Visual learning of arithmetic operations

A simple Neural Network model is presented for endto- end visual learning of arithmetic operations from pictures of numbers. The input consists of two pictures, each showing a 7-digit number. The output, also a picture, displays the number showing the result of an arithmetic operation (e.g., addition or subtraction) on the two input numbers. The concepts of a number, or of an operator, are not explicitly introduced. This indicates that addition is a simple cognitive task, which can be learned visually using a very small number of neurons. Other operations, e.g., multiplication, were not learnable using this architecture. Some tasks were not learnable end-To-end (e.g., addition with Roman numerals), but were easily learnable once broken into two separate sub-Tasks: A perceptual Character Recognition and cognitive Arithmetic sub-Tasks. This indicates that while some tasks may be easily learnable end-To-end, other may need to be broken into sub-Tasks.