A Compositional Neural Network Solution to Primality-Testing
Bibliographic record
Abstract
in my fourth year and graduating with an honours degree in psychology. In the last two years, he became interested in theoretical computer science and his future plans are to do research in this area, starting in 2005 as a Master's student. Dr. Thomas R. Shultz earned his PhD (psychology) from Yale University and is now a psychology professor at McGill University. He studies human cognition through a combination of psychological and computational approaches. A long-standing difficulty for connectionism has been to implement compositionality 1,2,3. Compositionality is the idea of building a problem representation out of components such that the meaning comes from the meanings of the components and the way they are combined. The way Fodor and Pylyshyn 1 put it is the following. In a compositional representation, there is a distinction between structurally atomic and molecular representations, structurally molecular representations have syntactic constituents that are themselves either structurally molecular or are structurally atomic, and the semantic content of a representation is a function of the semantic contents of its syntactic parts, together with its constituent structure. Shultz and Rivest 4,5 introduce a new learning algorithm called knowledge-based cascade-correlation (KBCC) that uses already acquired knowledge to learn a new task. In this paper, it is demonstrated how KBCC creates a compositional representation of the prime number concept and uses this representation to decide whether its input is a prime number or not. Component networks recruited by KBCC correspond to syntactic units and the way they are embedded in the overall network structure corresponds to constituent structure. Compositional KBCC networks learn much faster and generalize much better than ordinary cascade-correlation networks in the control condition.
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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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.017 | 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".