Double descent: When do neural quantum states generalize?

Abstract: Neural quantum states (NQS) provide flexible wavefunction parameterizations for numerical studies of quantum many-body physics. While inspired by deep learning, it remains unclear to what extent NQS share characteristics with neural networks used for standard machine learning tasks. We demonstrate that NQS exhibit the double descent phenomenon, a key feature of modern deep learning, where generalization worsens as network size increases before improving again in an overparameterized regime. Notably, we find the second descent to occur only for network sizes much larger than the Hilbert space dimension, indicating that NQS typically operate in an underparameterized regime, where increasing network size can degrade generalization. Our analysis reveals that the optimal network size in this regime depends on the number of unique training samples, highlighting the importance of sampling strategies. These findings suggest the need for symmetry-aware, physics-informed architecture design, rather than directly adopting machine learning heuristics.