## 4 Discussion
Another issue with DL is the \"no free lunch\" theorem, which postulates that a good DL model is theoretically impossible for any problem, and if one model outperforms another, it is specialized for a particular problem. In particular, if the problem changes, the algorithm should change, and it is important to devise a solution that is specific to each problem based on preconditions and prerequisite knowledge as much as possible. The performance of ML methods including DL can be improved forspecific problems by applying an inductive bias, which is prior knowledge or a hypothesis besides the training data. Then, in what kind of problems does DL specialize? Simple and realistically sized neural networks can sufficiently approximate the following problems:  
1. Low-degree polynomial models: any polynomial can be approximated by a neural network consisting of about four times as many neurons as the number of multiplications required for calculation. 2. Locality: a local Markov network can be approximated using a neural network consisting of a number of neurons proportional to the number of nodes. 3. Symmetry: CNNs that explicitly incorporate mobile and temporal universality can significantly reduce the number of parameters required for learning, which also greatly reduces the apparent complexity [74]. According to the \"ugly duckling\" theorem, it is theoretically impossible to classify or judge similarity without some prior knowledge or induction bias. This is conceptually similar to the no free lunch theorem, which argues that there is no universal one-size-fits-all ML model or search or optimization algorithm that can solve any problem efficiently. Meanwhile, the ugly duckling theorem argues that, without assumptions or prior knowledge, there is no optimal feature representation and feature set that will result in better classification performance. This raises the issue that objective or general-purpose classification is difficult. Therefore, this theorem also indicates that algorithms need to be formulated according to the classification problem to be solved. Also, in general, DL has some problems, such as \"overfitting or overtraining\", that if the training period is too long or the training data is not typical, it will adapt to certain random features of the training data, that are unrelated and unwanted features. The state in which unknown test data cannot be adapted and be generalized will lead to a lock of generalization ability [75; 76; 77; 78; 79; 80; 81; 82]. One of the causes is that the model is complicated and has too many degrees of freedom compared to the number of training data, such as too many parameters to fitting to the statistical model. The main strategies for suppressing the overfitting are the following  
1. Increase the number of training data  
To make sure that training is a better generalization, the variation of training data is increased. For the purpose, there is also a method of extending the existing training data by generating a variety of image data with changing the saturation, brightness, and direction of one image. Thus, these approaches make it possible to acquire abundant data and build a flat learning model that does not cause the overfitting by making good use of limited data. However, in the process of the increase of training data, if only biased data is given, it will adversely affect the construction of the model. If a bias, which is a representation of the difference between the predicted results and measured value, is small, the prediction, which represents variability in prediction results, accuracy is high, but if the variance is too large, the versatility is low, and overfitting may occur. In order to build an appropriate prediction model that does not cause the overfitting, it is necessary to keep the balance between bias and variance constant. 2. Model simplification  
Introduction complex and sophisticated algorithms allows for advanced analysis with the addition of various parameters, but at the same time increases the risk of the overfitting.