The paper introduces the Deep & Cross Network (DCN) for click-through rate (CTR) prediction, a critical task in online advertising. DCN combines a deep neural network (DNN) with a novel cross network to efficiently learn both sparse and dense feature interactions. The cross network explicitly applies feature crossing at each layer, allowing for the automatic learning of bounded-degree feature interactions without manual engineering. This approach reduces the complexity and computational cost compared to traditional DNNs, while maintaining or improving model accuracy. Experimental results on the Criteo CTR dataset and dense classification datasets demonstrate that DCN outperforms state-of-the-art algorithms in terms of both accuracy and memory usage. The paper also analyzes the effectiveness of the cross network through polynomial approximation, generalization to factorization machines, and efficient projection, providing theoretical insights into its performance.The paper introduces the Deep & Cross Network (DCN) for click-through rate (CTR) prediction, a critical task in online advertising. DCN combines a deep neural network (DNN) with a novel cross network to efficiently learn both sparse and dense feature interactions. The cross network explicitly applies feature crossing at each layer, allowing for the automatic learning of bounded-degree feature interactions without manual engineering. This approach reduces the complexity and computational cost compared to traditional DNNs, while maintaining or improving model accuracy. Experimental results on the Criteo CTR dataset and dense classification datasets demonstrate that DCN outperforms state-of-the-art algorithms in terms of both accuracy and memory usage. The paper also analyzes the effectiveness of the cross network through polynomial approximation, generalization to factorization machines, and efficient projection, providing theoretical insights into its performance.