  We present a general framework for symmetrizing an arbitrary neural-network
architecture and making it equivariant with respect to a given group. We build
upon the proposals of Kim et al. (2023); Kaba et al. (2023) for symmetrization,
and improve them by replacing their conversion of neural features into group
representations, with an optimization whose loss intuitively measures the
distance between group orbits. This change makes our approach applicable to a
broader range of matrix groups, such as the Lorentz group O(1, 3), than these
two proposals. We experimentally show our method's competitiveness on the SO(2)
image classification task, and also its increased generality on the task with
O(1, 3). Our implementation will be made accessible at
https://github.com/tiendatnguyen-vision/Orbit-symmetrize.
