  Neural quantum state (NQS) ans\"atze have shown promise in variational Monte
Carlo algorithms by their theoretical capability of representing any quantum
state. However, the reason behind the practical improvement in their
performance with an increase in the number of parameters is not fully
understood. In this work, we systematically study the efficiency of restricted
Boltzmann Machines (RBMs) to represent the ground states in different phases of
the spin-1 bilinear-biquadratic model, as the hidden layer density $\alpha$
increases. We train our ansatz by minimizing two different loss functions: 1)
energy, and 2) infidelity of the NQS ansatz w.r.t. that of the exact ground
state. We observe that the accuracy of our ansatz saturates with $\alpha$ in
both cases. We demonstrate that this can be explained by looking at the
spectrum of the quantum geometric tensor (QGT). We find that the rank of the
QGT saturates beyond a certain $\alpha$, and we emphasize that it corresponds
to the \textit{dimension of the relevant manifold} for an optimized NQS. This
provides a useful diagnostics for the practical representation power of an NQS
ansatz.
