Locality Preserving Loss to Align Vector Spaces

We present a locality preserving loss (LPL)that improves the alignment between vector space representations (i.e., word or sentence embeddings) while separating (increasing distance between) uncorrelated representations as compared to the standard method that minimizes the mean squared error (MSE) only. The locality preserving loss optimizes the projection by maintaining the local neighborhood of embeddings that are found in the source, in the target domain as well. This reduces the overall size of the dataset required to the train model. We argue that vector space alignment (with MSE and LPL losses) acts as a regularizer in certain language-based classification tasks, leading to better accuracy than the base-line, especially when the size of the training set is small. We validate the effectiveness ofLPL on a cross-lingual word alignment task, a natural language inference task, and a multi-lingual inference task.