netket.errors.InsufficientSamplesForSRWarning

exception netket.errors.InsufficientSamplesForSRWarning

Warning issued when using Stochastic Reconfiguration (SR) with insufficient samples.

This warning is raised when the number of samples is less than or equal to the number of parameters in a Stochastic Reconfiguration calculation. In this regime, the standard QGT-based formulation of SR becomes inefficient and potentially unstable.

Why this matters

The standard SR/Natural Gradient Descent computes updates as:

\[\delta \theta = \tau (X^TX + \lambda \mathbb{I}_{N_P})^{-1} X^T E^{loc}\]

where \(X \in \mathbb{R}^{N_s \times N_p}\) is the Jacobian of the log-wavefunction, with \(N_p\) the number of parameters and \(N_s\) the number of samples.

When \(N_s \leq N_p\), the matrix \(X^TX\) has rank at most \(N_s\), making it severely under-determined and requiring large regularization. This leads to poor convergence and potentially unstable optimization.

Recommended solution

Switch to the kernel/minSR formulation which uses the Neural Tangent Kernel (NTK):

\[\delta \theta = \tau X^T(XX^T + \lambda \mathbb{I}_{N_s})^{-1} E^{loc}\]

This formulation inverts a \(N_s \times N_s\) matrix instead of \(N_p \times N_p\), which is much more efficient and stable when \(N_s < N_p\).

Use :class:`netket.driver.VMC_SR` instead of :class:`netket.driver.VMC` with SR.

The VMC_SR driver automatically chooses the optimal formulation and provides the same mathematical result but with better performance and stability.

References

• The kernel trick for SR was introduced by Chen & Heyl and Rende et al..

• For a comprehensive discussion see the netket.driver.VMC_SR documentation.