论文标题
概括卷积神经网络以使均衡性置于任意连续数据上
Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data
论文作者
论文摘要
卷积层的翻译均衡使卷积神经网络能够很好地概括图像问题。虽然翻译均衡性为图像提供了强大的感应偏见，但我们通常还希望对其他转换（例如旋转，尤其是非图像数据）的等效性。我们提出了一种构造卷积层的通用方法，该方法与任何指数指数映射的指定谎言组的转换等效。与新组合并到新群体需要仅实施组指数和对数图，从而实现快速原型。展示了我们方法的简单性和通用性，我们将相同的模型结构应用于图像，球形分子数据和哈密顿动力学系统。对于哈密顿系统而言，我们模型的均衡性特别有影响力，从而确切地保存了线性和角动量。
The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire equivariance to other transformations, such as rotations, especially for non-image data. We propose a general method to construct a convolutional layer that is equivariant to transformations from any specified Lie group with a surjective exponential map. Incorporating equivariance to a new group requires implementing only the group exponential and logarithm maps, enabling rapid prototyping. Showcasing the simplicity and generality of our method, we apply the same model architecture to images, ball-and-stick molecular data, and Hamiltonian dynamical systems. For Hamiltonian systems, the equivariance of our models is especially impactful, leading to exact conservation of linear and angular momentum.
