The most influential associative learning model, RW1972 [@rescorla_theory_1972], learns from global error and posits no changes in stimulus associability.
Let $v_{k,j}$ denote the associative strength from stimulus $k$ to stimulus $j$. On any given trial, the expectation of stimulus $j$, $e_j$, is given by:
$$ \tag{Eq.1} e_j = \sum_{k}^{K}x_k v_{k,j} $$
$x_k$ denotes the presence (1) or absence (0) of stimulus $k$, and the set $K$ represents all stimuli in the design.
Changes to the association from stimulus $i$ to $j$, $v_{i,j}$, are given by:
$$ \tag{Eq.2} \Delta v_{i,j} = \alpha_i \beta_j (\lambda_j - e_j) $$
where $\alpha_i$ is the associability of stimulus $i$, $\beta_j$ is a learning rate parameter determined by the properties of $j$^note1, and $\lambda_j$ is a the maximum association strength supported by $j$ (the asymptote).
There is no specification of response-generating mechanisms in RW1972. However, the simplest response function that can be adopted is the identity function on stimulus expectations. If so, the responses reflecting the nature of $j$, $r_j$, are given by:
$$ \tag{Eq.3} r_j = e_j $$
The implementation of RW1972 allows the specification
of independent $\beta$ values for present and absent
stimuli (beta_on
and beta_off
, respectively).
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