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User response prediction is a crucial component for personalized information retrieval and filtering scenarios, such as recommender system and web search. The data in user response prediction is mostly in a multi-field categorical format and transformed into sparse representations via one-hot encoding. Due to the sparsity problems in representation and optimization, most research focuses on feature engineering and shallow modeling. Recently, deep neural networks have attracted research attention on such a problem for their high capacity and end-to-end training scheme. In this article, we study user response prediction in the scenario of click prediction.We first analyze a coupled gradient issue in latent vector-based models and propose kernel product to learn field-aware feature interactions. Then, we discuss an insensitive gradient issue in DNN-based models and propose Product-based Neural Network, which adopts a feature extractor to explore feature interactions. Generalizing the kernel product to a net-in-net architecture,we further propose Productnetwork in Network (PIN), which can generalize previous models. Extensive experiments on four industrial datasets and one contest dataset demonstrate that ourmodels consistently outperform eight baselines on both area under curve and log loss. Besides, PIN makes great click-through rate improvement (relatively 34.67%) in online A/B test. [ABSTRACT FROM AUTHOR]