Chapter 6: Autoencoder Neural Networks
Bibliographic record
Abstract
In this chapter we employ neural networks to provide optimal changes of variable to recast dynamics in simpler forms. The idea is to mimic topological conjugacies whose application in dynamical systems goes back almost to the beginning. Even without the proper mathematical underpinning, the idea of recasting dynamics in a simpler frame of reference has existed for centuries. For example, the geocentric model of the solar system was espoused by great thinkers such as Aristotle and Ptolemy and puts Earth at the center with the Sun and planets moving around it. As shown in Figure 6.1, the incommensurate periods of rotation of each planet about the Sun leads to epicyclic motion when observed from Earth. However, moving to a coordinate frame with the Sun at the center—a heliocentric frame—leads to all of the motions of the planets lying along ellipses. Moving between geocentric and heliocentric frames provides a tangible example of a simplifying coordinate transformation in which all motion is simple and predictable.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.021 | 0.011 |
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".