We present the Supervised Directional Similarity Network (SDSN), a novel neural architecture for learning task-specific transformation functions on top of general-purpose word embeddings. Relying on only a limited amount of supervision from task-specific scores on a subset of the vocabulary, our architecture is able to generalise and transform a general-purpose distributional vector space to model the relation of lexical entailment. Experiments show excellent performance on scoring graded lexical entailment, raising the state-of-the-art on the HyperLex dataset by approximately 25%.