AI technology is a discipline where practical applications are more common than theories, but it does not mean that there are no theories.

Meng Fanqi's current technological output includes many theoretical arguments and derivations in his papers.

However, most of this content comes from discussions with President Fu, which is like icing on the cake and not Meng Fanqi's original intention.

The reason for adding these mathematical derivations is mainly because the early AI community still values these theoretical arguments.

That's why those old scholars' eyes lit up and they couldn't stop praising when they heard Han Ci's content.

Although they admired Meng Fanqi's world-class breakthrough in his experiments, they didn't have the same genuine excitement.

For those who are obsessed with theory, understanding the theoretical reasons behind this phenomenon is far more important and attractive than making world-changing technological applications.

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It is this curiosity and exploration of truth that have led to the breakthroughs in human civilization and technology time and time again.

Unfortunately, on the path of AI, a theoretical direction is destined to be extremely difficult.

At least until around 2023-2024, there are still no significant breakthroughs.

In Meng Fanqi's future papers, the theoretical part will only become less and less, and more emphasis will be placed on the difficulties and content of industrial applications.

"Who is she? Is she your classmate?" Hinton felt that his mind suddenly opened up after hearing Han Ci's explanation of Meng Fanqi's residual thoughts.

If equivalence is constructed from the perspective of dynamical systems, many concepts from mathematics and physics can be introduced, and things can become promising.

"She is from Yan Jing University and is now a graduate student." Meng Fanqi implied that Han Ci already has a mentor.

"She should be studying applied mathematics." Li Feifei, unlike Hinton, didn't stick to formalities.

In her opinion, as long as the foundation is laid well, there will be no students who can't be found. "Who is her mentor?"

"Academician E Wei'nan." Meng Fanqi suddenly thought that Li Feifei went to Princeton for her undergraduate studies, and she might have some connection with E Wei'nan.

E Wei'nan started teaching applied mathematics and computational mathematics at Princeton in the late 20th century, which was around the time when Li Feifei was studying for her undergraduate degree.

"Okay, I'll think of a way to bring her over here for a few years of exchange." Li Feifei smirked. Although she wasn't familiar with E Wei'nan back then, she had at least attended his lectures and was considered a half student.

In her opinion, Han Ci has great potential in AI mathematics and optimization problems.

Pure mathematics will not yield results unless it solves major problems, but hitching a ride on the rapidly developing AI is a bright future.

For example, the residual thought that Han Ci is currently discussing is not considered profound in the fields of mathematics and physics.

But when combined with Meng Fanqi's applied achievements, it greatly enhances its significance.

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

On the stage, Han Ci's presentation continued.

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

If we use the Monte Carlo method and select N samples from specific independent and identically distributed samples, then we have the identity E(I(g)-Im(g))^2=var(g)/N, var(g)=Eg^2-(Eg)^2).

This tells us that the convergence rate is independent of dimension."

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

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

If we write a two-layer neural network in this form, it means that this class of expectation functions can be approximated by a two-layer neural network, and the approximation speed is independent of dimension."

"Let's turn to the perspective of discrete dynamical systems and take a random control problem as an example.

The 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 the curse of dimensionality.

The nature of this process is actually equivalent to residual networks."

"Finally, let me summarize. Deep learning is fundamentally a mathematical problem in high dimensions. Neural networks are an effective means of approximating high-dimensional functions, and residual networks are even easier to optimize high-dimensional functions.

This means that mathematics is at the forefront of technological innovation and has a direct impact on new fields. It also provides numerous possibilities for the field of artificial intelligence, science, and technology."

Han Ci's presentation took about twice as long as Meng Fanqi's. After the presentation, she was repeatedly questioned and discussed by several old scholars.

After a while, the host finally found an opportunity to go back on stage and invited Meng Fanqi up again.The host looked young, around thirty years old, probably a current doctoral student or a recent graduate lecturer from Stanford.

He was quite active and loved a good spectacle. After inviting Meng Fanqi back on stage, he even made a joke.

"This lecture was originally your stage, but now it has been somewhat stolen by Miss Han Ci. How do you feel about that?"

Meng Fanqi took the microphone with a smile. After the laughter from the audience subsided a bit, he answered generously, "We who focus on applications rely on our code to speak. Although I didn't mention the implementation and details of the technology today, I believe everyone who has seen my code has felt my thousand words."

Upon hearing this, many programmers in the audience immediately started to cheer, with whistles and shouts echoing around.

"My dream is for my technology to be widely applied around the world, making AI as indispensable as air, yet rarely noticed in daily life.

As for the theoretical research and exploration of AI, I may have to leave it to Han Ci and everyone else."

His words were modest and appropriate, and as expected, they received applause from the entire audience.

After the audience asked both of them some more questions, the main part of the meeting was over.

In addition to the public questions, many people had a lot of private matters to ask the two.

As a result, many people in the audience naturally divided into two factions: application and theory.

One faction, led by tech giants like Jeff, surrounded Meng Fanqi to discuss the application scenarios, market potential, and implementation difficulties of his outstanding achievements.

The other faction, led by several old scholars from Oxford University, was a group of theorists, with serious expressions, rigorously discussing some hypotheses and their theoretical proofs.

With the central aisle of the venue as the dividing line, one group was on the left and the other on the right.

It was quite an interesting scene.