Learning valid categorical syllogisms using an associative memory
Bibliographic record
Abstract
Reasoning is a high-level cognitive function that is gaining attention in the artificial neural network community. While there are many types of reasoning, this paper is specifically looking at valid categorical syllogisms. First we show that a standard bi-directional associative memory cannot learn all valid categorical syllogisms because these syllogisms are not linearly separable. Therefore a more complex architecture is proposed to learn the task. A combination of unsupervised and supervised learning networks are used. The unsupervised network compresses the input into novel solutions. The output from the unsupervised network in conjunction with the original input produces a new linearly separable input for the supervised network. This unsupervised-supervised learning network combination can successfully learn all the valid syllogisms. If there is a combination of valid and conditionally valid syllogisms, two different networks should be used. The conditionally valid syllogisms can be recalled using the bi-directional associative memory while the valid syllogisms need the more complex network.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".