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Compared to spectral norm, $\sigma$-Reparam introduces a dimensionless learnable variable $\gamma$ to force the updates of spectral norm to be dimensionality independent.
$$
\hat{W} = \frac{\gamma}{\sigma(W)}W
$$
Feedbacks and discussions are welcome on how we could make use of $\sigma$-Reparam to enhance our models.
Compatibility
The implementation is based on torch.nn.utils.parametrizations.spectral_norm in PyTorch v2.1.0. Incompability may arise in newer versions.