## 3 Materials and Methods
### Softmax Temperature Annealing  
When the input values of the Softmax function are divided by a temperature, the resulting probabilities can be adjusted to decrease or increase the variance compared to those obtained from the original Softmax function as follows:  
\[\vartheta_{i,j}(x)=\sum_{o\in\mathcal{O}}\frac{\exp\left(\alpha_{i,j}^{o}/T \right)}{\sum_{o^{\prime}\in\mathcal{O}}\exp\left(\alpha_{i,j}^{o^{\prime}}/T \right)}o(x) \tag{5}\]  
Applying a temperature value of 1 yields the same probabilities as the traditional Softmax function, while using a temperature value greater than 1 reduces the differences among the probabilities. Conversely, applying a temperature value between 0 to 1 accentuates the differences across the probabilities. By incorporating this approach into DARTS, we can converge the probabilities towards values closer to the extremes of 0 and 1. This approach effectively mitigates the discrepancy between the weighted encoded architecturesgenerated by continuous relaxation and the discrete architectures. Setting a lower temperature value allows DARTS, which may introduce discrepancies due to one-hot encoding, to perform the search process in an environment similar to testing. For example, let us say after an \(\alpha\) vector for an edge passes through Softmax function (\(\beta\) vector) shown in Figure 2, results as like [0.1537, 0.0959, 0.0956, 0.1136, 0.1425, 0.1366, 0.1349, 0.1272] from an operator pool of ['none','max pool 3 \(\times\) 3', 'avg pool 3 \(\times\) 3','skip connect','sep conv 3 \(\times\) 3','sep conv 5 \(\times\) 5', 'dil conv 3 \(\times\) 3', 'dil conv 5 \(\times\) 5']. In Figure 2 and Figure 3, each operator is represented as op0 to op7 based on the operator pool. The values are the architectural weights for each operator. In this case, only the first value (the highest value) remains, and the rest will be discarded to decide for that layer (edge). This result is pretty much different from the search phase. During the search phase, the contribution of the first operator was only 15.37% on the layer, but it has been chosen for the operator of that layer in this example. This can cause a problem because the actual contribution was similar to all the other operators and was identical. Moreover, we do not have enough confidence that the operator with the contribution of 0.1366 will perform better than the operator with 0.1349 on that layer. Therefore, with the Softmax temperature annealing method, we relieve this discrepancy between continuously relaxed architecture parameters (\(\beta\)) and discrete architecture (composition of operators). Temperature annealing can make the distribution of \(\beta\) values near discrete values 0 and 1. The temperature annealing method is a way to control the distribution of beta. Since the beta distribution itself is the prediction of operator selection, the temperature annealing method affects the search process. Operators are used in the form of one-hot encodings. During the operator search procedure, each operator exists as a one-hot encoded label. Each operator becomes a single label, and when the entire operator pool combines, it forms a vector of the same length as beta. The length of the beta vector is equal to the length of the operator pool. Furthermore, the values of the beta vector indicate the importance of each operator corresponding to its index. As the beta values are the softmax function's output, the sum of the entire vector is 1, and each value ranges between 0 and 1. However, since the softmax function does not alter the ranking of the alpha values, the beta values  
Figure 2: Visualization of an alpha vector at a certain edge during the search process. The horizontal axis represents the index of operators based on the operator pool. The vertical axis represents the \(\beta\) values for each operator. also maintain the same ranking as the alpha values. When the search process is completed, the operator with the highest beta value is determined to be the most effective operator.