Mathematical Psychology
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Pearce-Hall Model

The Pearce-Hall model proposes that the associability of a stimulus increases when outcomes are surprising, directing attention toward cues whose consequences are uncertain.

αₙ₊₁ = |λₙ − ΣVₙ|

The Pearce-Hall model (1980) addresses a limitation of the Rescorla-Wagner model by allowing the learning rate (associability, α) of a conditioned stimulus to change dynamically based on recent prediction errors. When outcomes are surprising (large prediction error), associability increases; when outcomes are well-predicted, associability decreases.

The Updating Rule

Pearce-Hall Model ΔVₙ = S · αₙ · (λₙ − ΣVₙ)
αₙ₊₁ = γ·|λₙ − ΣVₙ| + (1−γ)·αₙ₋₁

S = salience of the CS (fixed)
α = associability (variable, changes with surprise)
γ = weighting of current vs. previous associability

Key Predictions

The model explains latent inhibition (pre-exposure to a CS without the US reduces α, slowing subsequent learning), the Hall-Pearce effect (partial reinforcement maintains high α, facilitating later acquisition), and the finding that surprising events capture attention. Neurally, the associability signal has been linked to acetylcholine release from the basal forebrain — surprising events increase cholinergic activity, enhancing cortical plasticity and attention.

Related Topics

References

  1. Pearce, J. M., & Hall, G. (1980). A model for Pavlovian learning: Variations in the effectiveness of conditioned but not of unconditioned stimuli. Psychological Review, 87(6), 532–552. https://doi.org/10.1037/0033-295X.87.6.532
  2. Holland, P. C., & Gallagher, M. (1999). Amygdala circuitry in attentional and representational processes. Trends in Cognitive Sciences, 3(2), 65–73. https://doi.org/10.1016/S1364-6613(98)01271-6
  3. Wilson, R. C., & Niv, Y. (2012). Inferring relevance in a changing world. Frontiers in Human Neuroscience, 5, 189. https://doi.org/10.3389/fnhum.2011.00189

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