Loss function of the expectation value

[kdg930202]

This is a part of source code "netket/vqs/full_summ/expect.py"

I just don't understand "ΔOΨ".

I guess it is the loss function of the expectation value.

but cannot understand why it is defined like that ΔOΨ = (OΨ - expval_O * Ψ).conj() * Ψ.

expval_O = (Ψ.conj() * OΨ).sum()
variance = jnp.sum(jnp.abs(OΨ - expval_O * Ψ) ** 2)

ΔOΨ = (OΨ - expval_O * Ψ).conj() * Ψ

_, vjp_fun, *new_model_state = nkjax.vjp(
    lambda w: model_apply_fun({"params": w, **model_state}, σ, mutable=mutable),
    parameters,
    conjugate=True,
    has_aux=is_mutable,
)

Ō_grad = vjp_fun(ΔOΨ)[0]

new_model_state = new_model_state[0] if is_mutable else None

return (
    Stats(mean=expval_O, error_of_mean=0.0, variance=variance),
    Ō_grad,
    new_model_state,
)

[PhilipVinc]

What is not clear? May I suggest that you write the formula that you were expecting and show what lines don't match it?
By the way, consider that O in those lines is not the $O_k(\sigma)=\partial_k\log\psi(\sigma)$ but it's the operator of which we are computing the expectation value, and O_expval is $\langle\psi|\hat{O}|\psi\rangle/\langle\psi|\psi\rangle$ that is the expectation value of it.