The problem of permutation-invariant learning over set representations is particularly relevant in the field of multi-agent systems -- a few potential applications include unsupervised training of aggregation functions in graph neural networks (GNNs), neural cellular automata on graphs, and prediction of scenes with multiple objects. Yet existing approaches to set encoding and decoding tasks present a host of issues, including non-permutation-invariance, fixed-length outputs, reliance on iterative methods, non-deterministic outputs, computationally expensive loss functions, and poor reconstruction accuracy. In this paper we introduce a Permutation-Invariant Set Autoencoder (PISA), which tackles these problems and produces encodings with significantly lower reconstruction error than existing baselines. PISA also provides other desirable properties, including a similarity-preserving latent space, and the ability to insert or remove elements from the encoding. After evaluating PISA against baseline methods, we demonstrate its usefulness in a multi-agent application. Using PISA as a subcomponent, we introduce a novel GNN architecture which serves as a generalised communication scheme, allowing agents to use communication to gain full observability of a system.

翻译：在集合表示上实现置换不变学习的问题在多智能体系统中尤为关键——其潜在应用包括图神经网络（GNN）中聚合函数的无监督训练、图上的神经细胞自动机，以及包含多对象的场景预测。然而，现有集合编码与解码方法存在一系列问题：非置换不变性、固定长度输出、依赖迭代方法、非确定性输出、计算成本高昂的损失函数，以及重构精度低下。本文提出了一种置换不变集自编码器（PISA），该模型解决了上述问题，并生成了相比现有基准方法重构误差显著降低的编码。PISA还具备其他理想特性，包括保持相似性的潜空间以及从编码中插入或移除元素的能力。在与基准方法进行对比评估后，我们证明了PISA在多智能体应用中的实用性。通过将PISA作为子组件，我们引入了一种新型GNN架构，该架构可作为通用通信方案，使智能体能够通过通信实现对系统的完全可观测性。