## 3 Materials and Methods
### Softmax Temperature Annealing
As mentioned earlier, the beta values are derived from the alpha values, which are updated through backpropagation. Scaling the alpha values using Softmax temperature also affects the update process. In detail, even if the rankings of the beta and alpha values  
Figure 3: Comparison of beta values passed through Softmax function at different temperatures. The horizontal coordinates indicate each operator based on the index of the operator in the operator pool. (**a**) The values of an alpha vector before it passes through the mixed operator’s Softmax function. (**b**) The values of a beta vector passed through the original Softmax function. (**c**) The values of a beta vector passed through the Softmax function with a temperature of 10. (**d**) The values of a beta vector passed through the Softmax function with a temperature of 0.1  
are the same, scaling the beta values closer or further from one another during the search process influences the magnitude of the update. For example, assuming that the operators corresponding to the 1 st index to the 8 th index in Figure 3 are named op0 to op7, when the vector is in the alpha state (i.e., before passing through the softmax function), the gap between op3 and op4 is not significant. However, when the vector is in the beta state (i.e., after passing through the softmax function), the gap between them can increase or decrease depending on the temperature. In this way, if the gap widens, the model perceives a larger difference than the actual difference in the alpha values. This is similar to mean squared error (MSE), where squaring all errors causes them to become larger than the actual differences. However, the difference between MSE and temperature annealing is that it does not spread all differences equally. Some operators experience an increase in the difference, while others experience a decrease. Additionally, depending on the chosen temperature, the variance of the beta vector can be increased or decreased. In reality, operators are merely individual operators. To select one of these operators and do the operator, the only thing that we have to do is to set the value of the operator's index value as one or near to one. To make these operators similar to the one-hot encoded vector represented with 0s and 1s, the variance of the beta vector should be small. Having a beta vector similar to the one-hot encoded vector means that each beta value exists as a value very close to 0 or 1. However, in the original DARTS (Differentiable Architecture Search) method, there is no part that adjusts the variance of beta. Therefore, it cannot always yield results similar to the one-hot encoded vector. Instead, DARTS' mixed operators parameterize the architecture to make it continuous, resulting in beta values that are distant from the actual one-hot encoded architecture (discrete architecture) and far from 0 and 1. During the search process, alpha values are learned as continuous values. Although multiple operators with high contributions can exist during the search, after the final epoch, only one operator must be selected. We expect only one operator to have a value close to 1 while the others have values close to 0. By adjusting the beta values through temperature, the search process can be guided to yield results similar to the one-hot encoded vector. When scaling the alpha values during the search, the rankings of beta remain unchanged, only the differences change. Let's examine the changes in beta values between operators when adjusting the difference in beta values. The changes in alpha values depending on the temperature can be seen in Figure 3. When the temperature is 1, as shown in Figure 3, there is no change in the alpha values, so it follows the general softmax function. When the temperature is 0.1, as shown in Figure 3, the beta values approach 1 and 0, resulting in a larger difference between the operator with the highest beta value and the one with the lowest beta value. One or a few operators dominate this layer or edge.