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Recently, video recognition is emerging with the help of multi-modal learning, which focuses on integrating distinct modalities to improve the performance or robustness of the model. Although various multi-modal learning methods have been proposed and offer remarkable recognition results, almost all of these methods rely on high-quality manual annotations and assume that modalities among multi-modal data provide semantically relevant information. Unfortunately, the widely used video datasets are usually coarse-annotated or collected from the Internet. Thus, it inevitably contains a portion of noisy labels and noisy correspondence. To address this challenge, we use the audio-visual action recognition task as a proxy and propose a noise-tolerant learning framework to find anti-interference model parameters against both noisy labels and noisy correspondence. Specifically, our method consists of two phases that aim to rectify noise by the inherent correlation between modalities. First, a noise-tolerant contrastive training phase is performed to make the model immune to the possible noisy-labeled data. To alleviate the influence of noisy correspondence, we propose a cross-modal noise estimation component to adjust the consistency between different modalities. As the noisy correspondence existed at the instance level, we further propose a category-level contrastive loss to reduce its interference. Second, in the hybrid-supervised training phase, we calculate the distance metric among features to obtain corrected labels, which are used as complementary supervision to guide the training. Extensive experiments on a wide range of noisy levels demonstrate that our method significantly improves the robustness of the action recognition model and surpasses the baselines by a clear margin.