Contextual sequence mapping is one of the fundamental problems in Natural Language Processing. Instead of relying solely on the information presented in a text, the learning agents have access to a strong external signal given to assist the learning process. In this paper, we propose a novel family of Recurrent Neural Network unit: the Context-dependent Additive Recurrent Neural Network (CARNN) that is designed specifically to leverage this external signal. The experimental results on public datasets in the dialog problem (Babi dialog Task 6 and Frame), contextual language model (Switchboard and Penn Discourse Tree Bank) and question answering (TrecQA) show that our novel CARNN-based architectures outperform previous methods.