This repository accompanies the paper:

Harmonics of Learning: Universal Fourier Features Emerge in Invariant Networks (2024)

Here, we provide an implementation of a complex-valued Power-Spectral Network trained via contrastive learning on an invariance objective for a finite group. As shown in the companion paper, at convergence the network learns all the irreducible unitary representations of the group. In particular, the multiplication table can be extracted from its weights.

We provide implementations of the model and its training in both PyTorch and JAX.

python 3.8 
pip install -r requirements.txt

The file groups.py provides implementations of various finite groups, including cyclic, dihedral and symmetric.

In order to train the models in PyTorch and in JAX, run the files train_torch.py and train_JAX.py respectively. The training parameters are set at the beginning of these files.