GELNO-FD: gauge-equivariant Fourier liquid neural operators for interpretable Markovian Bayesian dynamics
Why this work is in the frame
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Bibliographic record
Abstract
We describe GELNO-FD, an innovative framework that combines Gauge-Equivariant Liquid Neural Operators with Fourier-domain representations to model intricate spatiotemporal dynamics amidst uncertainty. By in- corporating gauge-equivariant structures into the neural operator framework, GELNO-FD guarantees uniform physical symmetry across dynamic fields, while the Fourier-based architecture facilitates fast global context modeling. Additionally, we integrate Markovian temporal dependencies with a Bayesian inference layer to improve interpretability and uncertainty quantification, allowing the model to learn structured stochastic transitions and disseminate calibrated confidence estimates. Experimental findings from both synthetic and real-world dynamical systems illustrate GELNO-FD’s exceptional efficacy in predicting, resilience to distribution shifts, and dependability in decision-critical contexts. This study integrates equivariant learning, operator-based modeling, and probabilistic reasoning to enhance reliable AI for physics-informed and real-world dynamics.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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 it