# Natural Brain-Inspired Intelligence for Non-Gaussian and Nonlinear Environments with Finite Memory
## 4 Design of CDS Architecture for Finite Memory NGLNE
### Perceptor  
Conventionally, the perceptor of a CDS should have Bayesian filtering [3]. In this paper, we use the Bayesian equation and the decision-making tree approach for extracting the posterior in decision-making (i.e., \(P(\mathbf{X}_{n}|\mathbf{Y}_{n}^{m})\)), which is more straightforward than the Bayesian filtering approach. In addition, the multilayer Bayesian generative model using the decision trees concept is a typical method in machine learning. Here, we define \(m\) focus levels as the depth of the decision-making tree and \(i\) is the arbitrary decision-making node level between zero to \(m\) depth levels. This is because we need to design low-complexity and real-time algorithms for NGNLE applications. Therefore, the main sub-blocks of the perceptor are: (i) Bayesian generative model, (ii) previous model selection, and (iii) Bayesian equation and decision-making. The multilayer Bayesian generative model for different focus levels implementation is now presented. Bayesian Generative Model Extraction  
Suppose that there exists no relevant model in a model library. The three-layered Bayesian modeling block extracts the statistical model of the system (see [20; 23] for further details) using a decision-making tree. The three-layered Bayesian modeling consists of three layers for an arbitrary focus level of \(m\), as explained in (a), (b), and (c) below:  
1. Layer I:  
In a NGNLE, some observables could have any value, and hence, a large number of discretized cells are required for saving vacant spaces. For example, the output of the fiber optic link is a complex variable \(Y_{n}^{k,m}\), where \(n\) is the discrete time, \(k\) is the PAC number, and \(m\) is the current focus level. Therefore, we define the probability box (PB) percentage. The data normalized in this way is sent to Layer II as the \(\overline{Y}_{n}^{k,m}\) for further processing. For the 2D observables, this box can be determined as the \(x_{\min}^{k,m}\) and \(x_{\max}^{k,m}\) for the minimum and maximum of the probability box in the \(x\)-axis together with \(y_{\min}^{k,m}\) and \(y_{\max}^{k,m}\) for minimum and maximum of the box in the \(y\)-axis. The internal reward is used to select the borders of the probabilistic box adaptively as the internal commands by the executive. More details provided on the PB parameters can be found in references [20; 21; 22; 23]. 2. Layer II:  
In Layer II, the values related to observables are discretized with discretization steps \(\Delta x_{i}^{k}\) and \(\Delta y_{i}^{k}\), which can be two-dimensional if the observables are complex numbers (e.g., see [20; 21; 22; 23]) and \(0\leq i\leq m\). For simplicity, we define a precision factor \((P_{i}^{k})\) for each focus level as (assume \(\Delta x_{i}^{k}=\Delta y_{i}^{k}\)):  
\[P_{i}^{k}=10\Delta x_{i}^{k}=10\Delta y_{i}^{k},\qquad 0\leq i\leq m, \tag{3}\]  
\[\textbf{PF}^{k,m}=[P_{0}^{k},P_{1}^{k},\cdots,P_{i}^{k},\cdots,\,P_{P_{m}}^{k }], \tag{4}\]  
\[F_{i}^{k}=N_{x}^{k,i}N_{y}^{k,i},\quad\ 0\leq\ i\leq m, \tag{5}\]  
\[N_{x}^{k,i}=\frac{10(x_{\max}^{k,i}-x_{\min}^{k,i})}{P_{i}^{k}}, \tag{6}\]  
\[N_{y}^{k,i}=\frac{10(y_{\max}^{k,i}-y_{\min}^{k,i})}{P_{i}^{k}}, \tag{7}\]  
\[F_{m}^{total,k}=\prod\limits_{f=0}^{m}F_{i}^{k},\qquad m\in\{0,1,2,\ldots,M\}, \tag{8}\]  
\[\text{and, }F_{m}^{total,\ k}\leq Complexity\ threshold.\]  
Here, \(N_{x}^{k,i}\) and \(N_{y}^{k,i}\) are the number of discretized cells in the \(x\)-axis and \(y\)-axis, respectively. Furthermore, \(F_{i}^{k}\) corresponds to the number of decision-making tree branches (see Equations (3) and (5)). It should be noted that the required storage memory increases exponentially with increasing focus levels (see Equation (8)). In addition, the perceptor requires a larger database to extract a reliable model. Therefore, the complexity threshold is predefined based on the available storage memory for saving the model on hard disk or loading the model into RAM.