On the Symmetries of Deep Learning Models and their Internal Representations
This work provides a theoretical foundation for understanding symmetry propagation in deep learning, which could aid in model interpretability, but it is incremental as it builds on existing symmetry concepts without introducing a new paradigm.
The paper tackled the problem of connecting architectural symmetries in deep learning models to symmetries in their internal data representations by calculating intertwiner groups and conducting experiments on hidden state similarities. The result suggests that network symmetries propagate into data representation symmetries, offering insights into how architecture influences learning and prediction.
Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of a family of models with the symmetries of that family's internal representation of data. We do this by calculating a set of fundamental symmetry groups, which we call the intertwiner groups of the model. We connect intertwiner groups to a model's internal representations of data through a range of experiments that probe similarities between hidden states across models with the same architecture. Our work suggests that the symmetries of a network are propagated into the symmetries in that network's representation of data, providing us with a better understanding of how architecture affects the learning and prediction process. Finally, we speculate that for ReLU networks, the intertwiner groups may provide a justification for the common practice of concentrating model interpretability exploration on the activation basis in hidden layers rather than arbitrary linear combinations thereof.