One of the first tasks a developing human intelligence performs is learning the times tables. This can be seen as filling a 10x10 matrix (12x12 depending on the local traditions), but this blind learning alone would hardly classify as intelligence growth.
I believe intelligence starts, at least in this case, with the ability to rebuild a value that has been forgotten. In a sense, intelligence as a complement for limited and volatile memory. For instance, a kid forgets how much 6X7 is, but remembers 6x6 and applies an equivalent rule to 6x7 = 6x6 + 6. where 6x6 comes from memory, the addition is performed and the result goes to the cell (6,7) for a future lookup, hopefully succesful. This is mathematically equivalent to fitting a linear model, but if we are to define multiplication without using multiplication, the general linear regression is an overkill to learn the times tables.
Instead, we can think of learning the times tables as some process leading to
$kN = (k-1)N + N$
What is the simplest machine learning model that can get such a result?
