# Permutation Invariant Recurrent Neural Networks for Sound Source Tracking Applications

arXiv: https://arxiv.org/abs/2306.08510 · HTML: https://mlsanity.com/paper/2306.08510/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 16 references that are in the map.
- First posted on arXiv 14 Jun 2023.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [TrackFormer: Multi-Object Tracking with Transformers](https://mlsanity.com/paper/2101.02702/) (2021)
- [Sound Event Localization and Detection of Overlapping Sources Using Convolutional Recurrent Neural Networks](https://mlsanity.com/paper/1807.00129/) (2018)
- [A Survey of Sound Source Localization with Deep Learning Methods](https://mlsanity.com/paper/2109.03465/) (2021)
- [Minimal Gated Unit for Recurrent Neural Networks](https://mlsanity.com/paper/1603.09420/) (2016)
- [ACCDOA: Activity-Coupled Cartesian Direction of Arrival Representation for Sound Event Localization and Detection](https://mlsanity.com/paper/2010.15306/) (2020)
- [Direction of Arrival Estimation of Sound Sources Using Icosahedral CNNs](https://mlsanity.com/paper/2203.16940/) (2022)
- [Position tracking of a varying number of sound sources with sliding permutation invariant training](https://mlsanity.com/paper/2210.14536/) (2022)

## Built on by (most cited first, 1 of 1)

- [From General-Purpose Audio Tagging to Spatially Grounded Sound Event Localization and Detection](https://mlsanity.com/paper/2606.27751/) (2026)

## Abstract (arXiv)

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.