Exponential Separations in Symmetric Neural Networks

Aaron Zweig · Joan Bruna

Hall J #815

Keywords: [ deepsets ] [ separation ] [ relational network ] [ symmetric function ] [ self-attention ] [ set-based ]

Abstract: In this work we demonstrate a novel separation between symmetric neural network architectures. Specifically, we consider the Relational Network~\parencite{santoro2017simple} architecture as a natural generalization of the DeepSets~\parencite{zaheer2017deep} architecture, and study their representational gap. Under the restriction to analytic activation functions, we construct a symmetric function acting on sets of size $N$ with elements in dimension $D$, which can be efficiently approximated by the former architecture, but provably requires width exponential in $N$ and $D$ for the latter.

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