SOP model

A model associated with Allan R. Wagner in which stimulus elements occupy an inactive state $I$, primary activation $A_1$, or secondary activation $A_2$. External presentation recruits inactive elements into $A_1$; activity then passes through $A_2$ to inactivity. Learned associates can recruit elements into $A_2$. These are functional states, not established neuronal or receptor identities.

Represent a three-state probability distribution by occupancy fractions $\mathbf{p}=(p_I,p_1,p_2)$ in $I,A_1,A_2$. A nonnegative transfer $f_{ij}\le p_i$ subtracts the same amount from donor $i$ that it adds to recipient $j$. The total therefore remains $p_I+p_1+p_2=1$. If all simultaneous outflows from a state sum to at most its old occupancy, each occupancy remains nonnegative. This elementary conservation argument makes a proposed numerical realization checkable; it does not identify the states with biological compartments.

A development of the model by Allan R. Wagner and Susan E. Brandon distinguishing sensory-specific and emotive components of outcome representations, with potentially different activation time courses and response consequences. It allows one cue to influence multiple response systems differently without requiring contradictory values in one undifferentiated representation.

An extension allowing association changes involving associatively activated, physically absent cues. In the common symmetric formulation, matched $A_1/A_1$ and $A_2/A_2$ states support excitation, while mismatched $A_1/A_2$ and $A_2/A_1$ states support inhibition. The extra rules allow forms of retrospective revaluation; neural reactivation alone does not verify their signs.