A question about the potential normalization

[speedcell4]

Hi, thank you for sharing your source code.
Could you please give more explanation why do you need the potential normalization, the only description about it that I can find in your paper is the following,

Potential normalization (PN) is simple: we normalize the scores s to an empirical distribution of zero mean and one variance. The difference with batch-norm (BN) is that we apply PN at an instance-level, rather than a batch-level.

But I am still confused about what it is for. It's just for numerical stability?

And is the following the implementation of potential normalization?

Partially-Observed-TreeCRFs/tree_crf_layer.py

Lines 100 to 104 in c4040eb

	if (self.potential_normalization):
	lp_mean = log_potentials.reshape(batch_size, -1).mean(-1)
	lp_std = log_potentials.reshape(batch_size, -1).std(-1)
	log_potentials = log_potentials - lp_mean.view(batch_size, 1, 1, 1)
	log_potentials = log_potentials / lp_std.view(batch_size, 1, 1, 1)