Popular science: Is deep learning really so difficult?

Today, in the face of AI's status as an important river, deep learning is an important research branch, which appears in almost all popular AI applications, including semantic understanding, image recognition, speech recognition, natural language processing, etc. It is considered that current artificial intelligence is equivalent to the field of deep learning.

If in this era of artificial intelligence, as an ideal ambition programmer, or students, enthusiasts, do not understand the topic of deep learning, this hot topic seems to have been out of touch with the times.

However, the requirements of deep learning for mathematics, including calculus, linear algebra and probability theory and mathematical statistics, make most of the young people with ideal ambitions move forward. Then the question comes, understand deep learning, do you need this knowledge? The Guanzi will not be sold, and the title has already been explained.

Some time ago, the editors strolled through the major community forums and found a post-research post that was very suitable for beginners to learn. Using the funny vernacular and examples to analyze the process of deep learning, it is very easy to understand. Through communication with the teacher Yang Anguo who is engaged in the field of artificial intelligence in Siemens, the content editing authority is authorized, the content is reorganized and revised, and the content is more easy to understand. I hope everyone can understand deep learning.

There is a lot of information on the online learning about deep learning, but it seems that most of them are not suitable for beginners. Teacher Yang summed up several reasons:

1. Deep learning does require a certain mathematical foundation. If you don't need to go into the ground, some readers will have fears and it is easy to give up too early.

2. Books or articles written by Chinese or Americans are generally more difficult.

The mathematical foundation required for deep learning is not as difficult as imagined, just knowing the derivatives and related functional concepts. Have you not studied advanced mathematics? Very good, this article actually wants to be understood by liberal arts students. It is only necessary to learn junior high school mathematics.

In fact, there is no need to have fearful emotions, and the spirit of Li Shufu is more respected. In a TV interview, Li Shufu said: Who said that Chinese people can't make cars? It’s not difficult to make a car, it’s not four wheels plus two rows of sofas. Of course, his conclusion is biased, but his spirit is commendable.

What is the derivative? Nothing else is the rate of change.

For example: Wang Xiaoer sold 100 pigs this year, sold 90 last year, and sold 80 in the previous year. . . What is the rate of change or growth rate? It is much simpler to grow 10 pigs a year. Here you need to pay attention to a time variable --- year. The growth rate of Wang Xiaoer’s selling pigs is 10 heads/year, that is to say, the derivative is 10.

The function y=f(x)=10x+30, here we assume that Wang Xiaoer sold 30 heads in the first year, and then increased 10 heads every year, x represents time (year), and y represents the number of pigs.

Of course, this is a situation in which the growth rate is fixed. In real life, in many cases, the amount of change is not fixed, that is, the growth rate is not constant. For example, the function might look like this: y=f(x)=5x2; +30, where x and y still represent time and number of heads, but the growth rate has changed. How do we calculate this growth rate? Let's talk back. Or you can simply remember a few derivatives formulas.

Deep learning also has an important mathematical concept: partial derivatives, how do you understand partial derivatives? The bias of the migraine, or I will not let you guide, you want to guide? No, we also take Wang Xiaoer as an example. Just now we said that the x variable is time (year), but the pigs sold are not only related to time. As the business grows, Wang Xiaoer not only The pig farm was expanded and many employees were hired to raise pigs together. So the equation has changed: y=f(x)=5x2; +8x + 35x +30

Here x represents the area, x represents the number of employees, and of course x is still time.

As we said above, the derivative is actually the rate of change, so what is the partial derivative? The partial derivative is nothing more than the rate of change of a variable when it is more than one variable. In the above formula, if the partial derivative is obtained for x, that is, how much the employee contributes to the growth rate of the pig, or, as the (each) employee grows, how much the pig has increased, here is equal to 35-- - For each additional employee, sell more than 35 pigs. When calculating the partial derivative, other variables can be regarded as constants. This is very important. The rate of change of the constant is 0, so the derivative is 0, so the derivative is 35x, which is equal to 35. For x, the partial derivative is similar. of.

To find the partial derivative we use a symbol to indicate: for example, y / x means that y is partial to x.

Nonsense for a long time, these have a relationship with deep learning? Of course, there is a relationship. Deep learning uses neural networks to solve linear indivisible problems. In this regard, we will go back and discuss, you can also search the relevant articles online. Here mainly talk about the relationship between mathematics and deep learning. Let me show you a few pictures first:

Figure 1. The so-called deep learning is a neural network with many hidden layers.

Figure 2. How to find partial derivatives when single output

Figure 3. How to find partial derivatives when multi-output.

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