数理問題の難易度と機械学習

抄録

Recent developments have enabled us to employ machine learning techniques for a wide range of research. We propose here to classify mathematical problems by its difficulty using a simple 3-layer Neural Net learning algorithm. We applied the algorithm to learn simple binary addition and the Mackey-Glass equation, which gave us results with good precisions. On the other hand, learning of the prime number distribution posed a fair difficulty. Further, learning for the next ((n + 2)-th) Collatz-Kakutani minimal cycle length from odd number n and the associated cycle length showed us no sensible predictions. We view that this result is caused by the reflection of the difficulty of the problems in learning performances of the learning algorithm. This indicates that the levels of difficulties associated with mathematical problems may be measured by learning performances of the machine learning models.