# Singing-Voice Timbre Evaluations Based on Transfer Learning
## 4 Transfer Learning Model for Timbre Evaluation
### Transfer Learning Model
#### 4.2.2 Singing-Voice Timbre-Evaluation Network  
A sixteen-dimensional rating vector for timbre can be learned from the musical-instrument timbre-evaluation network. Each dimension in the vector represents a different aspect of the timbre's evaluation index, such as thin, bright, dark, sharp, etc. These indexes are closely related to the final score of the singing voice. For example, if timbre is too sharp, the auditory perception will be harsh and the final score will be low; if timbre is very rich, it will give the impression of a hierarchy and the final score may be higher. Transforming the original task from learning a rating from a mel diagram to learning the final score based on evaluation vectors can reduce the difficulty. The design of this transfer learning articulation can also verify whether the features of instrument timbre scores have commonality with singing-voice tones. If the perception of the human ear is similar for both types of audio, then machine learning rules that apply to instrument timbre also apply to singing-voice timbre. A twelve-dimensional vector is selected as the input to the model by eliminating error-prone vectors from sixteen-dimensional vectors. Since a twelve-dimensional vector has been learned, the training dimensionality is not too high, so the evaluation layer of the singing-voice timbre-evaluation model only has one dense layer. Using one dense layer for training can prevent overfitting more effectively. Among the four judges' scores for 132 songs, there were only a few cases in which the four judges scored exactly the same. More than half of the ranges are at two points or more, and there were even cases where the range reached four points. There is little point in using machine learning for subjective evaluations if true labels are chosen inappropriately. If the score label of the four judges is replaced by the average label commonly used in traditional models, it is a bit sloppy, especially in the case of small data, and it may lead to overfitting. If each score is entered into the model as an independent label, model training will be more difficult. Based on this consideration, the evaluation's probability distribution is used as the training target, with labels being 11-dimensional vectors representing the probability of evaluation at 0-10. For example, if a song Is scored as two 5 s and two 6 s, then its label will be [0., 0., 0., 0., 0., 0.5, 0., 0., 0., 0.]. In the actual experiment, due to the uneven distribution of samples, the regions are redivided--with 0, 1, and 2 being the same interval and 6, 7, 8, and 9 being the same interval. For example, if a song is scored with two 6 s and two 8 s, its label should be [0., 0., 0., 0., 0., 1.0, 0.0]. Cross entropy can focus on both the probability gap between the predicted and true values and the scatter of the predicted distribution. We define the loss function as the relative entropy of the predicted value to the true value minus the relative entropy of the true value itself. For different prediction cases, the custom loss function reflects the desired fitting ability. Taking the two-dimensional case as an example. Assuming that the true value of the probability distribution is [0.5, 0.5], the loss function is shown in Equation (2) as follows. loss \[=-\sum_{i=0}  
The dataset was divided into a ratio of 80% training set, 10% test set, and 10% validation set. The average cross-entropy of the control model under a 10-fold cross-validation is 1.126. The model significantly improved compared with the contrast model, but this research found that the model has the problem of overfitting from individual sample prediction results. After several experiments, we solved the overfitting problem by modifying the singing-voice timbre-evaluation network into a multi-input network.