H IGH S KIP N ETWORKS : A H IGHER O RDER G ENERAL - IZATION OF S KIP C ONNECTIONS
H IGH S KIP N ETWORKS : A H IGHER O RDER G ENERAL - IZATION OF S KIP C ONNECTIONS
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发表时间：
2022
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通讯作者：
Mustafa Hajij;K. Ramamurthy;Aldo Guzm´an-S´aenz;Ghada Zamzmi
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作者：
Mustafa Hajij;K. Ramamurthy;Aldo Guzm´an-S´aenz;Ghada Zamzmi
我们提出了高跳跃网络（HSNs），这是跳跃连接神经网络对简单复合体的一种高阶推广。hsn通过创建在输入复数上计算的信号的多个前馈路径，利用在简单域中编码的高阶结构。一些前馈路径可以通过各种高阶结构传播信号；例如，如果我们想要在边缘上传播信号，一些前馈路径可能会从边缘到三角形，然后再回到边缘。与欧几里得跳跃连接网络类似，所有路径在最后通过添加或连接组合在一起。我们在合成数据集和真实数据集上证明了hsn的有效性。我们的初步结果表明，与没有高跳跃分量的基本模型相比，hsn在统计上显著改善了泛化误差。
We present High Skip Networks (HSNs), a higher order generalization of skip connection neural networks to simplicial complexes. HSNs exploit higher order structure encoded in a simplicial domain by creating multiple feed-forward paths of signals computed over the input complex. Some feed-forward paths may propagate the signal through various higher order structures; e.g., if we want to propagate signals over edges, some feed-forward paths may go from edges to triangles and then back to edges. Similar to the Euclidean skip connection networks, all paths are combined together at the end by addition or concatenation. We demonstrate the effectiveness of HSNs on synthetic and real datasets. Our preliminary results show that HSNs lead to a statistically significant improvement in the generalization error when compared to base models without high skip components.