Preschool Children's Learning and Generalization of Continuous Causal Functions
Bibliographic record
Abstract
Many causal relations can be represented by continuous functions that map inputs to outputs. Can young children learn continuous causal functions and generalize them from observed data to new scenarios? We found that 4- and 5-year-olds can represent continuous functions with different abstract forms. After observing a few input-output pairs, children can accurately infer positive linear and step functions by predicting the outputs of novel input values. They also have emerging knowledge of negative linear and triangular functions. While children do not yet make consistently accurate predictions for these functions, they can distinguish these functions from the positive linear function and show inferential patterns that are consistent with the respective functions. Like adults and older children, preschoolers show an inductive bias towards positive linear functions. Their understanding of negative linear functions--which strongly requires inhibiting this inductive bias--improves with age.
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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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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; both teacher heads agree on what is shown here.
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".