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While mislabeled or ambiguously-labeled samples in the training set could negatively affect the performance of deep models, diagnosing the dataset and identifying mislabeled samples helps to improve the generalization power. Training dynamics, i.e., the traces left by iterations of optimization algorithms, have recently been proved to be effective to localize mislabeled samples with hand-crafted features. In this paper, beyond manually designed features, we introduce a novel learning-based solution, leveraging a noise detector, instanced by an LSTM network, which learns to predict whether a sample was mislabeled using the raw training dynamics as input. Specifically, the proposed method trains the noise detector in a supervised manner using the dataset with synthesized label noises and can adapt to various datasets (either naturally or synthesized label-noised) without retraining. We conduct extensive experiments to evaluate the proposed method. We train the noise detector based on the synthesized label-noised CIFAR dataset and test such noise detector on Tiny ImageNet, CUB-200, Caltech-256, WebVision and Clothing1M. Results show that the proposed method precisely detects mislabeled samples on various datasets without further adaptation, and outperforms state-of-the-art methods. Besides, more experiments demonstrate that the mislabel identification can guide a label correction, namely data debugging, providing orthogonal improvements of algorithm-centric state-of-the-art techniques from the data aspect.