFF on the central cloud for air pollution prediction using two real-world datasets. Experimental results proved that DAQFF achieved satisfactory prediction accuracy. As the number of monitoring sites increases and the volume of collected data sharply rises, massive amounts of data and computational tasks are uploaded to the server, which leads to two issues: (1) This can put tremendous computational pressure on the central cloud, manifested by extended training times and high GPU memory usage. Hence, it is difficult to achieve timely prediction. For instance, in some large-scale air pollution predictions, i.e., with a large number of sensors, the central cloud typically takes approximately 30 min to complete an epoch of training. (2) We store all data on this server, thus creating a greater security risk [7; 8; 9]. The main reason for this is that the central cloud typically consolidates a large volume of data. In the event of a data leakage, this could lead to incalculable losses. External factors, e.g., wind speed, temperature, precipitation, humidity, etc., have a significant impact on changes in urban \(PM_{2.5}\). For instance, temperature influences the atmosphere and ventilation states. The deposition of particulate matter is affected by precipitation and humidity. High wind speeds accelerate the diffusion of particulate matter [10; 11; 12]. However, the existing models neglect these external features or adopt equal weights for various external features when integrating them into prediction approaches [13; 14; 15; 16]. For instance, [PERSON] et al. [15] fused meteorological factors with air pollution data through direct summation in air pollution prediction. As a result, these methods fail to adaptively capture different impacts of diverse external features. It is challenging to develop an adaptive mechanism to extract the different impacts originating from external factors. One main reason exists: it is nontrivial to quantify the effects of external factors on urban \(PM_{2.5}\) and assign weights when integrating them with forecasting approaches. In summary, two urgent issues need solutions in urban \(PM_{2.5}\) forecasting: (1) Dealing with massive amounts of data on a central cloud generates huge computational pressures and security risks. (2) The different impacts caused by various external features on urban \(PM_{2.5}\) cannot be adaptively extracted. To tackle these issues, we present a novel federated deep learning network entitled FedDeep for multi-urban \(PM_{2.5}\) forecasting. FedDeep is inspired by horizontal federated learning. In particular, we first deploy an edge computing server (ECS) [17] separately in each urban region. The data collected by the sensors within the urban region are sent to the corresponding ECS. Leveraging the ability of edge computing and data caching, the computing pressure on the central cloud can be effectively alleviated through deploying an ECS adjacent to the source of data generation. Meanwhile, data leakage on the central cloud can be circumvented.