Using Borsuk-Ulam theorem we show that multiple aggregation functions are necessary for nodes to distinguish their neighbourhoods in GNN with continuous features. (2/n)
We also propose scalers as a way to give nodes information about their degree and so generalise the injectivity property of the sum aggregator (from
@KeyuluXu
&
@weihua916
et al.). (3/n)
We then integrate these theoretical findings to propose an aggregation method, which we call Principal Neighbourhood Aggregation or PNA, combining multiple aggregators and logarithmic degree scalers. (4/n)
Finally, we insert this aggregation method in an MPNN framework and show that it outperforms other methods both in a new synthetic multi-task benchmark and in real-world ones (from
@vijaypradwi
&
@chaitjo
et al.). (5/n)
You can find the paper on arXiv (new version will be out soon) , the code on GitHub , a short presentation on SlidesLive and a talk by
@PetarV_93
on YouTube . (6/n)