Representing Unordered Data Using Multiset Automata and Complex Numbers
Authors: Justin DeBenedetto, David Chiang
Keywords: sets, multisets, automata, complex numbers, position encodings
TL;DR: Automata for multisets and complex numbers give a new way of thinking about DeepSets and Transformer position encodings.
Abstract: Unordered, variable-sized inputs arise in many settings across multiple fields.  The ability for set- and multiset- oriented neural networks to handle this type of input has been the focus of much work in recent years.  We propose to represent multisets using complex-weighted multiset automata and show how the multiset representations of certain existing neural architectures can be viewed as special cases of ours.  Namely, (1) we provide a new theoretical and intuitive justification for the Transformer model's representation of positions using sinusoidal functions, and (2) we extend the DeepSets model to use complex numbers, enabling it to outperform the existing model on an extension of one of their tasks.