Inconsitent results with qgt

[nkaeming]

Hi all,

currently, we are experimenting with the QGT and I found a strange behavior calculating it with the different implementations.

hilbert = nk.hilbert.Spin(s=0.5, N=2)
model = nk.models.ARNNDense(hilbert=hilbert, layers=2, features=10, param_dtype=jnp.complex128)
state = nk.vqs.FullSumState(hilbert=hilbert, model=model)

qgt_dense_otf = nk.optimizer.qgt.QGTOnTheFly(state, holomorphic=True).to_dense()
qgt_dense_jac = nk.optimizer.qgt.QGTJacobianDense(state, holomorphic=True).to_dense()
print(jnp.max(jnp.abs(qgt_dense_otf - qgt_dense_jac)))

output: 1.2837812382952014

is this by intention or is it a bug?

Best wishes
Niklas

[gcarleo]

Can you apply it to a vector? Not sure what you are doing automatically triggers the conversion to a dense matrix

[gcarleo]

Ah yes sorry I didn't see you are converting to dense explicitly uhmm that's unexpected then

[nkaeming]

I corsschecked with an RBM. Seems to work correctly in that case.

[PhilipVinc]

It's because an autoregressive network is not holomorphic

[PhilipVinc]

You lie to netket, netket lies to you :P

[nkaeming]

Sure. That's true. Sorry :)

[PhilipVinc]

I recently added nk.utils.is_probably_holomorphic exactly to check this (am not sure if it is in a released version yet or not. If not... will soon be).
If you run it on your model you'll see it returning False.

[PhilipVinc]

And more generally, nk.optimizer.qgt.QGTOnTheFly cannot be converted to dense for non holomorphic objects that have complex parameters.
The way it is computed is such that we cannot extract it. You have to resort to real parameters or QGTJacobian if you want a dense representation.