The paper "Linear-Time Graph Neural Networks for Scalable Recommendations" addresses the scalability issue of Graph Neural Networks (GNNs) in recommender systems. Despite the strong expressive power of GNNs in capturing high-order connectivities in user-item interaction data, their computational complexity often limits their practical application, especially in large-scale industrial settings. The authors propose a novel model called Linear-Time Graph Neural Networks (LTGNN) to achieve linear-time complexity while maintaining the expressive capabilities of GNNs. LTGNN introduces implicit graph modeling and an efficient variance-reduced neighbor sampling strategy. The implicit modeling leverages the fixed-point equation of Personalized PageRank (PPRP) to capture long-range dependencies with a single forward propagation layer, reducing the number of layers and computational complexity. The variance-reduced neighbor sampling technique approximates the gradient of historical embeddings, further improving efficiency. Experiments on three real-world datasets (Yelp2018, Alibaba-iFashion, and Amazon-Large) demonstrate that LTGNN achieves comparable or better recommendation performance compared to state-of-the-art GNN models like LightGCN, while being significantly more efficient. The proposed method shows great potential for industrial recommendation applications, as it balances prediction accuracy with computational efficiency.The paper "Linear-Time Graph Neural Networks for Scalable Recommendations" addresses the scalability issue of Graph Neural Networks (GNNs) in recommender systems. Despite the strong expressive power of GNNs in capturing high-order connectivities in user-item interaction data, their computational complexity often limits their practical application, especially in large-scale industrial settings. The authors propose a novel model called Linear-Time Graph Neural Networks (LTGNN) to achieve linear-time complexity while maintaining the expressive capabilities of GNNs. LTGNN introduces implicit graph modeling and an efficient variance-reduced neighbor sampling strategy. The implicit modeling leverages the fixed-point equation of Personalized PageRank (PPRP) to capture long-range dependencies with a single forward propagation layer, reducing the number of layers and computational complexity. The variance-reduced neighbor sampling technique approximates the gradient of historical embeddings, further improving efficiency. Experiments on three real-world datasets (Yelp2018, Alibaba-iFashion, and Amazon-Large) demonstrate that LTGNN achieves comparable or better recommendation performance compared to state-of-the-art GNN models like LightGCN, while being significantly more efficient. The proposed method shows great potential for industrial recommendation applications, as it balances prediction accuracy with computational efficiency.