# Generalizing Neural Wave Functions

arXiv: https://arxiv.org/abs/2302.04168 · HTML: https://mlsanity.com/paper/2302.04168/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 49 references that are in the map.
- First posted on arXiv 8 Feb 2023.

## Builds on (most cited first, 15 of 15)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Large Batch Optimization for Deep Learning: Training BERT in 76 minutes](https://mlsanity.com/paper/1904.00962/) (2019)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [A Self-Attention Ansatz for Ab-initio Quantum Chemistry](https://mlsanity.com/paper/2211.13672/) (2022)
- [Spherical Channels for Modeling Atomic Interactions](https://mlsanity.com/paper/2206.14331/) (2022)
- [Ab-Initio Potential Energy Surfaces by Pairing GNNs with Neural Wave Functions](https://mlsanity.com/paper/2110.05064/) (2021)
- [Ab-initio quantum chemistry with neural-network wavefunctions](https://mlsanity.com/paper/2208.12590/) (2022)
- [Better, Faster Fermionic Neural Networks](https://mlsanity.com/paper/2011.07125/) (2020)
- [Gold-standard solutions to the Schr"odinger equation using deep learning: How much physics do we need?](https://mlsanity.com/paper/2205.09438/) (2022)
- [Discovering Quantum Phase Transitions with Fermionic Neural Networks](https://mlsanity.com/paper/2202.05183/) (2022)
- [Solving the electronic Schr"odinger equation for multiple nuclear geometries with weight-sharing deep neural networks](https://mlsanity.com/paper/2105.08351/) (2021)
- [Sampling-free Inference for Ab-Initio Potential Energy Surface Networks](https://mlsanity.com/paper/2205.14962/) (2022)

## Built on by (most cited first, 28 of 28)

- [An ab initio foundation model of wavefunctions that accurately describes chemical bond breaking](https://mlsanity.com/paper/2506.19960/) (2025)
- [Wasserstein Quantum Monte Carlo: A Novel Approach for Solving the Quantum Many-Body Schr"odinger Equation](https://mlsanity.com/paper/2307.07050/) (2023)
- [Uncertainty Estimation for Molecules: Desiderata and Methods](https://mlsanity.com/paper/2306.14916/) (2023)
- [Variational Monte Carlo on a Budget -- Fine-tuning pre-trained Neural Wavefunctions](https://mlsanity.com/paper/2307.09337/) (2023)
- [Neural Pfaffians: Solving Many Many-Electron Schr"odinger Equations](https://mlsanity.com/paper/2405.14762/) (2024)
- [Accurate Ab-initio Neural-network Solutions to Large-Scale Electronic Structure Problems](https://mlsanity.com/paper/2504.06087/) (2025)
- [Towards a Foundation Model for Neural Network Wavefunctions](https://mlsanity.com/paper/2303.09949/) (2023)
- [Ab-initio variational wave functions for the time-dependent many-electron Schr"odinger equation](https://mlsanity.com/paper/2403.07447/) (2024)
- [Transferable Neural Wavefunctions for Solids](https://mlsanity.com/paper/2405.07599/) (2024)
- [Forward Laplacian: A New Computational Framework for Neural Network-based Variational Monte Carlo](https://mlsanity.com/paper/2307.08214/) (2023)
- [Learning Equivariant Non-Local Electron Density Functionals](https://mlsanity.com/paper/2410.07972/) (2024)
- [Large Electron Model: A Universal Ground State Predictor](https://mlsanity.com/paper/2603.02346/) (2026)
- [On Representing Electronic Wave Functions with Sign Equivariant Neural Networks](https://mlsanity.com/paper/2403.05249/) (2024)
- [Is attention all you need to solve the correlated electron problem?](https://mlsanity.com/paper/2502.05383/) (2025)
- [Ab-initio simulation of excited-state potential energy surfaces with transferable deep quantum Monte Carlo](https://mlsanity.com/paper/2503.19847/) (2025)
- [Effective Data Pruning through Score Extrapolation](https://mlsanity.com/paper/2506.09010/) (2025)
- [Sorting Out Quantum Monte Carlo](https://mlsanity.com/paper/2311.05598/) (2023)
- [Benchmarking Simulacra AI's Quantum Accurate Synthetic Data Generation for Chemical Sciences](https://mlsanity.com/paper/2511.07433/) (2025)
- [Excited Pfaffians: Generalized Neural Wave Functions Across Structure and State](https://mlsanity.com/paper/2603.14515/) (2026)
- [A Systematic Survey and Benchmark of Deep Learning for Molecular Property Prediction in the Foundation Model Era](https://mlsanity.com/paper/2604.16586/) (2026)
- [M=oLe-Lambda: Learning the Coupled-Cluster Response State for Energies, Gradients, and Properties](https://mlsanity.com/paper/2605.29622/) (2026)
- [Hamilton-Zero: A Neural Tensor-Network Foundation Model for Ground States of Arbitrary Quadratic Qubit Hamiltonians](https://mlsanity.com/paper/2608.11911/) (2026)
- [A Score-Based Model for Learning Neural Wavefunctions](https://mlsanity.com/paper/2305.16540/) (2023)
- [A Theoretical Framework for an Efficient Normalizing Flow-Based Solution to the Electronic Schrodinger Equation](https://mlsanity.com/paper/2406.00047/) (2024)
- [Coupled Cluster con M=oLe: Molecular Orbital Learning for Neural Wavefunctions](https://mlsanity.com/paper/2602.20232/) (2026)
- [Is Variational Monte Carlo Robust? Sharp Moment Thresholds and Heavy-tailed Stochastic Optimization](https://mlsanity.com/paper/2606.26009/) (2026)
- [Foundation Neural-Network Quantum States for Molecular Potential Energy Surfaces in Second Quantization](https://mlsanity.com/paper/2609.37733/) (2026)
- [NucleoNet: A Nuclear-Aware Determinant Ansatz for Multi-Geometry Neural Variational Monte Carlo](https://mlsanity.com/paper/2610.12985/) (2026)

## Abstract (arXiv)

Recent neural network-based wave functions have achieved state-of-the-art accuracies in modeling ab-initio ground-state potential energy surface. However, these networks can only solve different spatial arrangements of the same set of atoms. To overcome this limitation, we present Graph-learned orbital embeddings (Globe), a neural network-based reparametrization method that can adapt neural wave functions to different molecules. Globe learns representations of local electronic structures that generalize across molecules via spatial message passing by connecting molecular orbitals to covalent bonds. Further, we propose a size-consistent wave function Ansatz, the Molecular orbital network (Moon), tailored to jointly solve Schr"odinger equations of different molecules. In our experiments, we find Moon converging in 4.5 times fewer steps to similar accuracy as previous methods or to lower energies given the same time. Further, our analysis shows that Moon's energy estimate scales additively with increased system sizes, unlike previous work where we observe divergence. In both computational chemistry and machine learning, we are the first to demonstrate that a single wave function can solve the Schr"odinger equation of molecules with different atoms jointly.