# Emulating Cued Recall of Abstract Concepts via Regulated Activation Networks
## 3 RAN Methodology to Simulate Recall Operations
### Recall Demonstration with Toy-Data
#### 3.5.1 Single-Cue Recall (SCR) Experiment
```
Input: A \(ExpectActivation\) activation \(A_{n}^{\prime}\) (\(<A_{1}^{\prime},..,A_{j}^{\prime},..,A_{n}^{\prime}>\)) at layer \(L\), with \(n\) nodes Input: Desired Maximum Iteration \(maxIter\) Output: An activation pattern \(a_{m}\) (\(<a_{1},..,a_{i},..,a_{m}>\)) at layer \(L\)-1, with \(m\) nodes Set Regulation Factor \(\rho\) between [0, 1]; Set \(currentActivation=StartingPoint\) (a vector of activation \(<a_{1},\ldots,a_{m}>\)); Set \(previousActivation=currentActivation\); Set \(PropagateActivation\)= CCUAP of \(currentActivation\) to layer L (see Section 3.2.5); Set \(ObservedLtivation(A)\)= Regulate \(PropagateActivation\) via Algorithm 1; Calculate error vector (\(e\)) at layer \(L\) using Equation (10); Set \(iter=0\); repeat Set \(iter=iter+1\); foreach\(a_{i}\) in previousActivationdo  Calculate the delta (\(\triangle_{a_{i},A_{i}}\)) using Equation (11);  Calculate the sum of delta for \(a_{i}\), i.e., \(\triangle_{a_{i}}\), using Equation (12); if\(\triangle_{a_{i}}>0\)then \(a_{temp}=a_{i}+\triangle_{a_{i}}*(1-a_{i})\); if\(a_{temp}>1\)then  Assign \(a_{i}=1\);  end if else if\(a_{temp}<0\)then  Assign \(a_{i}^{new}=0\);  end if else  Assign \(a_{i}^{new}=a_{temp}\);  end if  end if else \(a_{temp}=a_{i}+\triangle_{a_{i}}*(a_{i})\); if\(a_{temp}>1\)then  Assign \(a_{i}^{new}=1\);  end if else if\(a_{temp}<0\)then  Assign \(a_{i}^{new}=0\);  end if else  Assign \(a_{i}^{new}=a_{temp}\);  end if  end if  end for  end for  Set \(currentActivation=<a_{1}^{new},..,a_{i}^{new},..,a_{m}^{new}>\) (new activation vector at layer \(L\)-1);  Set \(previousActivation=currentActivation\);  Set \(PropagateActivation\)= CCUAP of \(currentActivation\) to layer L (see Section 3.2.5);  Set \(ObservedLtivation(A)\)= Regulate \(PropagateActivation\) via Algorithm 1; Calculate error vector (\(e\)) at layer \(L\) using Equation (10); until\(iter=maxIter\); return\(currentActivation\)
```  
**Algorithm 2**Geometric Back-Propagation Operation \begin{table}
\begin{tabular}{r c c c c c c c c c c c} \hline \hline
**Regulation** & **Experiment** & \multicolumn{5}{c}{**E-A at Layer 1**} & \multicolumn{5}{c}{**O-A at Layer 1**} \\ \hline
**\%** & & & **C\({}_{1}\)** & **C\({}_{2}\)** & **C\({}_{3}\)** & **C\({}_{4}\)** & **C\({}_{5}\)** & **C\({}_{1}\)** & **C\({}_{2}\)** & **C\({}_{3}\)** & **C\({}_{4}\)** & **C\({}_{5}\)** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 1: Observations of activations at abstract concept layer 1 for SCR experiments. Figure 8: The trajectories of activation observed at input layer 0 while carrying out one thousand iterations of the geometric back-propagation (GBP) algorithm. The red circle is the starting point of trajectory, and the black circle is the activation value after the thousandth iteration. The graphs also depict the trajectories observed at input layer 0 with six regulation factors \(\rho\) (0%, 0.5%, 0.75%, 1%, 1.25%, and 1.5%). Each graph visualizes the recalled activation for five single-cue recall (SCR) experiments.