In addition to the data representation, continuity also benefits learning models by aligning with the manifold hypothesis, suggesting that highdimensional data resides on lower-dimensional latent manifolds. This principle guides the success of deep learning by enabling smoother and more continuous latent representations. As such, Yunlu introduced the Mixup augmentation to point cloud recognition, which jointly interpolates input data and corresponding labels. The paper that appeared at ECCV2020 developed the PointMixup strategy based on the idea of the optimal transport, with mathematical justifications of the effectiveness. The application of continuity in 3D deep learning has shown promising results in terms of improving the efficiency and accuracy of 3D data representation and learning algorithms. Future research can focus on addressing the limitations of oversmoothing and lack of efficiency for downstream tasks, as well as on incorporating designs that consider the continuous and discrete nature of real-world data. 7 YunluChen Computer Vision News Fig 1. The emerging hierarchical structure in implicit neural representation layers Fig 2. The equivariant implicit representation generalizes to unseen transformations
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