Representing an Intrinsically Nonmetric Space of Compass Directions in an Artificial Neural Network
Bibliographic record
Abstract
The purpose of the article is to train an artificial neural network to make a judgment that is intrinsically antisymmetric, and to determine how such a judgment is mediated by the network’s internal representations. One key component of navigation is judging the distance from one location to another. A second key component of navigation is judging heading – that is, judging the direction from one location to another. Importantly, heading judgments do not preserve the metric properties of space. In particular, they are antisymmetric: the judged heading from location x to location y should be opposite to the judged heading from location y to location x. What kind of representation can mediate such nonmetric navigational judgments? To explore this question, we trained an artificial neural network to judge the various bearings amongst 13 different cities in Alberta. We then interpreted the internal structure of this network in order to determine the nature of its internal representations. We found that he artificial neural network had developed a coarse directional code, and that one of the advantages of such coding was its ability to represent antisymmetric spatial regularities.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".