## 1 Introduction
However, these models exhibit limited capability in capturing the nonlinear features of traffic flow data, leading to suboptimal prediction performance. Standard models like k-nearest neighbors (KNNs) and support vector regression (SVR) also share these drawbacks. Recently, the surge in machine learning and deep learning has led to the development of various neural networks, including Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs). Models based on these neural networks have found widespread applications in traffic flow prediction. These neural network models, leveraging deep learning, outperform traditional traffic flow prediction models by effectively extracting spatial and temporal features from time-series data and modeling nonlinear, nonsmooth time series to accommodate the complex dynamics of traffic flow. Additionally, researchers have increasingly studied the Transformer-based model in recent years, demonstrating its superior long-range traffic flow prediction accuracy over prior models. Long Short-Term Memory (LSTM) [5], a Recurrent Neural Network (RNN) variant, effectively addresses the long-term dependency issue, utilizing past information for future predictions. The state has three gates to control, which can selectively store, update, and output information. Central to LSTM is a unitary state governed by three gates that selectively store, update, and output information. It excels in processing and predicting significant events within traffic flows characterized by time series, especially those with lengthy intervals and delays. However, LSTM is not ideal for long-term prediction due to its computational intensity. The Convolutional Neural Network-Long Short-Term Memory (CNN-LSTM) [6] model combines CNN and LSTM network structures to extract spatio-temporal featuresand accomplish sequence modeling. This model preprocesses original traffic flow data, inputs it into the CNN to extract spatial features, then inputs this CNN-processed data into the LSTM layer for next-moment time-series prediction, and finally applies inverse normalization to obtain the predicted value. However, akin to LSTM, this model requires substantial computational resources, and its training process is susceptible to overfitting. The advent of large-scale artificial intelligence models has spurred extensive research into the Transformer architecture. This deep learning model, predicated on the self-attention mechanism, demonstrates remarkable proficiency in processing sequential data, including text, speech, and images. The Transformer architecture differs from traditional RNN and CNN structures, relying solely on the self-attention mechanism to discern sequence dependencies. The Transformer offers significant advantages, including parallel computation capabilities that enhance training speed and the ability to learn long-distance dependencies, thereby yielding superior outcomes for extensive time-series data. In recent years, extensive scholarly attention has been directed toward the Transformer architecture, resulting in the proposition of numerous enhanced models. These include the Autoformer [7], ETSformer [8], and FEDformer [9], among others. However, these Transformer model variants are computationally intensive and characterized by complex parameters, leading to significant memory usage and computational resource consumption. The GBT (Two-stage Transformer) [10] addresses the critical issue of overfitting associated with improper decoder input initialization by innovatively dividing the traditional Transformer architecture into two segments: the Auto-Regression and Self-Regression stages. This approach enables the model to enhance its predictive capacity while maintaining low temporal and spatial complexity. The quality and characteristics of input data significantly influence the accuracy and efficiency of predictive models, which are crucial for the models' performance.