# A Perspective on Information Optimality in a Neural Circuit and Other Biological Systems
## 4 Discussion  
### The Utility of a Logic Gate Model  
Figure 2 shows a logic gate model of an idealized neural circuit. This assumes a level of abstraction of the individual parts of the system, and a static snapshot of neuronal dynamics. In a larger network, such as in advanced information processing, it is expected that the use of nonlinear dynamics will better capture the deeper complexity of the system, such as that used in comparisons of an animal's neural network to an artificial neural network [57, 58]. However, at these scales, there is typically a limitation in the explainability of a model, particularly at the neuronal level. Instead, use of a logic gate model may provide better explainability and offer intuition on the routing and efficiency of information flow in a neural network.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Mathematical Operations**} \\
**Input 1** & **Input 2** & **Output (Multiplication)** & **Output (Division)** \\ \hline
**A A** & **B B** & **AA \(\times\) BB =** & **AA/BB = QQ (ERRR)** \\ \hline
1 1 & 1 1 & 1 0 0 1 & 0 1 0 0 0 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Truth table for binary multiplication and division in the case of two 2-bit input values. Input 1 is a 2-bit value labeled AA; Input 2 is a 2-bit value labeled BB. The output value for multiplication is the product of AA multiplied by BB. The output value for division is AA divided by BB; the quotient value QQ is stored in the 2 most significant bits, and the divide-by-zero error bit is the next adjacent bit, while the 3 least significant bits store the unrounded remainder value (RRR). Specific to this case of lower precision, the remainder value is stored in a 3-bit value since the highest possible remainder value is not greater than 7 (base 10 number system).  
The logic gate model is also more applicable for a neural circuit in an unchanging environment. For a dynamic environment, it becomes difficult to disentangle the inner workings of a neural circuit, since it is expected that some of its many functions remain unknown. This is a reminder that past studies have identified roles of neurons in a controlled setting; however, these roles are often specific to a single environment, or a few environments, and are not tested across all potential environments (Figure 3). This problem is compounded by the complexity inherent in the dynamics of an animal's physiology and its interactions. This complexity may also be described as a system of high dimensionality, so that the number of parameters is large and difficult to estimate in practice.  
The use of the logic-gate model depends on information flowing from sensory input to output, such as in the case of a sensory neuron to a motor neuron [59]. The organization of a neural network and its circuits is expected to depend on the values at the input and output layers, especially during the relatively rapid modifications in an animal's early development. These systems are essentially programmable network systems of neurons and synaptic connections. The connections, at least as idealized features, are dynamic with respect to gain, loss, and in the strength of connection. The connectivity and the network structure show evidence of optimality in structure, as described in the Introduction, and so it is reasonable to consider optimality in the information flow across a neural system, too. Theory provides an important guide, while the above method offers an alternative method where theory is not applicable, or interpretable.