Artificial Neural networks are mathematical models at their core. This truism presents some fundamental difficulty when networks are tasked with Natural Language Processing. A key problem lies in measuring the similarity or distance among vectors in NLP embedding space, since the mathematical concept of distance does not always agree with the linguistic concept. We suggest that the best way to measure linguistic distance among vectors is by employing the Language Model (LM) that created them. We introduce Language Model Distance (LMD) for measuring accuracy of vector transformations based on the Distributional Hypothesis ( LMD Accuracy ). We show the efficacy of this metric by applying it to a simple neural network learning the Procrustes algorithm for bilingual word mapping.