Minimal Neural Network Models for Permutation Invariant Agents

Organisms in nature have evolved to exhibit flexibility in face of changes to the environment and/or to themselves. Artificial neural networks (ANNs) have proven useful for controlling of artificial agents acting in environments. However, most ANN models used for reinforcement learning-type tasks have a rigid structure that does not allow for varying input sizes. Further, they fail catastrophically if inputs are presented in an ordering unseen during optimization. We find that these two ANN inflexibilities can be mitigated and their solutions are simple and highly related. For permutation invariance, no optimized parameters can be tied to a specific index of the input elements. For size invariance, inputs must be projected onto a common space that does not grow with the number of projections. Based on these restrictions, we construct a conceptually simple model that exhibit flexibility most ANNs lack. We demonstrate the model's properties on multiple control problems, and show that it can cope with even very rapid permutations of input indices, as well as changes in input size. Ablation studies show that is possible to achieve these properties with simple feedforward structures, but that it is much easier to optimize recurrent structures.