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Neural networks (NNs) have been shown to be competitive againststate-of-the-art feature engineering and random forest (RF) classification ofperiodic variable stars. Although previous work utilising NNs has made use ofperiodicity by period folding multiple-cycle time-series into a single cycle --from time-space to phase-space -- no approach to date has taken advantage ofthe fact that network predictions should be invariant to the initial phase ofthe period-folded sequence. Initial phase is exogenous to the physical originof the variability and should thus be factored out. Here, we presentcyclic-permutation invariant networks, a novel class of NNs for whichinvariance to phase shifts is guaranteed through polar coordinate convolutions,which we implement by means of "Symmetry Padding." Across three differentdatasets of variable star light curves, we show that two implementations of thecyclic-permutation invariant network: the iTCN and the iResNet, consistentlyoutperform non-invariant baselines and reduce overall error rates by between 4%to 22%. Over a 10-class OGLE-III sample, the iTCN/iResNet achieves an averageper-class accuracy of 93.4%/93.3%, compared to RNN/RF accuracies of 70.5%/89.5%in a recent study using the same data. Finding improvement on a non-astronomybenchmark, we suggest that the methodology introduced here should also beapplicable to a wide range of science domains where periodic data abounds dueto physical symmetries.

Classification of Periodic Variable Stars with Novel Cyclic-Permutation Invariant Neural Networks