During the training stage, for each language, we find mappings (or projection directions) and U i ∈ R (c×k) from the character and phonemic spaces into a k-dimensional subspace (or an interlingual representation) such that a name gets mapped to the same k-dimensional vector irrespective of the language.
given a name x i it gets mapped to the vector A T i x i and similarly its IPA sequence p i gets mapped to U T i p i .