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 complete invariant maps purely from the symmetries implicit in data. Further, we demonstrate that the completeness property endows these networks with strong adversarial robustness. This work establishes Bispectral Neural Networks as a powerful computational primitive for robust invariant representation learning.

翻译：我们提出了一个神经网络结构,即双光谱神经网络(BNNs),用于学习对界定信号空间的紧凑通量组的行动有差异的演示。模型包含双光谱(bispectrum)的炭酸盐,这是经过分析界定的完整组合,即它保留了所有信号结构,同时只消除由于群体行动而产生的变异。在这里,我们证明BNS能够同时学习群体、其不可复制的演示,以及完全从数据所隐含的对称中的相应完整的变量图。此外,我们证明完整性特性使这些网络具有很强的对抗性强力。这项工作将双光谱神经网络确立为强大的反向表达学习的强大计算原始体。