This paper investigates an extremely large-scale reconfigurable intelligent surface (XL-RIS) assisted near-field integrated sensing and communication (ISAC) system, where a multi-antenna base station (BS) simultaneously sends unicast data to multiple single-antenna communication users (CUs) and senses multiple targets (TGTs). The BS, CUs and TGTs are \emph{all} assumed to be located in the near-field region of the XL-RIS. We aim to maximize the weighted sum rate (WSR) of all CUs, subject to the sensing beampattern gain constraint for each TGT, the transmit power constraint for the BS, and the unit modulus constraints on the XL-RIS phase shift. First, we develop a fractional programming (FP) based block coordinate descent (BCD) algorithm to obtain a locally optimal solution for such a non-convex joint design problem. Secondly, to address the high-dimensional spatial correlations and scalability of the XL-RIS near-field channels, we propose a customized graph neural network (GNN) scheme to generate the BS transmit beamforming variables and the XL-RIS reflecting coefficient vector for ISAC, where the near-field ISAC system is modeled as a heterogeneous graph comprising XL-RIS/CU/TGT nodes. The proposed GNN scheme can effectively learn the near-field channel state information (CSI) features, in which the message passing mechanism is employed to exchange CSI among these directly connected nodes in the graph. Furthermore, each XL-RIS/CU/TGT node maintains a feature vector for mapping to the BS transmit beamforming variables or the XL-RIS reflecting coefficient vector. Numerical results show that the proposed GNN-based beamforming design scheme achieves a better performance than the existing baselines, in terms of computational efficiency, feasibility, robustness, and the ability of generalization.

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