An optimizer plays a decisive role in the efficiency and effectiveness of model training in deep learning. Although Adam and its variants are widely used, the impact of model complexity on training is not considered, which leads to instability or slow convergence when a complex model is trained. To address this issue, we propose an AMC (Adam with Model Complexity) optimizer, which dynamically adjusts the learning rate by incorporating model complexity, thereby improving training stability and convergence speed. AMC uses the Frobenius norm of the model to measure its complexity, automatically decreasing the learning rate of complex models and increasing the learning rate of simple models, thus optimizing the training process. We provide a theoretical analysis to demonstrate the relationship between model complexity and learning rate, as well as the convergence and convergence bounds of AMC. Experiments on multiple benchmark datasets show that, compared to several widely used optimizers, AMC exhibits better stability and faster convergence, especially in the training of complex models.

Item-to-group recommendation identifies the most compatible user groups for a specific item provider to enable precision marketing, such as recommending fruit products to the most receptive consumer communities. Existing graph-based recommendations typically treat social relationships as static binary links, failing to capture variations in interaction intensity driven by user preferences. Moreover, these models largely overlook the structural relevance of intra-group connections, leading to unreliable group representations. To address these challenges, we propose the Preference-Weighted Neighbor-Aware Group Recommendation Network (PNGRN). Specifically, social edges are first reweighted using preference signals derived from historical user–item rating interactions, thereby suppressing socially connected but preference-inconsistent neighbors during aggregation. Structurally cohesive candidate groups are then identified via k-core decomposition, retaining only subgraphs where every member has at least k internal connections. A neighbor-aware graph convolutional network (GCN) module is further introduced to incorporate external social neighborhood features into group representations. This ensures that the learned group profiles reflect both internal structural stability and the external social context. Experiments on three real-world datasets demonstrate that PNGRN consistently outperforms competitive baselines across all evaluation metrics. Notably, on the MovieLens-1M dataset, PNGRN achieves up to a 9.85% improvement in Precision@20 and a 8.98% gain in NDCG@20. These results validate the necessity of coupling topological density with external social influence, and this work offer a scalable framework for precision group-targeted marketing.