论文标题
双光谱神经网络
Bispectral Neural Networks
论文作者
论文摘要
我们提出了一个神经网络架构，双光谱神经网络（BNN），用于学习表征，这些表示表示紧凑的交换组在定义信号的空间上的行为不变。该模型结合了双光谱的ANSATZ，这是一个完整的分析定义的组不变式的 - 也就是说，它保留了所有信号结构，同时仅删除由于组动作而造成的变化。在这里，我们证明了BNN能够同时学习群体，它们不可约的表示以及相应的均值和完全不变的映射，这纯粹来自数据中隐含的对称性。此外，我们证明完整性属性赋予这些网络具有强大的基于不变性的对抗性鲁棒性。这项工作将双光谱神经网络建立为强大的计算原始性，可用于健壮的代表性学习
We present a neural network architecture, Bispectral Neural Networks (BNNs) for learning representations that are invariant to the actions of compact commutative groups on the space over which a signal is defined. The model incorporates the ansatz of the bispectrum, an analytically defined group invariant that is complete -- that is, it preserves all signal structure while removing only the variation due to group actions. Here, we demonstrate that BNNs are able to simultaneously learn groups, their irreducible representations, and corresponding equivariant and complete-invariant maps purely from the symmetries implicit in data. Further, we demonstrate that the completeness property endows these networks with strong invariance-based adversarial robustness. This work establishes Bispectral Neural Networks as a powerful computational primitive for robust invariant representation learning
