Can artificial intelligence allow computers to ensure safe autonomous systems and prior optimization? Two Princeton teachers think it can, and they have received a research grant earlier this year to explore IA improvement in mathematical evidence systems used to ensure the safety and efficiency of complex technologies.
Operational research and financial engineering teacher Amir Ali Ahmadi and IT teacher Pravesth Kothari received a Lab Princeton AI seed subsidy in February for their research project “Algebraic evidence assisted by AI with engineering applications”.
The objective of this collaborative company is to take advantage of the data specific to the application as well as IA tools to increase the algebraic evidence-based systems based on semi-finite programming. Semi -finished programming is a powerful method used to solve complex optimization problems – in particular those involving uncertainty or safety – which are often too complicated for regular algorithms. These proof systems rigorously help confirm whether certain mathematical conditions are true, which is essential in engineering applications where failure is not an option.
Their work will focus on key applications, including checking the safety of robotic systems, automated theorem proving in geometry and robust algorithmic statistics. Security verification is to prove that a system, such as a drone or an autonomous car, will always behave in complete safety in all conditions. The automated Proving theorem uses computers to logically prove mathematical declarations, and robust statistics deal with data analysis in a way that resists being misleading by aberrant values or errors.
“This collaboration has been in our minds for some time,” Ahmadi told Daily Princetonian. “We are working on the sum of square optimization, [Kothari] On the theoretical computer side and I on the side of optimization and control. »»
The optimization of the sum of the squares (SOS) is a advanced mathematical technique which allows researchers to verify that the systems governed by polynomial equations behave as planned. Essentially, this helps to prove whether certain results are impossible or guaranteed, which is particularly important in fields such as robotics and control theory, where security must be mathematically. For example, to ensure that an autonomous vehicle avoids obstacles, SOS can be used to prove that the vehicle path will never meet with any object in its environment.
Despite its theoretical power, SOS often comes up against calculation limits, because it is based on semi-finished programming, which tends to become intractable on a larger scale. In this case, means intractable that the calculations become so large and complex that even powerful computers are fighting or do not finish them within a reasonable time. This is where automatic learning enters the equation: Ahmadi and Kothari use AI tools formed with previous data to guide and accelerate the process of searching for these mathematical evidence.
“If I already have a set of unrealizable polynomial systems data and their algebraic proofs of infection, can I use it to shorten the following evidence?” Ahmadi asked. In other words, if the system has already encountered problems that did not have a solution, can AI learn from these examples to identify or exclude similar problems in the future more quickly? “It is our vision of guiding future calculations.”
Although the funding of the grant is relatively modest, Ahmadi noted that she had still stimulated the project. The additional support of the School of Engineering and Applied Sciences Innovation Fund will allow the team to involve more students and lay the basics of the project.
The first project that the team attacks implies interpreting the SOS algorithms to find the coloring number of a graph. In simple terms, they want to find the minimum number of colors necessary to color the nodes (or points) of a network so that the connected nodes do not share the same color.
“This problem has many applications,” said Ahmadi. “For example, if the nodes of the graph represent princeton courses and the edges represent conflicts in these courses (they meet at the same time), the coloring number is exactly the minimum number of classrooms necessary to keep all courses without conflict.”
Ahmadi continued with a second lighter application. “If the same nodes represent the guests during your wedding and the edges represent interpersonal conflicts (guests who cannot stand each other), then the coloring number corresponds to the minimum number of dinner tables necessary to ensure a wedding without drama!”
“Just like many AI tools like those based on neural networks act as black boxes ” – systems that work well but do not easily reveal how they have come to a particular response -” SOS algorithms are powerful but can also be mysterious, “Ahmadi told” prince “.
“There is a growing interest in the automatic learning community to replace them with more interpretable models. Our goal is to understand how these algorithms solve difficult combinatorial problems for which there are no alternative and more interpretable algorithms, “he said.
In the long term, Ahmadi and Kothari hope that their work will contribute to one of the most ambitious borders of artificial intelligence: automated mathematical reasoning.
“One of the important objectives of this project is the proxy of the automated theorem,” said Ahmadi. “Can a machine really prove deep and non -trivial theorems alone – and do it on a large scale?” It is a great challenge, and the sum of the optimization of the squares gives us a structured path towards him. ”
“It is a deeply interdisciplinary effort,” he added. “And it’s just to start.”
Adam Moussa is a contributor research writer for the “prince”.
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