# AI limit reflected from mathematical paradox

Source: Principle

The Achilles heel of AI & nbsp& nbsp;

Deep learning is an artificial intelligence technology for pattern recognition, which is a successful technology entering the field of scientific computing. We often see it in many eye-catching news headlines. For example, it can diagnose diseases more accurately than doctors, and it can prevent traffic accidents through automatic driving. However, many deep learning systems are not trustworthy, and they are easy to be fooled.

This makes artificial intelligence systems, like some overconfident humans, often have much more confidence than their actual ability. Human beings are also better at discovering their mistakes, but many AI simply can’t know when they made a mistake. It is sometimes more difficult for AI systems to realize that they have made a mistake than to produce a correct result.

This instability is not only the fatal weakness of modern artificial intelligence, but also a paradox. This paradox can be traced back to two great mathematical masters in the 20th century, Alan Turing and Kurt g ö del. In the early 20th century, mathematicians were trying to prove that mathematics was the ultimate language of unified science. However, Turing and Godel found a paradox in the core of Mathematics: the authenticity of some mathematical propositions cannot be proved, and some computational problems cannot be solved by algorithms.

At the end of the 20th century, the mathematician Steve Smale put forward a list of 18 unsolved mathematical problems at that time. The last question discussed the intelligent limit of human and machine. This problem has not been solved so far, but it brings the paradox first proposed by Turing and Godel into the world of artificial intelligence: mathematics has inherent basic limits. Similarly, artificial intelligence algorithms also have unsolvable problems.

Inherent limits of Artificial Intelligence & nbsp& nbsp;

A new study shows that there are inherent limits in artificial intelligence, which can be attributed to this century long mathematical paradox. The researchers show the existence of the algorithm and the extension of the neural network proposed by Godel. They proposed a classification theory, which describes the situation that neural networks can be trained to provide reliable artificial intelligence systems under specific conditions.

The results were published in the recent proceedings of the National Academy of Sciences. The new research points out that there are problems with stable and accurate neural networks, and no algorithm can produce such networks. Only in specific cases can the algorithm calculate a stable and accurate neural network.

Neural network is the most advanced tool in the field of artificial intelligence. It is called “neural network” because it is a rough simulation of the relationship between brain neurons. In the new study, the researchers said that although a good neural network can exist in some cases, due to the existence of this paradox, we cannot create an inherently reliable neural network. In other words, no matter how accurate the data we use to build a neural network is, we will never get the perfect information we need to build this neural network.

At the same time, no matter how much data is trained, it is impossible to calculate a good existing neural network. No matter how much data an algorithm can access, it will not generate the required network. This is similar to Turing’s view: there are unsolvable computing problems regardless of computing power and running time.

The researchers said that not all artificial intelligence has inherent defects. In some cases, artificial intelligence has no problem making mistakes, but it needs to be honest with these problems. However, this is not what we see in many systems.

Understanding the basis of Artificial Intelligence & nbsp& nbsp;

When we try something and find it doesn’t work, we may add something else in the hope that it will work. However, if we still can’t get what we want when we add it to a certain extent, we will choose to try different methods. It is important to understand that different methods have their own limits. Now, artificial intelligence is in the stage where its practical success is far ahead of its theory and understanding. Therefore, we urgently need to understand the computing basis of artificial intelligence to make up for this gap.

When mathematicians in the 20th century found different paradoxes, they did not stop studying mathematics. They must find a new path because they understand the limits. Accordingly, in the field of artificial intelligence, this may mean changing paths or developing new paths to build systems that can solve problems in a reliable and transparent way and understand their limits at the same time.

The next stage for researchers is to combine approximation theory, numerical analysis and computational basis to determine which neural networks can be calculated by algorithm and which neural networks can become stable and reliable. As Godel and Turing put forward the rich basic theories brought about by the paradox of mathematical and computer limits, perhaps similar basic theories may blossom and bear fruit in artificial intelligence.

# creative team:

Author: Xiaoyu

Typesetting: Wen Wen

# reference source:

https：//www.cam. ac.uk/research/news/mathematical-paradox-demonstrates-the-limits-of-ai

https：//www.pnas. org/doi/10.1073/pnas. 2107151119#sec-4

# picture source:

Cover image: julientromeur / pixabay

First picture: chenspec / pixabay