Tech Hammer

40 million yuan?

It seemed like a lot, but Ning Wei didn't feel anything.

No, it’s not that much. After tax is deducted, there is only about 20 million left, which is actually not a lot.

Gone...

In fact, Ning Wei's mind was not entirely focused on the money issue. Thinking that the EDA project had finally found its home, he remembered the ambition he and Yu Xingwei had set when the project was first established. When they proved that this EDA software had practical significance, Now, bring back Professor Han and let him code until he is bald.

Now that he is about to leave the project team, if he doesn't make this request, he probably won't have a chance.

As soon as he thought about this, Ning Wei said: "You can take care of the money matter. As for the Professor Han I selected before, I wonder if I can let him return to our project team now?"

"Old Han? Oh, it's not a question of whether he can. The main reason is that he has applied for a project and is busy. He probably won't have time to come here." Lu Changbin replied.

"Oh? What project did Professor Han apply for? Can you tell me?" Ning Wei asked curiously.

Although Professor Han didn't give him face at the time, Ning Wei actually had a good impression of the professor and was indeed curious about what project the professor had chosen.

"Are you interested in Lao Han's project? Wait a minute, I'll look for his proposal report." After saying that, Lu Changbin stood up, went to the filing cabinet behind him, and started searching.

Soon Professor Han's proposal report was found by Lu Changbin and handed to Ning Wei.

Ning Wei read it carefully and found that it was indeed very pragmatic.

Professor Han’s topic is about shortening the time of random walk algorithms, which is also related to the direction of artificial intelligence. For example, this type of algorithm involves the sampling speed issue in machine learning models.

But what is very interesting is that this proposition overlaps with a geometric problem that has troubled the mathematics community for many years.

A simple description of this geometric problem in everyday language is that if there is a watermelon, how can it be divided into two equal parts and keep it fresh for a longer time?

To keep the pulp fresh as long as possible, the idea is to minimize the area of ​​the pulp exposed to the air, that is, to minimize the area of ​​​​slicing with one cut, which is of course achievable.

But this can lead to a more advanced question, that is, whether the three-dimensional result can also be established in high-dimensional space.

To describe it in specific mathematical language, if a convex body of any dimension is bisected by a lower one-dimensional plane, is there a constant c that allows the convex body to have at least one tangent plane with an area greater than c?

This is the KLS conjecture problem that is not too famous among the general population but is of great practical value.

The proposition of three-dimensional space in life is actually easy to understand.

Because no matter how the watermelon grows, it will never grow like thin strips from every angle. If it is a long watermelon, cut it vertically and the cut surface will be smaller. Of course, you can also cut it at a horizontal angle, so that the cut surface will be much larger.

But if you put it in a higher dimension, it's not that simple.

But everyone knows that mathematicians are not born to make people worry-free. They can always interpret a problem from various strange angles. So the mathematical community put forward another proposition: Why should a cut watermelon be flat?

Can you find the smallest surface area that can be used to bisect this watermelon?

This is the issue that the KLS conjecture is most concerned about.

As mathematicians further abstract, the KLS conjecture can be understood as the shape of this watermelon in high-dimensional space is a container encapsulating gas, and finding the best section is to find the bottleneck of this container. Just imagine, if the watermelon becomes a dumbbell-shaped container in a high-dimensional space, with a gas molecule moving randomly in it, then the thinner the connecting part in the middle of the dumbbell, the harder it will be for the molecule to run to the other side.

So the real problem that Professor Han wants to solve now is to find out how thin the thinnest part of this convex container can be in high-dimensional space.

To put it more simply and crudely, we need to prove whether there is such a constant c. In any dimension, this constant c is a fixed value. If there is, it means that this watermelon cannot be like a dumbbell in high-dimensional space, with two sides being large and connected in the middle. Sections can be very thin. Because this constant c determines that its shape cannot have such a thin connecting part.

And if this cannot be proven, then everything is possible. Gas molecules may move on one side of the container for a long time in high-dimensional space, and it is difficult to go to the other side.

Therefore, by solving this problem, the existing computer random walk time can be optimized accordingly.

If put into mathematics, if this proposition is solved, it will accelerate the volume research in the high-dimensional space of approximate convex bodies.

But in fact, although this is a geometric problem, previous breakthroughs in research on this problem were all contributions made by scientists in the computer industry.

As early as nine years ago, a computer scientist used random positioning technology to reduce the upper bound of the dimension of this problem when studying this problem, but the effect was not obvious.

Six years ago, two PhDs from the University of Washington improved the previous random positioning technology and further reduced the KLS factor, which is the factor used to describe the existence of bottlenecks, to the fourth root of the dimension.

If they can reduce the unique power exponent to almost 0, then the 0th power of this number is always equal to 1, which proves that the KLS factor is a constant that has nothing to do with the dimension, thus completely ending this problem. These two It was indeed tried, but in the end it failed. The proof process was proved to be wrong, so it only left some ideas for future generations to learn from.

The topic Professor Han is applying for now is to solve this problem.

To others, this was just an ordinary proposal report, but after Ning Wei read it, an idea suddenly flashed in his mind, because he found that this problem could be solved using the statistical knowledge he had just sorted out recently. solve.

Yes, you don’t need to use algebraic geometry or advanced computer technology. You only need to use statistics to solve this problem. And if this problem is solved, his statistics graduation thesis can be completed. At the same time, Lao Han will probably have nothing to do in the near future, so he can rejoin the EDA project team as he wishes.

Yes, at this moment Ningwei just feels that some things in this world are too coincidental.

I had been searching for the graduation thesis topic for a long time, but it was solved because of a casual agreement with Yu Xingwei and a proposal report.

If nothing else, if the idea in his brain at this time can stand verification, and the mathematical community has indeed not solved this conjecture, then it seems that it would not be a big problem to publish this paper in a top journal, let alone SCI area one. .

More importantly, the laboratory seems to be producing multiple results again.

Ning Wei subconsciously looked at the funding Professor Han applied for, which was three hundred thousand.

"Well, Professor Lu, I suddenly thought of something urgent, so I'm going back to the dormitory first. I can handle other things as you have thought. I'll be fine." Ning Wei said, and put Professor Han's proposal report back on Lu Changbin's desk. superior.

"Ah? It's an emergency?" Lu Changbin was a little confused. The little guy was just reading Han's report leisurely. Why did it suddenly become an emergency?

"Yes, it's urgent." Ning Wei said.

"Okay, then go quickly." Lu Changbin said quickly.

"Goodbye, Professor Lu."

…

Ning Wei hurried back to the dormitory, where three people were also reading at the table and writing a thesis.

There is no way, the final hurdle of graduating from 985 University is really not that easy, especially for students who are not very interested in mathematics. Sometimes when writing a paper, you really need to look up formula after formula, and it takes a page of books. Even after flipping through a page of the book, what's even more annoying is that I often can't find the knowledge point I need to use.

Fortunately, several people had some ideas in mind and didn't let Ning Wei give any guidance. If they didn't think about it themselves, they wouldn't be able to pass the defense, which would be even more disgusting.

After saying hello to his roommates, Ning Wei woke up the computer.

In the dormitory these days, March, the virtual little kitten, has successfully gained the love of several people in the dormitory. This kitten is particularly popular because of its bluffing eyes when it is anxious.

However, like Yu Xingwei, none of the other three people regarded March as an intelligent display program, but just as a pet applet developed by Ning Wei when he was bored living alone in the laboratory.

Xu Ruixuan also mentioned copying the program to his computer as a surprise for Xu Mo, but after being directly rejected by Ning Wei, he gave up the idea.

Ning Wei occasionally spoke to March, but was regarded by the three of them as a pastime for the god of learning.

After all, it is somewhat understandable for a guy with outstanding abilities to have some quirks.

For example, Ningwei not only has the quirk of teasing virtual cats, but also has the quirk of hiding clumsiness, and he has been hiding for three years.

This is the conclusion that the three people came up with during night talks every night when Ning Wei lived in the laboratory.

After all, they couldn't accept the fact that Ning Wei suddenly became enlightened. The most reasonable explanation is that in the past three years, Ning Wei has been using his highly intelligent mind and insightful and caring eyes to silently watch the three mentally retarded people and Trying hard to suppress his IQ until he can blend in with them perfectly.

It wasn't until his senior year that everyone was about to separate, and the stimulation of the unfair treatment of the students who were exempted from promotion finally made this child explode...

In this way, everything can have a perfect explanation.

…

He would rather not care at all what the three people in the dormitory think of him.

Anyway, everyone is familiar with it.

At this time, he had temporarily exited the March program, and then began to search for content about the KLS conjecture in the library's search system.

Soon he found the paper mentioned in Professor Han's opening report in the NeurIPS2016 conference report. Through this paper, he roughly understood the previous ideas of solving this problem, and then began to compare with the solutions in his mind.

After careful analysis by his brain, Ning Wei started programming first. He needed to verify whether his idea was correct.

Computer deep learning, from a statistical perspective, can basically be regarded as a recursive generalized linear model.

To put it simply, the idea derived from Ning Wei's brain is to use the recursive method to reduce the upper bound of the KLS factor. After repeated iterations, the KLS conjecture problem is brought back to the upper bound of d0 to solve this problem.

Now Ningwei is no longer satisfied with writing a paper directly when he has an idea in his mind. Instead, he must first try to solve the problem by himself before writing the paper.

"Eh? What are Ning Wei doing for you?" Xu Ruixuan stood up to pour water, happened to see what Ning Wei was typing, and asked casually.

"We have just decided on the topic for our dissertation. Let's do a small experiment first." Ning Wei replied without looking back.

Everyone is used to this state. When Ning Wei focuses on something, he often becomes arrogant.

"Huh...it turns out that great people have to program and verify before writing a thesis. I love it..." Xu Ruixuan sighed, and then went straight back to his seat.

"I'll go, are you so arrogant? Let me take a look..."

This sentence attracted the other two people to watch. After seeing it, they said "I love you, love you" twice more, and then returned to their seats.

I can't help it, I can't quite understand it, but if I don't sigh a few words, I'll look like I'm not very smart.

Of course, this small disturbance will not affect Ning Why at all.

It took him an afternoon to roughly verify that his idea was indeed correct. This method could indeed prove that the KLS factor was a constant that had nothing to do with dimensions. In other words, no matter which dimension you upgrade to, there is indeed a constant, so that the area of ​​at least one section of the convex body is larger than this constant.

Then comes the thesis.

After personal verification, the paper became more fluent in writing.

Asking Liu Cong to bring dinner, it took about five hours for Ning Wei to finish this graduation thesis, which he spent a week studying and got inspiration from Professor Han's project - "Using the Recursive Method to Prove that the KLS Factor is A dimension-independent constant".

The title is simple and crude, but Ning Wei feels it is very aesthetic.

After all, this result is enough to prove that in high-dimensional space, convex objects cannot have a structure like a dumbbell. Therefore, random walking in an n-dimensional convex body can cover the entire graph faster than anyone previously expected.

Ning Wei felt that Professor Han would be very pleased when he saw his paper, so Ning Wei was quite satisfied with his paper.

But unfortunately, this is his graduation thesis and must be sent to his graduation thesis advisor first.

With this idea in mind, Ning Wei checked the paper again, corrected a few typos, saved the paper, and sent it directly to Professor Yuan via email.

This was followed by a rerun in March.

On weekends, when there is no power at night, you can leave March here and let it continue to think about things that interest you, although the little guy's thinking mode is definitely still very simple now.

Ning Wei has already thought about it. When he goes to the capital after graduation, he will arrange a special room for March with a workstation, which will make it stronger in learning ability and easier to train. If the dormitory arranged by the school is not convenient, then he will rent a suite in the school.

Anyway, he is a rich man now...

I don't care about the expense.

The three people who had been working on papers in the dormitory all day had already fallen asleep. They would rather not make any noise, so they used the mouse to tease the little guy. Although the sound of the laptop was turned off and no feedback could be heard, he looked at the little guy. Jumping around on the screen is quite fun.

It wasn't until a few minutes later that San Yue was too lazy to pay attention to the mouse dangling in front of its eyes and was lying blankly in front of the screen. Only then did Ning Wei put down the mouse with satisfaction, then took off his coat and climbed directly onto the bed.

Well, yes, is this a biological instinct that has evolved to sense the fatigue caused by repeated movements?

…