Title: Robust Meta-learning with Noise via Eigen-Reptile. Abstract: Recent years have seen a surge of interest in meta-learning techniques for tackling the few-shot learning (FSL) problem. However, the meta-learner's initial model is prone to meta-overfit, as there are only a few available samples with sampling noise. Besides, when handling the data sampled with label noise for FSL, meta-learner could be extremely sensitive to label noise. To address these two challenges that FSL with sampling and label noise. In particular, we first cast the meta-overfitting problem (overfitting on sampling and label noise) as a gradient noise problem since few available samples cause meta-learner to overfit on existing examples (clean or corrupted) of an individual task at every gradient step. We present Eigen-Reptile (ER) that updates the meta-parameters with the main direction of historical task-specific parameters to alleviate gradient noise. Specifically, the main direction is computed by a special mechanism for the parameter's large size. Furthermore, to obtain a more accurate main direction for Eigen-Reptile in the presence of label noise, we propose Introspective Self-paced Learning (ISPL) that constructs a plurality of prior models to determine which sample should be abandoned. We have proved the effectiveness of Eigen-Reptile and ISPL, respectively, theoretically and experimentally. Moreover, our experiments on different tasks demonstrate that the proposed methods outperform or achieve highly competitive performance compared with the state-of-the-art methods with or without noisy labels.