Permutation Invariant Recurrent Neural Networks for Sound Source
  Tracking Applications
David Diaz-Guerra Archontis Politis Antonio Miguel Jose R. Beltran Tuomas Virtanen
Many multi-source localization and tracking models based on neural networks
use one or several recurrent layers at their final stages to track the movement
of the sources. Conventional recurrent neural networks (RNNs), such as the long
short-term memories (LSTMs) or the gated recurrent units (GRUs), take a vector
as their input and use another vector to store their state. However, this
approach results in the information from all the sources being contained in a
single ordered vector, which is not optimal for permutation-invariant problems
such as multi-source tracking. In this paper, we present a new recurrent
architecture that uses unordered sets to represent both its input and its state
and that is invariant to the permutations of the input set and equivariant to
the permutations of the state set. Hence, the information of every sound source
is represented in an individual embedding and the new estimates are assigned to
the tracked trajectories regardless of their order.