TY - JOUR

T1 - Machine learning and information theory concepts towards an AI mathematician

AU - Bengio, Yoshua

AU - Malkin, Nikolay

PY - 2024/5/15

Y1 - 2024/5/15

N2 - The current state of the art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from how the brains of mathematicians go about their craft? This essay builds on the idea that current deep learning mostly succeeds at system 1 abilities—which correspond to our intuition and habitual behaviors—but still lacks something important regarding system 2 abilities—which include reasoning and robust uncertainty estimation. It takes an information-theoretical posture to ask questions about what constitutes an interesting mathematical statement, which could guide future work in crafting an AI mathematician. The focus is not on proving a given theorem but on discovering new and interesting conjectures. The central hypothesis is that a desirable body of theorems better summarizes the set of all provable statements, for example, by having a small description length while at the same time being close (in terms of number of derivation steps) to many provable statements.

AB - The current state of the art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from how the brains of mathematicians go about their craft? This essay builds on the idea that current deep learning mostly succeeds at system 1 abilities—which correspond to our intuition and habitual behaviors—but still lacks something important regarding system 2 abilities—which include reasoning and robust uncertainty estimation. It takes an information-theoretical posture to ask questions about what constitutes an interesting mathematical statement, which could guide future work in crafting an AI mathematician. The focus is not on proving a given theorem but on discovering new and interesting conjectures. The central hypothesis is that a desirable body of theorems better summarizes the set of all provable statements, for example, by having a small description length while at the same time being close (in terms of number of derivation steps) to many provable statements.

UR - http://www.scopus.com/inward/record.url?scp=85197879395&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2403.04571

DO - 10.48550/arXiv.2403.04571

M3 - Article

AN - SCOPUS:85197879395

SN - 0273-0979

VL - 61

SP - 457

EP - 469

JO - Bulletin of the American Mathematical Society

JF - Bulletin of the American Mathematical Society

IS - 3

ER -