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Symmetry is a fundamental tool in the exploration of a broad range of complexsystems. In machine learning symmetry has been explored in both models anddata. In this paper we seek to connect the symmetries arising from thearchitecture of a family of models with the symmetries of that family'sinternal representation of data. We do this by calculating a set of fundamentalsymmetry groups, which we call the intertwiner groups of the model. We connectintertwiner groups to a model's internal representations of data through arange of experiments that probe similarities between hidden states acrossmodels with the same architecture. Our work suggests that the symmetries of anetwork are propagated into the symmetries in that network's representation ofdata, providing us with a better understanding of how architecture affects thelearning and prediction process. Finally, we speculate that for ReLU networks,the intertwiner groups may provide a justification for the common practice ofconcentrating model interpretability exploration on the activation basis inhidden layers rather than arbitrary linear combinations thereof.

On the Symmetries of Deep Learning Models and their Internal Representations