Waveflow: Boundary-conditioned normalizing flows applied to fermionic wave functions
Bibliographic record
Abstract
An efficient and expressive wave function Ansatz is key to scalable solutions for complex many-body electronic structures. While Slater determinants are predominantly used for constructing antisymmetric electronic wave function Ansätze, this construction can result in limited expressiveness when the targeted wave function is highly complex. In this work, we introduce Waveflow, an innovative framework for learning many-body fermionic wave functions using boundary-conditioned normalizing flows. Instead of relying on Slater determinants, Waveflow imposes antisymmetry by defining the fundamental domain of the wave function and applying necessary boundary conditions. A key challenge in using normalizing flows for this purpose is addressing the topological mismatch between the prior and target distributions. We propose using O-spline priors and I-spline bijections to handle this mismatch, which allows for flexibility in the node number of the distribution while automatically maintaining its square-normalization property. We apply Waveflow to a one-dimensional many-electron system, where we variationally minimize the system’s energy using variational quantum Monte Carlo (VQMC). Our experiments demonstrate that Waveflow can effectively resolve topological mismatches and faithfully learn the ground-state wave function.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".