The article discusses the current state of neural networks, a type of machine learning model that has gained significant attention in recent years due to its success in various applications such as image recognition, speech recognition, and natural language processing. The author provides an overview of the generalization error of neural networks, which can be decomposed into two components: approximation error and sampling error. The article highlights how careful design of neural network architectures can reduce approximation error, while reliable data resources are necessary to control sample error.
Approximation Error
The author explains that the approximation capabilities of neural networks with sigmoid activation functions have been explored in various works. Non-polynomial activation functions, such as rectified linear units (ReLU) and its variants, have also been studied for their univarsal properties. The author notes that these activation functions can be combined to achieve better approximation capabilities.
Sampling Error
The article emphasizes the importance of reliable data resources in controlling sample error. The author cites works such as [31] and [5], which established the universality of neural networks with non-polynomial activation functions. Additionally, the author mentions that approximation by combinations of ReLU and squared ReLU functions with ℓ1 and ℓ0 controls can also help reduce sample error.
Conclusion
In conclusion, the article provides a comprehensive overview of the current state of neural networks, highlighting their approximation capabilities and the importance of reliable data resources in controlling sample error. By using everyday language and engaging metaphors, the author demystifies complex concepts, making it easier for readers to understand the essence of the article without oversimplifying.
