In the overlay D2D networks, multiple D2D pairs coexist with full frequency reuse resulting in complicated interference. Traditional centralized power control methods require instantaneous interference information and so are difficult to implement in a D2D network due to the backhaul delay and high computational requirements. To overcome this challenge, we propose a distributed power allocation algorithm called interference feature extractor aided recurrent neural network (IFE-RNN). The core idea of the scheme is described as follows. First, we design linear filters with various sizes termed IFEs to extract the local interference patterns from the outdated interference information. This feature extraction process enables our network to precisely learn the interference patterns around D2D links, and so as to provide more effective power allocation strategies. Then, we propose to predict the real-time interference pattern based on the outputs of the IFEs and further make power decision. The prediction and decision can be modelled as a Markov decision problem (MDP) and solved by using a recurrent neural network (RNN). The acquisition of the channel correlation can greatly improve the efficiency and the accuracy of our network according to our simulation results. It is worth noting that an input reduction process is also designed to reduce the space complexity from $O(N^{2})$ to $O(1)$ which speeds up the operation time and reduces the system overhead. Finally, extensive simulation results show that the proposed algorithm achieves an encouraging performance compared to the state-of-the-art power allocation algorithm.