We introduce SignNet and BasisNet -- new neural architectures that are
invariant to two key symmetries displayed by eigenvectors: (i) sign flips,
since if $v$ is an eigenvector then so is $-v$; and (ii) more general basis
symmetries, which occur in higher dimensional eigenspaces with infinitely many
choices of basis eigenvectors. We prove that under certain conditions our
networks are universal, i.e., they can approximate any continuous function of
eigenvectors with the desired invariances. When used with Laplacian
eigenvectors, our networks are provably more expressive than existing spectral
methods on graphs; for instance, they subsume all spectral graph convolutions,
certain spectral graph invariants, and previously proposed graph positional
encodings as special cases. Experiments show that our networks significantly
outperform existing baselines on molecular graph regression, learning
expressive graph representations, and learning neural fields on triangle
meshes. Our code is available at this https URL .

介绍了两种新的神经网络结构: SignNet 和 BasisNet，它们对特征向量显示的两个关键对称性具有不变性，并证明它们在光谱图上比现有的光谱方法更加有效。

用于谱图表示学习的签名和基础不变网络

Sign and Basis Invariant Networks for Spectral Graph Representation  Learning

In this work, we present BasisNet which combines recent advancements in
efficient neural network architectures, conditional computation, and early
termination in a simple new form. Our approach incorporates a lightweight model
to preview the input and generate input-dependent combination coefficients,
which later controls the synthesis of a more accurate specialist model to make
final prediction. The two-stage model synthesis strategy can be applied to any
network architectures and both stages are jointly trained. We also show that
proper training recipes are critical for increasing generalizability for such
high capacity neural networks. On ImageNet classification benchmark, our
BasisNet with MobileNets as backbone demonstrated clear advantage on
accuracy-efficiency trade-off over several strong baselines. Specifically,
BasisNet-MobileNetV3 obtained 80.3% top-1 accuracy with only 290M Multiply-Add
operations, halving the computational cost of previous state-of-the-art without
sacrificing accuracy. With early termination, the average cost can be further
reduced to 198M MAdds while maintaining accuracy of 80.0% on ImageNet.

本文提出了 BasisNet，它采用轻量级模型和两阶段模型合成策略，结合了高效神经网络体系结构、条件计算和早期终止，具有高效且精确的性能。在 ImageNet 分类基准测试中，使用 BasisNet 的 MobileNets 作为骨干网络，相比于其他基准测试，BasisNet-MobileNetV3 获得了显著的精度 - 效率平衡优势，仅需 290M 的乘加操作即可达到 80.3% 的 top-1 准确率，而且在不降低准确率的情况下，平均成本可进一步降低至 198M MAdds。