Character-position arithmetic for analogy questions between word forms

We show how to answer analogy questions A:B::C:D of unknown D between word forms, by essentially relying on the basic arithmetic equality D[i_b - i_a + i_c] = B[i_b] - A[i_a] + C[i_c] on characters and positions at the same time. We decompose the problem into two steps: specification and decoding. We examine several techniques to implement each of these two steps. We perform experiments on a set of positive and negative examples and assess the accuracy of combinations of techniques. We then evaluate the performance of the best combination of techniques on a large set of more than 40 million analogy questions from the training data of a shared task in morphology. We obtain the correct answer in 94 % of the cases.