Finite Group Equivariant Neural Networks for Games

TL;DR

This paper introduces Finite Group Neural Networks (FGNNs), which leverage symmetries in board games to improve learning efficiency and performance, and can be adapted to various architectures including U-Net.

Contribution

FGNNs provide a novel way to incorporate symmetry understanding into neural networks for games and other tasks, including architectures with skip connections.

Findings

FGNNs improve checkers performance.

FGNN-U-Net outperforms standard U-Net in image segmentation.

FGNNs can be derived from existing architectures.

Abstract

Games such as go, chess and checkers have multiple equivalent game states, i.e. multiple board positions where symmetrical and opposite moves should be made. These equivalences are not exploited by current state of the art neural agents which instead must relearn similar information, thereby wasting computing time. Group equivariant CNNs in existing work create networks which can exploit symmetries to improve learning, however, they lack the expressiveness to correctly reflect the move embeddings necessary for games. We introduce Finite Group Neural Networks (FGNNs), a method for creating agents with an innate understanding of these board positions. FGNNs are shown to improve the performance of networks playing checkers (draughts), and can be easily adapted to other games and learning problems. Additionally, FGNNs can be created from existing network architectures. These include, for the first time, those with skip connections and arbitrary layer types. We demonstrate that an equivariant version of U-Net (FGNN-U-Net) outperforms the unmodified network in image segmentation.