Multiset-Equivariant Set Prediction with Approximate Implicit DifferentiationDownload PDF

Sep 29, 2021 (edited Feb 03, 2022)ICLR 2022 PosterReaders: Everyone
  • Keywords: set prediction, permutation equivariance, implicit differentiation
  • Abstract: Most set prediction models in deep learning use set-equivariant operations, but they actually operate on multisets. We show that set-equivariant functions cannot represent certain functions on multisets, so we introduce the more appropriate notion of multiset-equivariance. We identify that the existing Deep Set Prediction Network (DSPN) can be multiset-equivariant without being hindered by set-equivariance and improve it with approximate implicit differentiation, allowing for better optimization while being faster and saving memory. In a range of toy experiments, we show that the perspective of multiset-equivariance is beneficial and that our changes to DSPN achieve better results in most cases. On CLEVR object property prediction, we substantially improve over the state-of-the-art Slot Attention from 8% to 77% in one of the strictest evaluation metrics because of the benefits made possible by implicit differentiation.
  • One-sentence Summary: We propose a better permutation-equivariance property for multisets and improve an existing set predictor that has this property with approximate implicit differentiation
  • Supplementary Material: zip
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