This paper introduces a new graph neural network model called personalized propagation of neural predictions (PPNP) and its fast approximation, APPNP. The model leverages the relationship between graph convolutional networks (GCN) and PageRank to improve the propagation scheme used in semi-supervised classification. PPNP and APPNP use a personalized PageRank-based propagation scheme that allows for a larger, adjustable neighborhood for classification, enabling the model to propagate information more effectively. The model's training time is on par or faster than previous models, and its number of parameters is on par or lower. It can be easily combined with any neural network and outperforms several recently proposed methods for semi-supervised classification in the most thorough study done so far for GCN-like models. The model's performance is evaluated on four text-classification datasets, including CITESEER, CORA-ML, PUBMED, and MICROSOFT ACADEMIC. The results show that PPNP and APPNP significantly outperform the state-of-the-art baseline models on all datasets. The model is computationally efficient and scales well to large graphs. The paper also discusses the limitations of traditional message passing algorithms and how PPNP and APPNP address these limitations by decoupling prediction and propagation. The model's performance is further validated through extensive experiments, including a rigorous evaluation protocol that ensures statistical robustness. The results demonstrate that PPNP and APPNP are effective for semi-supervised classification on graphs and can be combined with pretrained neural networks to significantly improve their accuracy.This paper introduces a new graph neural network model called personalized propagation of neural predictions (PPNP) and its fast approximation, APPNP. The model leverages the relationship between graph convolutional networks (GCN) and PageRank to improve the propagation scheme used in semi-supervised classification. PPNP and APPNP use a personalized PageRank-based propagation scheme that allows for a larger, adjustable neighborhood for classification, enabling the model to propagate information more effectively. The model's training time is on par or faster than previous models, and its number of parameters is on par or lower. It can be easily combined with any neural network and outperforms several recently proposed methods for semi-supervised classification in the most thorough study done so far for GCN-like models. The model's performance is evaluated on four text-classification datasets, including CITESEER, CORA-ML, PUBMED, and MICROSOFT ACADEMIC. The results show that PPNP and APPNP significantly outperform the state-of-the-art baseline models on all datasets. The model is computationally efficient and scales well to large graphs. The paper also discusses the limitations of traditional message passing algorithms and how PPNP and APPNP address these limitations by decoupling prediction and propagation. The model's performance is further validated through extensive experiments, including a rigorous evaluation protocol that ensures statistical robustness. The results demonstrate that PPNP and APPNP are effective for semi-supervised classification on graphs and can be combined with pretrained neural networks to significantly improve their accuracy.