Extremely large-scale reconfigurable intelligent surface (XL-RIS) has recently been proposed and is recognized as a promising technology that can further enhance the capacity of communication systems and compensate for severe path loss . However, the pilot overhead of beam training in XL-RIS-assisted wireless communication systems is enormous because the near-field channel model needs to be taken into account, and the number of candidate codewords in the codebook increases dramatically accordingly. To tackle this problem, we propose two deep learning-based near-field beam training schemes in XL-RIS-assisted communication systems, where deep residual networks are employed to determine the optimal near-field RIS codeword. Specifically, we first propose a far-field beam-based beam training (FBT) scheme in which the received signals of all far-field RIS codewords are fed into the neural network to estimate the optimal near-field RIS codeword. In order to further reduce the pilot overhead, a partial near-field beam-based beam training (PNBT) scheme is proposed, where only the received signals corresponding to the partial near-field XL-RIS codewords are served as input to the neural network. Moreover, we further propose an improved PNBT scheme to enhance the performance of beam training by fully exploring the neural network's output. Finally, simulation results show that the proposed schemes outperform the existing beam training schemes and can reduce the beam sweeping overhead by approximately 95%.