mlsanityData to 7 Oct 2026

Excited Pfaffians: Generalized Neural Wave Functions Across Structure and State

arXiv 2603.14515 ↗First posted 15 Mar 2026cs.LG physics.chem-ph physics.comp-phcited by 1

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Abstract (arXiv)

Neural-network wave functions in Variational Monte Carlo (VMC) have achieved great success in accurately representing both ground and excited states. However, achieving sufficient numerical accuracy in state overlaps requires increasing the number of Monte Carlo samples, and consequently the computational cost, with the number of states. We present a nearly constant sample-size approach, Multi-State Importance Sampling (MSIS), that leverages samples from all states to estimate pairwise overlap. To efficiently evaluate all states for all samples, we introduce Excited Pfaffians. Inspired by Hartree-Fock, this architecture represents many states within a single neural network. Excited Pfaffians also serve as generalized wave functions, allowing a single model to represent multi-state potential energy surfaces. On the carbon dimer, we match the O(Ns4)-scaling natural excited states while training >200× faster and modeling 50% more states. Our favorable scaling enables us to be the first to use neural networks to find all distinct energy levels of the beryllium atom. Finally, we demonstrate that a single wave function can represent excited states across various molecules.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 21 of its 69 references that are in the map. First posted on arXiv 15 Mar 2026.

Builds on

21 of 69 references.

References · 21

  1. 2019Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networkscited by 195
  2. 2023Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systemscited by 118
  3. 2022A Self-Attention Ansatz for Ab-initio Quantum Chemistrycited by 45
  4. 2021Ab-Initio Potential Energy Surfaces by Pairing GNNs with Neural Wave Functionscited by 36
  5. 2020Better, Faster Fermionic Neural Networkscited by 28
  6. 2022Ab-initio quantum chemistry with neural-network wavefunctionscited by 28
  7. 2023Generalizing Neural Wave Functionscited by 26
  8. 2022Gold-standard solutions to the Schr"odinger equation using deep learning: How much physics do we need?cited by 25
  9. 2024A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctionscited by 24
  10. 2022Electronic excited states in deep variational Monte Carlocited by 21
  11. 2022Sampling-free Inference for Ab-Initio Potential Energy Surface Networkscited by 19
  12. 2023Accurate Computation of Quantum Excited States with Neural Networkscited by 16
9 more
  1. 2023Neural Wave Functions for Superfluidscited by 12
  2. 2025An ab initio foundation model of wavefunctions that accurately describes chemical bond breakingcited by 11
  3. 2023Variational Monte Carlo on a Budget -- Fine-tuning pre-trained Neural Wavefunctionscited by 8
  4. 2024Neural Pfaffians: Solving Many Many-Electron Schr"odinger Equationscited by 8
  5. 2025Accurate Ab-initio Neural-network Solutions to Large-Scale Electronic Structure Problemscited by 8
  6. 2025Accurate and scalable exchange-correlation with deep learningcited by 8
  7. 2024Transferable Neural Wavefunctions for Solidscited by 7
  8. 2024Highly Accurate Real-space Electron Densities with Neural Networkscited by 4
  9. 2021Determinant-free fermionic wave function using feed-forward neural networkscited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Position: The Inevitable Transition to Machine Learning in Quantum Chemistrycited by 0