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

Finite Group Equivariant Neural Networks for Games