Has anyone attempted to compress network size further by extracting the symmetry invariants of the network—e.g., those that correspond to the permutation invariance of node shufflings that leave the DAG unchanged?

I did a rough calculation, and as the precision of the scalar weights decreases, the information content of the specific network permutation becomes a much higher percentage of its overall size.

Depending on the particular neural network architecture, there may be other symmetries beside the symmetric group that also represent compressible redundancies.