Report on scipost_202201_00036v1
Bibliographic record
Abstract
We use deep neural networks to machine learn correlations between knot invariants in various dimensions.The three-dimensional invariant of interest is the Jones polynomial J(q), and the four-dimensional invariants are the Khovanov polynomial Kh(q, t), smooth slice genus g, and Rasmussen's s-invariant.We find that a two-layer feed-forward neural network can predict s from Kh(q, -q -4 ) with greater than 99% accuracy.A theoretical explanation for this performance exists in knot theory via the now disproven knight move conjecture, which is obeyed by all knots in our dataset.More surprisingly, we find similar performance for the prediction of s from Kh(q, -q -2 ), which suggests a novel relationship between the Khovanov and Lee homology theories of a knot.The network predicts g from Kh(q, t) with similarly high accuracy, and we discuss the extent to which the machine is learning s as opposed to g, since there is a general inequality |s| ≤ 2g.The Jones polynomial, as a three-dimensional invariant, is not obviously related to s or g, but the network achieves greater than 95% accuracy in predicting either from J(q).Moreover, similar accuracy can be achieved by evaluating J(q) at roots of unity.This suggests a relationship with SU (2) Chern-Simons theory, and we review the gauge theory construction of Khovanov homology which may be relevant for explaining the network's performance.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.008 | 0.005 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.929 | 0.896 |
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; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
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".