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Many multi-source localization and tracking models based on neural networksuse one or several recurrent layers at their final stages to track the movementof the sources. Conventional recurrent neural networks (RNNs), such as the longshort-term memories (LSTMs) or the gated recurrent units (GRUs), take a vectoras their input and use another vector to store their state. However, thisapproach results in the information from all the sources being contained in asingle ordered vector, which is not optimal for permutation-invariant problemssuch as multi-source tracking. In this paper, we present a new recurrentarchitecture that uses unordered sets to represent both its input and its stateand that is invariant to the permutations of the input set and equivariant tothe permutations of the state set. Hence, the information of every sound sourceis represented in an individual embedding and the new estimates are assigned tothe tracked trajectories regardless of their order.

Permutation Invariant Recurrent Neural Networks for Sound Source Tracking Applications