We believe that the WSABIE EMBEDDING model performs better than the LOG-LINEAR EMBEDDING baseline (that uses the same input representation) because the former setting allows examples with different labels and confusion sets to share information; this is due to the fact that all labels live in the same label space, and a single projection matrix is shared across the examples to map the input features to this space.
the WSABIE EMBEDDING model can share more information between different examples in the training data than the LOG-LINEAR EMBEDDING model.