论文标题
对称亚组的作用不变的新神经网络架构
A New Neural Network Architecture Invariant to the Action of Symmetry Subgroups
论文作者
论文摘要
我们提出了一个计算高效的$ g $ - invariant神经网络，该网络将功能近似于输入数据上对称组的给定排列子组$ g \ leq s_n $的动作。提出的网络体系结构的关键要素是一个新的$ g $ - invariant转换模块，该模块会产生输入数据的$ g $ invariant潜在表示。理论上的考虑得到了数值实验的支持，这些实验证明了与其他$ g $ invariant神经网络相比，该方法的有效性和强大的概括性。
We propose a computationally efficient $G$-invariant neural network that approximates functions invariant to the action of a given permutation subgroup $G \leq S_n$ of the symmetric group on input data. The key element of the proposed network architecture is a new $G$-invariant transformation module, which produces a $G$-invariant latent representation of the input data. Theoretical considerations are supported by numerical experiments, which demonstrate the effectiveness and strong generalization properties of the proposed method in comparison to other $G$-invariant neural networks.
