# STFEformer: Spatial-Temporal Fusion Embedding Transformer for Traffic Flow Prediction
## 1 Introduction  
In the contemporary era of rapid urbanization, the limitations of current urban traffic management systems are becoming glaringly evident. Issues such as frequent traffic jams, ineffective congestion management, and delayed emergency response times not only hinder daily commutes but also pose significant challenges to sustainable urban development. Intelligent Transportation Systems (ITSs), as indivisible components of today's smart urban environments [1], are instrumental in analyzing, managing, and improving traffic conditions. Within the realm of ITSs, the domain of traffic flow prediction,recognized as a pivotal technology [2], has garnered extensive research attention. This research is primarily directed towards the development of predictive models that predict future traffic flow by leveraging historical data. The precise predictions generated by these models find application in a diverse array of traffic-related domains [3], encompassing route optimization, vehicular scheduling strategies, and effective congestion alleviation measures. Accurate traffic flow predictions not only improve traffic management but also contribute to broader societal benefits, such as reduced environmental pollution, significant economic savings by decreasing time spent in traffic, and enhanced quality of life through less stressful commuting experiences. Therefore, we propose a novel traffic flow prediction model designed to comprehensively explore the spatial-temporal characteristics of traffic data and achieve accurate traffic flow prediction. Predicting traffic flow represents a quintessential challenge in the realm of spatial-temporal data forecasting. Traffic data are captured at predetermined intervals and at distinct locations within a continuous spatial framework. Evidently, observations at neighboring locations and sequential time intervals are not isolated but dynamically interconnected. The principal challenge is effectively capturing and modeling the intricate spatial-temporal dependencies inherent in traffic data [4]. A multitude of studies have endeavored to develop diverse deep-learning models to tackle this task. Initially, several studies employed convolutional neural networks (CNNs) to analyze traffic data based on grid structures to capture spatial correlations [5; 6]. Subsequently, graph neural networks (GNNs) demonstrated their suitability to model underlying graph structures [7; 8]; thus, the methods based on GNNs have been extensively investigated for traffic flow prediction [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. Considering the handling of temporal correlations, these GNN models primarily fall into two categories: RNN-based and CNN-based models. RNN-based methods, utilizing RNNs and their variants, such as GRUs, capture the temporal correlations in traffic data. Approaches utilizing convolutional neural networks (CNNs) capture the temporal dependencies either through a temporal convolutional network (TCN) or a standard CNN. Details are shown in Table 1. However, RNNs face challenges in effectively learning long-term temporal dependencies, often failing to provide accurate predictions for extended time series. Similarly, CNNs are constrained by their limited receptive fields and local biases, which prevent them from capturing long-term temporal correlations. Additionally, the modeling of spatial correlations using existing GNN methods tends to be static, whereas in traffic systems, spatial dependencies between locations are highly dynamic and change over time due to diverse travel patterns and unforeseen events. Furthermore, these GNN models also suffer from over-smoothing as the network depth increases, which limits their ability to learn spatial correlations from a long-range perspective.