The scientific world has long recognized that proving mathematical theorems is an essential first step in the development of artificial intelligence. To prove the correctness or falsity of a conjecture, one must use symbolic reasoning and sort through an unlimited number of alternatives. These tasks are beyond the capabilities of even the most complex artificial intelligence systems.
The cutting edge of artificial intelligence today is the creation of machines that can “solve on the spot” or come up with a complete answer to a problem in one go. However, this is not the way most individuals deal with difficult situations. Mathematical reasoning is more difficult to formalize and measure.
Meta AI is an important development at the intersection of artificial intelligence and mathematics. The team’s neural theory installer completed five times more IMO problems as any other AI system before it, for a total of ten. In terms of miniF2F, a popular math test, the AI model outperforms the latest model by 20% and outperforms Metamath by 10%.
The team’s HyperTree Proof Search (HTPS) approach is taught to generalize from a data set of valid mathematical proofs to entirely new challenges. Using some computational shorthand for a finite number of examples, he can deduce a suitable proof for the problem IMO.
Neurological theory has demonstrated that it is required to relate a “state” to an existing (incomplete) understanding of the problem in order to behave like a human being. Initially, the researchers used a reinforcement learning strategy combined with pre-existing proof tools such as Lean.
The “current state” of the (incomplete) proof is a node in the graph, and each subsequent step is an edge. This allows visualization of the directory as a whole. Proof aides use the process of deductive reasoning to make this method possible.
The AI for playing chess requires a similar mechanism: the ability to assess the strength of a given chess position, and in this case, a proof state. To achieve this, the team adopted a strategy reminiscent of the Monte Carlo Tree Research (MCTS), in which the model iteratively estimates that:
- A set of plausible counterarguments to use in a particular case of proof
- The result of the proof after a specified number of counterarguments are presented.
This allows for online training to significantly improve the performance of a previously tested prototype on specific issues.
As a result, the proposed method outperforms the currently published latest by 20% over the accuracy of the Minif2f validation set and solves ten previously unresolved problems IMO. The team hopes their work will help the community build on their work so we can all take more rapid steps forward in this wonderful field.
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Tanushree Shenwai is a Consultant Intern at MarktechPost. She is currently pursuing a Bachelor of Technology degree from the Indian Institute of Technology (IIT), Bhubaneswar. She is passionate about data science and has a keen interest in the scope of application of artificial intelligence in various fields. She is passionate about exploring new developments in technologies and their real-world applications.