AI challenged by a 100-year-old mathematical paradox

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Are AIs “big-headed”? It’s a bit like what scientists from the universities of Cambridge and Oslo say. They found that the reliability of AIs faced mathematical limits. Problem: they are not always transparent about their failures.

As we know, overconfidence can prevent questioning. Well it seems, according to a team of scientists from the universities of Cambridge and Oslo, that this is not unique to humans. Indeed, according to them, it is even more complicated for artificial intelligences (AI) to recognize an error in a result than to give a correct result.

However, it would seem that these errors are inevitable. As a reminder, artificial intelligence today is mainly available in a practical application called “machine learning”, an automatic learning technique which consists of training artificial neural networks (inspired by the functioning of the brain) by providing them with large quantities of data as a basis for learning, from which they must “deduce” results. In fact, these neural networks are most of the time dematerialized: they are calculations carried out on computers.

Many hopes are based on these learning algorithms, whether in the field of voice recognition, images, various diagnoses… However, the authors of this new study underline the lack of reliability of some of them. them. ” We are at a stage where the practical success of AIs is well ahead of theory and understanding. A program on understanding the foundations of AI computing is needed to fill this gap “, declares Anders Hansen, professor of the department of applied mathematics and theoretical physics of Cambridge, in a communicated of the University.

The researchers have indeed identified a paradox that weakens the operating principle of AIs. This limit is derived from a fairly old mathematical paradox demonstrated by Alan Turing and Kurt Gödel in the 20th century. Both were indeed made famous by their ability to show that mathematics could not be completely demonstrable. In summary, their conclusions were as follows: there are certain mathematical statements which are neither provable nor refutable, and certain computational problems cannot be solved with algorithms. Moreover, astonishing paradox, a coherent theory cannot demonstrate its own coherence, as long as it is sufficiently “rich”.

Inherently unreliable neural networks

The paradox first identified by Turing and Gödel was introduced to the world of AI by Smale and others says study co-author Matthew Colbrook of the Department of Applied Mathematics and Theoretical Physics. ” There are fundamental limitations inherent in mathematics and similarly AI algorithms cannot exist for certain problems. “. The researchers explain that because of this paradox, there are many cases where good neural networks can exist, but an intrinsically reliable network cannot be built.

This assertion is not necessarily dramatic in many areas, say the scientists. On the other hand, there are others where any error, especially unrecognized, can be risky. ” Many AI systems are unstable, and this is becoming a major handicap, especially as they are increasingly used in high-risk areas such as disease diagnosis or autonomous vehicles. explains Anders Hansen. “ If AI systems are used in areas where they can cause real harm if they go wrong, trust in these systems must be the top priority. “. However, the team says that in many systems, “ there is no way to tell when AIs are more or less confident about a decision “.

However, this is not a reason to abandon research on machine learning and AI as we know it, say the scientists. ” When 20th century mathematicians identified different paradoxes, they did not stop studying mathematics. They just had to find new ways, because they understood the limits “recalls Matthew Colbrook. ” For AI, this may mean changing paths or developing new ones to design systems that can solve problems reliably and transparently, while understanding their limitations. “.

Source : PNAS

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AI challenged by a 100-year-old mathematical paradox


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