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Existing permutation-invariant methods can be divided into two categoriesaccording to the aggregation scope, i.e. global aggregation and local one.Although the global aggregation methods, e. g., PointNet and Deep Sets, getinvolved in simpler structures, their performance is poorer than the localaggregation ones like PointNet++ and Point Transformer. It remains an openproblem whether there exists a global aggregation method with a simplestructure, competitive performance, and even much fewer parameters. In thispaper, we propose a novel global aggregation permutation-invariant networkbased on dual MLP dot-product, called DuMLP-Pin, which is capable of beingemployed to extract features for set inputs, including unordered orunstructured pixel, attribute, and point cloud data sets. We strictly provethat any permutation-invariant function implemented by DuMLP-Pin can bedecomposed into two or more permutation-equivariant ones in a dot-product wayas the cardinality of the given input set is greater than a threshold. We alsoshow that the DuMLP-Pin can be viewed as Deep Sets with strong constraintsunder certain conditions. The performance of DuMLP-Pin is evaluated on severaldifferent tasks with diverse data sets. The experimental results demonstratethat our DuMLP-Pin achieves the best results on the two classification problemsfor pixel sets and attribute sets. On both the point cloud classification andthe part segmentation, the accuracy of DuMLP-Pin is very close to the so-farbest-performing local aggregation method with only a 1-2% difference, while thenumber of required parameters is significantly reduced by more than 85% inclassification and 69% in segmentation, respectively. The code is publiclyavailable on https://github.com/JaronTHU/DuMLP-Pin.

DuMLP-Pin: A Dual-MLP-dot-product Permutation-invariant Network for Set Feature Extraction