  In this work we propose a new neural network architecture that efficiently
implements and learns general purpose set-equivariant functions. Such a
function f maps a set of entities x = {x1, . . . , xn} from one domain to a set
of same cardinality y = f (x) = {y1, . . . , yn} in another domain regardless
of the ordering of the entities. The architecture is based on a gated recurrent
network which is iteratively applied to all entities individually and at the
same time syncs with the progression of the whole population. In reminiscence
to this pattern, which can be frequently observed in nature, we call our
approach SWARM mapping. Set-equivariant and generally permutation invariant
functions are important building blocks for many state of the art machine
learning approaches. Even in applications where the permutation invariance is
not of primary interest, as to be seen in the recent success of attention based
transformer models (Vaswani et. al. 2017). Accordingly, we demonstrate the
power and usefulness of SWARM mappings in different applications. We compare
the performance of our approach with another recently proposed set-equivariant
function, the Set Transformer (Lee et.al. 2018) and we demonstrate that models
solely based on SWARM layers gives state of the art results.
