## 1 Introduction
Convolution neural network (CNN), recurrent neural network (RNN), and self-attention network are three renowned neural network architectures adept at effectively processing time series data [27]. CNN can extract high-dimensional features from RS data's spatial and temporal domains for crop recognition [28; 29; 30]. [PERSON] et al. [20] extracted the temporal feature from MODIS NDVI time series data using CNN and LSTM classifiers to identify the 14 categories of crops in the San Joaquin Valley, California. RNN observes the connected neurons to learn the time sequence relationship and performs better in processing time series data. LSTM is a variant of RNN that shows long-term temporal dependence by incorporating a gate control mechanism [31]. To further improve the temporal feature extraction of the LSTM model, the bi-directional flow method is introduced to form BiLSTM [32]. [PERSON] et al. [33] combined ARD data, Landsat 7 Enhanced Thematic Mapper Plus, Landsat8 Operational Land Imager data, and the DCM classifier to identify the main crops in six study sites. Based on the deep learning algorithm, [PERSON] et al. [29] and [PERSON] et al. [34] combined the multi-temporal images to extract features with 1D convolution and RNN classification algorithms for land cover classification in Ukraine and crop classification, respectively. In 2017, the self-attention mechanism was proposed for analyzing sequences in natural language processing [35]. It facilitates parallel feature extraction from super-long sequences and achieves excellent recognition results. [PERSON] and [PERSON] [36] used the self-attention classification method to identify the crop type. With the aim of improving the efficacy of deep learning models, many strategies have emerged. Based on the CIFAR-10 and CIFAR-100 datasets, [PERSON] et al. [37] and [PERSON] et al. [38] combined the Snapshot and SWA strategies with the DenseNet and ResNet-164 network for image identification, and the results showed that, compared to the single model, Snapshot's performance was improved by 0.34% and 1.84% and, compared with the SGD optimization algorithm, SWA's performance was enhanced by 0.61% and 1.86%, respectively. The combination of multi-temporal satellite data with a deep learning model for identifying crop types has been widely used, and favorable results have been obtained. [PERSON] et al. [39] combined NDVI time series, textural, and phenological features from Sentinel-2 data with an artificial neural network (ANN) for multiple-crop identification in North China; However, the accuracy and kappa coefficient failed to exceed 80% and 0.7, respectively. [PERSON] et al. [40] proposed an object-based convolutional neural network (TS-OCNN) combined with UAVSAR images for multiple-crop classification at two stations in the Sacramento Valley, with an accuracy of 81.63% and 85.88%, respectively. [PERSON] et al. [7] used EVI time series with phenology information for corn identification, achieving an accuracy of over 85% and an R\({}^{2}\) value of 0.81 at the city level. However, there are still two problems in the above research. Firstly, the study with higher accuracy only identified a single crop or small-large area. In addition, the model's accuracy is worse with multiple-crop classification. Hence, the potential and performance of this method for identifying multiple-crop areas have not been fully exploited. Developing deep learning models suitable for multiple-crop areas by comparing them to PB-Transformer is necessary to assess the latter's potential and capabilities. Overall, mapping multiple-crop spatial distribution is crucial for national food security. Nevertheless, most existing studies on multiple-crop identification were conducted with single crops or unsatisfying results. This study aims to develop a pixel-based deep learning algorithm that is adaptable to the multi-temporal data from the MODIS satellite for classifying multi-crop cultivation areas in North China.