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The development of state-of-the-art (SOTA) Natural Language Processing (NLP)systems has steadily been establishing new techniques to absorb the statisticsof linguistic data. These techniques often trace well-known constructs fromtraditional theories, and we study these connections to close gaps around keyNLP methods as a means to orient future work. For this, we introduce ananalytic model of the statistics learned by seminal algorithms (including GloVeand Word2Vec), and derive insights for systems that use these algorithms andthe statistics of co-occurrence, in general. In this work, we derive -- to thebest of our knowledge -- the first known solution to Word2Vec'ssoftmax-optimized, skip-gram algorithm. This result presents exciting potentialfor future development as a direct solution to a deep learning (DL) languagemodel's (LM's) matrix factorization. However, we use the solution todemonstrate a seemingly-universal existence of a property that word vectorsexhibit and which allows for the prophylactic discernment of biases in data --prior to their absorption by DL models. To qualify our work, we conduct ananalysis of independence, i.e., on the density of statistical dependencies inco-occurrence models, which in turn renders insights on the distributionalhypothesis' partial fulfillment by co-occurrence statistics.

To Know by the Company Words Keep and What Else Lies in the Vicinity