Feature Learning in Attention Mechanisms Is More Compact and Stable Than in Convolution

Attention and convolution are fundamental techniques in machine learning. While they use different approaches to learn features - attention mechanisms capture both global and local data relathionships, while convolutional layers focus on local patterns - both methods are effective for various tasks. Although the feature learning of both models is well-studied individually, there has not been a direct comparison of their feature learning dynamics. In this paper, we compare their Lipschitz continuity with respect to the Wasserstein distance and covering numbers under similar settings. We demonstrate that attention processes data in a more compact and stable manner. Compactness refers to the lower variance and intrinsic dimensionality of the activation outputs, while stability refers to the changes between inputs and outputs. We validate our findings through experiments using topological data analysis, measuring the 1-, 2-, and infinity-Wasserstein distances between the outputs of each layer from both models. Furthermore, we extend our comparison to Vision Transformers (ViTs) and ResNets, showing that while ViTs have higher output variance, their feature learning is more stable than that of ResNets.

Exploiting Topological Prior for Boosting Point Cloud Generation

This paper presents an innovative enhancement to the Sphere as Prior Generative Adversarial Network (SP-GAN) model, a state-of-the-art GAN designed for point cloud generation. A novel method is introduced for point cloud generation that elevates the structural integrity and overall quality of the generated point clouds by incorporating topological priors into the training process of the generator. Specifically, this work utilizes the K-means algorithm to segment a point cloud from the repository into clusters and extract centroids, which are then used as priors in the generation process of the SP-GAN. Furthermore, the discriminator component of the SP-GAN utilizes the identical point cloud that contributed the centroids, ensuring a coherent and consistent learning environment. This strategic use of centroids as intuitive guides not only boosts the efficiency of global feature learning but also substantially improves the structural coherence and fidelity of the generated point clouds. By applying the K-means algorithm to generate centroids as the prior, the work intuitively and experimentally demonstrates that such a prior enhances the quality of generated point clouds.