统一了三种等变激活函数，提升神经网络设计灵活性。
Activation Functions for "A Feedforward Unitary Equivariant Neural Network"
- 提出统一的激活函数形式，兼容多种等变需求。
- 保持单位等变性，支持更丰富的网络结构设计。
- 适合研究对称性建模与等变神经网络的开发者。
在先前工作中，我们提出了前馈单位等变神经网络，并设计了三种专为此网络定制的激活函数：带小残差的softsign函数、恒等函数和Leaky ReLU函数。尽管这些函数具备所需的等变性质，但限制了网络架构的设计自由度。本文将这三种激活函数推广为单一函数形式，该形式涵盖广泛函数类别，保持单位等变性，同时为等变神经网络的设计提供更大灵活性。
原文摘要 · Abstract (English)
In our previous work [Ma and Chan (2023)], we presented a feedforward unitary equivariant neural network. We proposed three distinct activation functions tailored for this network: a softsign function with a small residue, an identity function, and a Leaky ReLU function. While these functions demonstrated the desired equivariance properties, they limited the neural network's architecture. This short paper generalises these activation functions to a single functional form. This functional form represents a broad class of functions, maintains unitary equivariance, and offers greater flexibility for the design of equivariant neural networks.
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