Many-body mobility edges in one and two dimensions revealed by convolutional neural networks
Bibliographic record
Abstract
We adapt a machine-learning approach to study the many-body localization transition in interacting fermionic systems on disordered one-dimensional (1D) and two-dimensional (2D) lattices. We perform supervised training of convolutional neural networks (CNNs) using labeled many-body wave functions at weak and strong disorder. In these limits, the average validation accuracy of the trained CNNs exceeds 99.95%. We use the disorder-averaged predictions of the CNNs to generate energy-resolved phase diagrams, which exhibit many-body mobility edges. We provide finite-size estimates of the critical disorder strengths at ${W}_{c}\ensuremath{\sim}2.8$ and 9.8 for 1D and 2D systems of 16 sites, respectively. Our results agree with the analysis of energy-level statistics and inverse participation ratio. By examining the convolutional layer, we unveil its feature extraction mechanism which highlights the pronounced peaks in localized many-body wave functions while rendering delocalized wave functions nearly featureless.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".