Probability matching in perceptrons: Effects of conditional dependence and linear nonseparability
Bibliographic record
Abstract
Probability matching occurs when the behavior of an agent matches the likelihood of occurrence of events in the agent's environment. For instance, when artificial neural networks match probability, the activity in their output unit equals the past probability of reward in the presence of a stimulus. Our previous research demonstrated that simple artificial neural networks (perceptrons, which consist of a set of input units directly connected to a single output unit) learn to match probability when presented different cues in isolation. The current paper extends this research by showing that perceptrons can match probabilities when presented simultaneous cues, with each cue signaling different reward likelihoods. In our first simulation, we presented up to four different cues simultaneously; the likelihood of reward signaled by the presence of one cue was independent of the likelihood of reward signaled by other cues. Perceptrons learned to match reward probabilities by treating each cue as an independent source of information about the likelihood of reward. In a second simulation, we violated the independence between cues by making some reward probabilities depend upon cue interactions. We did so by basing reward probabilities on a logical combination (AND or XOR) of two of the four possible cues. We also varied the size of the reward associated with the logical combination. We discovered that this latter manipulation was a much better predictor of perceptron performance than was the logical structure of the interaction between cues. This indicates that when perceptrons learn to match probabilities, they do so by assuming that each signal of a reward is independent of any other; the best predictor of perceptron performance is a quantitative measure of the independence of these input signals, and not the logical structure of the problem being learned.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.007 | 0.071 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 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".