The human visual system preserves the hierarchy of two-dimensional pattern regularity
Bibliographic record
Abstract
Symmetries are present at many scales in natural scenes. Humans and other animals are highly sensitive to visual symmetry, and symmetry contributes to numerous domains of visual perception. The four fundamental symmetries—reflection, rotation, translation and glide reflection—can be combined into exactly 17 distinct regular textures. These wallpaper groups represent the complete set of symmetries in two-dimensional images. The current study seeks to provide a more comprehensive description of responses to symmetry in the human visual system, by collecting both brain imaging (steady-state visual evoked potentials measured using high-density EEG) and behavioural (symmetry detection thresholds) data using the entire set of wallpaper groups. This allows us to probe the hierarchy of complexity among wallpaper groups, in which simpler groups are subgroups of more complex ones. We find that both behaviour and brain activity preserve the hierarchy almost perfectly: subgroups consistently produce lower-amplitude symmetry-specific responses in visual cortex and require longer presentation durations to be reliably detected. These findings expand our understanding of symmetry perception by showing that the human brain encodes symmetries with a high level of precision and detail. This opens new avenues for research on how fine-grained representations of regular textures contribute to natural vision.
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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 | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".