# Emulating Cued Recall of Abstract Concepts via Regulated Activation Networks
## 4 Cued Recall Demonstration with MNIST Data  
The MNIST [70] dataset is a collection of handwritten images of digits (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9), where each image is black and white in color and has a 28 \(\times\) 28 pixel size. This dataset of image domains is used to demonstrate the Ccued recall operation of learned abstract concepts representing different digits. Two types of investigations were conducted with this dataset: first, multiple binary valued cue recall (MBVCR), where the E-A vector is a binary value ([0, 1]) vector, and second, multiple-cue recall (MCR). For this experiment, one thousand images were selected randomly from the MNIST dataset. The 28 \(\times\) 28 image was transformed in a single vector of 784 attributes, where each attribute corresponds to a pixel of the image. Additionally, the attribute values of the \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Regulation** & **Experiment** & \multicolumn{6}{c}{**E-A at Layer 1**} & \multicolumn{6}{c}{**O-A at Layer 1**} \\ \hline \multirow{2}{*}{**\%**} & & **C\({}_{1}\)** & **C\({}_{2}\)** & **C\({}_{3}\)** & **C\({}_{4}\)** & **C\({}_{5}\)** & **C\({}_{1}\)** & **C\({}_{2}\)** & **C\({}_{3}\)** & **C\({}_{4}\)** & **C\({}_{5}\)** \\ \hline
0.4 & Exp-9 & 0.09 & 0.40 & 0.28 & 0.07 & 0.35 & 0.109 & 0.388 & 0.282 & 0.087 & 0.362 \\
0.5 & Exp-9 & 0.09 & 0.40 & 0.28 & 0.07 & 0.35 & 0.112 & 0.385 & 0.281 & 0.090 & 0.363 \\
**0** & **Exp-10** & 0.07 & 0.09 & 0.44 & 0.26 & 0.10 & 0.068 & 0.093 & 0.440 & 0.263 & 0.099 \\
**0.1** & Exp-10 & 0.07 & 0.09 & 0.44 & 0.26 & 0.10 & 0.073 & 0.098 & 0.437 & 0.264 & 0.105 \\
0.2 & Exp-10 & 0.07 & 0.09 & 0.44 & 0.26 & 0.10 & 0.076 & 0.103 & 0.434 & 0.264 & 0.110 \\
0.3 & Exp-10 & 0.07 & 0.09 & 0.44 & 0.26 & 0.10 & 0.079 & 0.106 & 0.431 & 0.264 & 0.114 \\
0.4 & Exp-10 & 0.07 & 0.09 & 0.44 & 0.26 & 0.10 & 0.082 & 0.109 & 0.428 & 0.265 & 0.117 \\
0.5 & Exp-10 & 0.07 & 0.09 & 0.44 & 0.26 & 0.10 & 0.084 & 0.112 & 0.425 & 0.265 & 0.120 \\ \hline \multicolumn{10}{l}{E-A, expected activation, O-A, observed activation.} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: \(Cont.\)data were normalized between 0 and 1 using min-max normalization (black pixel is min, i.e., 0, and white pixel is max, i.e., 255). Having preprocessed the data, the RAN modeling procedure was instantiated by selecting the K-mean clustering algorithm as the concept identifier. \(K\) was initialized with 30 to determine thirty categories in the input space. The model was configured to grow one level deep and build convex abstract concept (CAC) layer 1. After carrying out all four steps of RAN modeling (see Section 3.2), a model was obtained--see Figure 10.  
In Figure 10, layer 0 has 784 nodes representing each pixel; CAC layer 1 has 30 nodes representing the thirty categories identified during the CCI process in RAN modeling. The inter-layer weights (ILWs) are the cluster centers (CRDPs) of the thirty clusters. Figure 11 shows the ILWs reconstructed in image form of \(28\times 28\) pixels. In RAN modeling, a CRDP is the optimum representative of an input level category at CAC layer 1. Therefore, Figure 11a-ad are the best represented by CAC node N\({}_{1}\),..., N\({}_{30}\), respectively. In Figure 11 it is noticeable that each digit is represented by at least two CAC node of layer 1. The digit 9 is represented by the largest number of nodes, i.e., N\({}_{2}\), N\({}_{15}\), N\({}_{18}\), and N\({}_{24}\). In contrast, digit 4 is represented by two nodes, N\({}_{1}\) and N\({}_{10}\). Figure 11d,m,u,x show that the CAC nodes N\({}_{4}\), N\({}_{13}\), N\({}_{21}\), and N\({}_{24}\) do not represent an individual digit. Node N\({}_{4}\) and N\({}_{13}\) jointly represent digits 3 and 8; node N\({}_{21}\) looks like two digits, 3 and 5; and N\({}_{24}\) depicts digits 7 and 9. For simplicity, Figure 10 shows only inter-layer learning; intra-Layer learning (CSRL weights) was also performed on both the input layer 0 and CAC layer 1.