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An unconventional magnet may be mapped onto a simple ferromagnet by theexistence of a high-symmetry point. Knowledge of conventional ferromagneticsystems may then be carried over to provide insight into more complex orders.Here we demonstrate how an unsupervised and interpretable machine-learningapproach can be used to search for potential high-symmetry points inunconventional magnets without any prior knowledge of the system. The method isapplied to the classical Heisenberg-Kitaev model on a honeycomb lattice, whereour machine learns the transformations that manifest its hidden $O(3)$symmetry, without using data of these high-symmetry points. Moreover, weclarify that, in contrast to the stripy and zigzag orders, a set of $D_2$ and$D_{2h}$ ordering matrices provides a more complete description of themagnetization in the Heisenberg-Kitaev model. In addition, our machine alsolearns the local constraints at the phase boundaries, which manifest asubdimensional symmetry. This paper highlights the importance of explicit orderparameters to many-body spin systems and the property of interpretability forthe physical application of machine-learning techniques.

Inferring Hidden Symmetries of Exotic Magnets from Detecting Explicit Order Parameters