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This paper revisits the optimization of neural quantum states (NQS) by framing variational energy minimization as an advantage policy-gradient problem, leading to the development of Proximal Wavefunction Optimization (PWO). PWO employs a trust-region approach that clips probability-ratio changes and phase increments, enhancing stability and convergence speed compared to existing methods like Adam and stochastic reconfiguration. The authors demonstrate PWO's effectiveness by optimizing a 1.5B-parameter RWKV-7 model, achieving significant improvements in training efficiency across various spin systems.
Trust-region optimization can dramatically enhance the training of neural quantum states, achieving stability and speed at unprecedented scales.
Neural quantum states (NQS) provide a flexible and scalable framework for approximating quantum many-body wavefunctions. Among NQS parameterizations, autoregressive models are especially attractive because they enable exact, independent sampling from the Born distribution, avoiding the autocorrelation and mixing issues of Markov chain methods. Yet their optimization remains comparatively underexplored: Adam is a scalable method but ignores function space geometry, while stochastic reconfiguration is principled but costly and numerically fragile in large models. To address this gap, we show that variational energy minimization can be viewed as an advantage policy-gradient problem over the Born distribution, motivating trust-region optimization for NQS training. We introduce Proximal Wavefunction Optimization (PWO), a principled trust-region algorithm that clips probability-ratio changes in the amplitude channel and phase increments in the phase channel. PWO avoids explicit matrix inversion, reuses samples across multiple updates, and combines the scalability of first-order optimization with theoretical guarantees. Across Ising and frustrated $J_1$-$J_2$ one- and two-dimensional spin systems, PWO improves stability and wall-clock convergence over Adam, minSR, and SPRING. Finally, we fine-tune a $1.5$B-parameter RWKV-7 model, demonstrating NQS optimization at a scale over three orders of magnitude beyond prior work.
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