Adaptation to non-numeric features reveals mechanisms of visual number encoding
Bibliographic record
Abstract
When observing a simple visual scene such as an array of dots, observers can easily and automatically extract their number. How does our visual system accomplish this? Current theories on visual number encoding have argued that a variety of primary visual features – from low and high spatial frequency, size, contrast, etc., — might all contribute to our visual percept of number. Here, we test the role of spatial frequency by adapting observers to sinusoidal gratings, observing whether this adaptation has an effect on their subsequent perception of number. In Experiment 1 (N = 40; Figure 1A and 1B), on each trial, observers were adapted to six, randomly generated Gabor gratings at either a low-spatial frequency (M = 0.94 c/deg) or a high-spatial frequency (M = 12.25 c/deg); the adapter was presented on either the left or the right side of fixation. Subsequently, observers judged which side of the screen had a higher number of dots. We found a strong number-adaptation effect to low-spatial frequency gratings (i.e., participants significantly underestimated the number of dots on the adapted side) and a significantly reduced adaptation effect for high-spatial frequency gratings. In Experiment 2 (N = 20; Figure 1B) we demonstrate that adaptation to a solid grey patch fails to produce a number-adaptation effect, suggesting that the results in Experiment 1 are not due to a generic response bias. Further experiments with adaptation to mixed spatial frequencies show attenuated effects. Together, our results point towards a key role for low-spatial frequency in visual number encoding, consistent with some existing models of visual number perception (e.g., Dakin et al., 2011) and not with others (e.g., Dehaene & Changeaux, 1993). They also provide a novel methodology for using adaptation to discover the primitives of visual number encoding.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".