  In spite of remarkable progress in machine learning techniques, the
state-of-the-art machine learning algorithms often keep machines from real-time
learning (online learning) due in part to computational complexity in parameter
optimization. As an alternative, a learning algorithm to train a memory in real
time is proposed, which is named as the Markov chain Hebbian learning
algorithm. The algorithm pursues efficient memory use during training in that
(i) the weight matrix has ternary elements (-1, 0, 1) and (ii) each update
follows a Markov chain--the upcoming update does not need past weight memory.
The algorithm was verified by two proof-of-concept tasks (handwritten digit
recognition and multiplication table memorization) in which numbers were taken
as symbols. Particularly, the latter bases multiplication arithmetic on memory,
which may be analogous to humans' mental arithmetic. The memory-based
multiplication arithmetic feasibly offers the basis of factorization,
supporting novel insight into the arithmetic.
