论文标题
对对称子组的作用的计算有效的神经网络不变
A Computationally Efficient Neural Network Invariant to the Action of Symmetry Subgroups
论文作者
论文摘要
我们介绍了一种设计一种计算高效的$ g $ -INARIANT神经网络的方法，该神经网络将功能近似于给定置换子组在输入数据上的对称组的$ 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。然后，使用网络中的多层感知器处理此潜在表示。我们证明了所提出的体系结构的普遍性，讨论其属性并突出其计算和内存效率。与其他$ g $ - invariant神经网络相比，涉及不同网络配置的数值实验支持了理论上的考虑。
We introduce a method to design 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. This latent representation is then processed with a multi-layer perceptron in the network. We prove the universality of the proposed architecture, discuss its properties and highlight its computational and memory efficiency. Theoretical considerations are supported by numerical experiments involving different network configurations, which demonstrate the effectiveness and strong generalization properties of the proposed method in comparison to other $G$-invariant neural networks.
