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Stochastic Reconfiguration as Statistical Filtering for Overparameterized Neural Quantum States

arXiv · AI, language, vision and robotics · article · Sep 20, 2026 · UTC

Stochastic reconfiguration (SR) is the standard optimizer for neural quantum states (NQS), but modern NQS often have far more parameters than Monte Carlo samples. We show that in this regime the diagonal shift is more than a numerical stabilizer. It acts as a statistical filter for finite-sample generalization. At a fixed wave function, SR is ridge regression from tangent features to the centered local energy. Its residual is the expressivity gap, the part of imaginary-time evolution outside the current tangent space. This gap is orthogonal to the tangent space in population, but finite batche

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