Optimal sampling and signal detection: unifying models of attention and speed–accuracy trade-offs
Bibliographic record
Abstract
Signal detection theory, speed–accuracy trade-offs, and attentional allocation trade-offs all describe trade-offs between different components of performance in a detection task; however, these phenomena have generally been considered independently and their relationships are unclear. In this article, we expand the classical signal detection model in a way that allows us to incorporate speed, accuracy, and attention into a single unifying framework. Classical signal detection theory generally assumes fixed overlapping distributions of the perceived stimuli generated by desirable and undesirable objects. The variability of these distributions is typically assumed to be attributable either to the true variation among objects or perceptual error. Our new framework considers how investment in learning about the signal being emitted by encountered objects (sampling) might reduce one component of this variability, namely that generated by perceptual error. First, we identify the optimal sampling strategy, based on the payoff-maximizing time or attention a receiver should allocate to a given object. Next, we show how this optimal strategy can vary with parameters such as the ratio of desirable to undesirable objects and the initial perceptual error. Finally, we highlight the consequences of these optimal sampling strategies, using Batesian mimicry as a central example. The implications of the ability of receivers to reduce perceptual error by allocating more time or attention are potentially far reaching. For instance, snap decisions by predators will arise when predators do not gain from allocating more time to make better informed decisions, and under some conditions, this behavior will allow more imperfect mimicry to persist.
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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 | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".