AI technology is a relatively rare discipline with applications far greater than theory, but it is not without theory.

All the technologies that Meng Fanqi has produced so far, and there are still many theoretical arguments and derivations in his papers.

However, most of this part of the content comes from the discussion with Dean Fu, which is the icing on the cake, not Meng Fanqi's original intention.

The main reason for the addition of these mathematical derivations is that the early AI community still attached great importance to this aspect of argumentation.

This is also why those old scholars have a light in their eyes when they hear the content of Han Ci, and their mouths are full of admiration.

And when I listened to Meng Fanqi's world-class breakthrough in experiments, although I was amazed, I didn't have this heartfelt excitement.

For those who are obsessed with theory, understanding what the theoretical causes of this phenomenon are are far more important and attractive than making technological applications that affect the world.

It is precisely this curiosity and the search for truth that have created breakthroughs in human civilization and technology.

It's just a pity that on the road of AI, the direction of partial theory is destined to be bumpy.

At least until around 2023-2024, there is still no decent breakthrough.

In his future papers, there will only be fewer and fewer theoretical parts, and more attention will be paid to the difficulties and content of industrial applications.

"Who is she? Your classmates? After listening to Han Ci's explanation of Meng Fanqi's residual thoughts, Hinton felt that his thoughts had suddenly opened up a lot.

If equivalence is constructed from the perspective of dynamical systems, then many concepts from the mathematical and physical worlds can be introduced, and things can be done.

"She is from Yenching University and is now a graduate student." Meng Fanqi's implication is that Han Ci already has a mentor.

"She's probably doing applied math." Li Feifei is not like Hinton, who abides by etiquette.

In her opinion, as long as the foot of the wall is dug well, no student can't find it, "Who is her mentor?" ”

"Academician Ewenan." Meng Fanqi suddenly thought that Li Feifei was from Princeton as an undergraduate, so he had a bit of an intersection with Evenan.

He began teaching applied and computational mathematics at Princeton at the end of the last century, around the time when Li Feifei was an undergraduate.

"Okay, I'll think of a way to bring her here for a few years." Li Feifei smiled. Although I was not familiar with Ewenan back then, I could be regarded as having listened to each other's classes, and I was half a student.

In her opinion, Han Ci has a lot to offer in AI math and optimization problems.

As long as pure mathematics does not solve big problems, it will be difficult to produce results after all, and riding the rapid development of AI will have a bright future.

For example, the idea of residuals that Han Ci is talking about now is not a profound thing in the world of mathematics and physics.

It can be displayed in combination with Meng Fanqi's application achievements, which is a great plus and of great significance.

The intersection of different fields has always been a shortcut to results.

On stage, Han Ci's narration continued.

"Let's assume a simple high-dimensional integration problem, calculate an integral I(g) that can be expressed as a expectation, and approximate it by a finite summation Im(g).

If the Monte Carlo method is used instead, selecting N samples from a specific independent and homogeneous sample selection, there is the identity E(I(g)- Im(g))^2 = var(g)/N, var(g)= Eg^2 -(Eg)^2)

This tells us that the convergence speed is dimension-independent. ”

"If we use the traditional Fourier transform first, and then approximate it with a uniform discrete Fourier transform. The error is ~m^-a/d, which is inevitably affected by the dimension.

However, if a function can be expressed in the desired form, and all samples are independent and identically distributed, then the fitting difference is var(f)/m, independent of the dimension.

If a two-layer neural network is written as a form, it means that this kind of expectation function can be approximated by a two-layer neural network, and its approximation speed is dimension-independent. ”

"Let's turn to the perspective of discrete dynamical systems and give us a stochastic control problem.

Dynamic model Zl+1 = Zl + g1(z1,a1) + n, where z is the state, a is the control signal, and n is the noise. If we want to find a feedback control signal function, and solve the dynamic programming Bellman equation, we will inevitably encounter a dimensional disaster.

The nature of this process is actually equivalent to a residual network.

..................”

Finally, I conclude. Deep learning is fundamentally a mathematical problem in higher dimensions. Neural networks are an effective means of approximating high-dimensional functions, while residual networks are high-dimensional functions that are easier to optimize.

This means that mathematics is at the real forefront of scientific and technological innovation and has a direct impact on new areas. At the same time, it also opens up many new possibilities in the field of artificial intelligence, science and technology. ”

Han Ci's total narration time was about twice that of Meng Fanqi, and after the narration was completed, he was repeatedly asked and discussed by several old scholars.

After a while, the host found an opportunity to re-appear on stage and invited Meng Fanqi again.

The moderator looked young, about 30 years old, and was probably a Ph.D. student at Stanford or a recent graduate lecturer.

is quite active, and it is not a big deal to watch the excitement, and after he invited Meng Fanqi again, he also made a joke.

"This speech was originally your stage, but now Miss Han Ci has stolen a lot of limelight and attention, I don't know how you feel?"

Meng Fanqi took the microphone with a smile, and after the laughter in the audience subsided a little, he replied very generously, "We focus on the application side, and we rely on code to speak." Although I didn't mention the implementation or details of the technology today, I think everyone who has read my code has already felt my words. ”

Many programmers in the audience immediately began to heckle when they heard this, and whistles and shouts came one after another.

"My dream is that my technology can be widely applied around the world, so that AI intelligence is like air, and everyone can't do without it, but they rarely notice it in life.

As for the theoretical research and exploration of AI, it may be up to Han Ci and everyone. ”

These words were humble and decent, and they were expected to be applauded by the audience.

After everyone in the audience asked some questions to the two of them separately, the main process of the meeting was completed.

In addition to the questions asked publicly, many people also have a lot of things that are convenient to ask in private.

As a result, many of the people present were naturally divided into two factions: applied and theoretical.

A group of tech giants, such as Jeff, gathered around Meng Fanqi to discuss the application scenarios of his outstanding results, and the market potential and difficulties in landing.

On the other hand, led by a few old scholars from Oxford, a group of theorists, with serious expressions, were discussing some of the ideas and their theoretical proofs in a rigorous manner.

With the corridor in the center of the venue as the dividing line, a group of people is on the left and a group of people is on the right.

It's an unexpectedly interesting picture.