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Reconfigurable intelligent surface (RIS) can significantly enhance the service coverage of Tera-Hertz massive multiple-input multiple-output (MIMO) communication systems. However, obtaining accurate high-dimensional channel state information (CSI) with limited pilot and feedback signaling overhead is challenging, severely degrading the performance of conventional spatial division multiple access. To improve the robustness against CSI imperfection, this paper proposes a deep learning (DL)-based rate-splitting multiple access (RSMA) scheme for RIS-aided Tera-Hertz multi-user MIMO systems. Specifically, we first propose a hybrid data-model driven DL-based RSMA precoding scheme, including the passive precoding at the RIS as well as the analog active precoding and the RSMA digital active precoding at the base station (BS). To realize the passive precoding at the RIS, we propose a Transformer-based data-driven RIS reflecting network (RRN). As for the analog active precoding at the BS, we propose a match-filter based analog precoding scheme considering that the BS and RIS adopt the LoS-MIMO antenna array architecture. As for the RSMA digital active precoding at the BS, we propose a low-complexity approximate weighted minimum mean square error (AWMMSE) digital precoding scheme. Furthermore, for better precoding performance as well as lower computational complexity, a model-driven deep unfolding active precoding network (DFAPN) is also designed by combining the proposed AWMMSE scheme with DL. Then, to acquire accurate CSI at the BS for the investigated RSMA precoding scheme to achieve higher spectral efficiency, we propose a CSI acquisition network (CAN) with low pilot and feedback signaling overhead, where the downlink pilot transmission, CSI feedback at the user equipments (UEs), and CSI reconstruction at the BS are modeled as an end-to-end neural network based on Transformer.