Improving with Practice: A Neural Model of Mathematical Development.
Bibliographic record
Abstract
The ability to improve in speed and accuracy as a result of re-peating some task is an important hallmark of intelligent bio-logical systems. Although gradual behavioural improvementsfrom practice have been modelled in spiking neural networks,few such models have attempted to explain cognitive devel-opment of a task as complex as addition. In this work, wemodel the progression from a counting-based strategy for ad-dition to a recall-based strategy. The model consists of twonetworks working in parallel: a slower basal ganglia loop, anda faster cortical network. The slow network methodically com-putes the count from one digit given another, correspondingto the addition of two digits, while the fast network gradually“memorizes” the output from the slow network. The faster net-work eventually learns how to add the same digits that initiallydrove the behaviour of the slower network. Performance ofthis model is demonstrated by simulating a fully spiking neu-ral network that includes basal ganglia, thalamus and variouscortical areas. Consequently, the model incorporates variousneuroanatomical data, in terms of brain areas used for calcula-tion and makes psychologically testable predictions related tofrequency of rehearsal. Furthermore, the model replicates de-velopmental progression through addition strategies in termsof reaction times and accuracy, and naturally explains observedsymptoms of dyscalculia.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.013 | 0.002 |
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".