Characterize optimization dynamics for finite-parameter neural quantum states

Investigate and resolve the outstanding questions about the optimization landscape and training dynamics of neural-network quantum state models with a finite number of parameters, going beyond the infinite-width neural tangent kernel regime to understand practical implementations.

Background

The paper highlights that our understanding of the optimization landscape for neural quantum states is incomplete. Although recent work has analyzed the infinite-width limit using neural tangent kernel techniques, practical models have finite parameter counts.

The authors explicitly state that open questions persist in the finite-parameter regime, emphasizing the need for theoretical and empirical understanding that can guide real-world optimization strategies.

References

Initial progress has been made in its characterization using neural tangent kernel techniques in the limit of infinite width NQS. However, there are still open questions in practical implementations with finite numbers of parameters.

— Neural-network quantum states for many-body physics  (2402.11014 - Medvidović et al., 2024) in Concluding remarks and outlook (Section 5)

An open question raised by our results is whether the geometry of the variational manifold can predict when minSR outperforms first-order optimizers. In particular, the spectrum of the QGT and the effective dimension of the sample-spanned tangent space may quantify how much curvature information is captured by a finite number of samples. Relating these information-geometric quantities to the observed performance gap between minSR and Adam across models and spatial dimensions is therefore a promising direction for future work.

— Quantum Geometric Tensor Preconditioning for Stable Training of Recurrent Neural Quantum States  (2608.18065 - Attar et al., 18 Aug 2026) in Section 7, Conclusions

While various works have exploited the capabilities of NQS for novel insights into the non-equilibrium dynamics of quantum many-body systems beyond linear response , severe bottlenecks have been reported in other cases ---the precise origin of which, however, remains unclear.

— Neural quantum states in condensed matter: advances, best practices, and prospects  (2608.21291 - Rigo et al., 21 Aug 2026) in Section C, “Accessing dynamical response and non-equilibrium evolution”