In this paper, we develop a learning-based symbol detection algorithm for massive MIMO systems. To exploit the structural information inherited in the received signals from massive antenna array, multi-mode reservoir computing is adopted as the building block to facilitate over-the-air training. In addition, alternating recursive least square optimization method, and decision feedback mechanism are utilized in our algorithm to achieve the real-time learning capability. That is, the neural network is trained purely online with its weights updated on an OFDM symbol basis to promptly and adaptively track the dynamic environment. Evaluation results demonstrate that our algorithm achieves substantial gain over traditional model-based approach and state-of-the-art learning-based techniques in dynamic channel environment. Moreover, empirical result reveals our NN model is robust to training label error, which benefits the decision feedback mechanism.