Deciphering individual cell phenotypes from cell-specific transcriptional processes requires high dimensional single cell RNA sequencing. However, current dimensionality reduction methods aggregate sparse gene information across cells, without directly measuring the relationships that exist between genes. By performing dimensionality reduction with respect to gene co-expression, low-dimensional features can model these gene-specific relationships and leverage shared signal to overcome sparsity. We describe GeneVector, a scalable framework for dimensionality reduction implemented as a vector space model using mutual information between gene expression. Unlike other methods, including principal component analysis and variational autoencoders, GeneVector uses latent space arithmetic in a lower dimensional gene embedding to identify transcriptional programs and classify cell types. In this work, we show in four single cell RNA-seq datasets that GeneVector was able to capture phenotype-specific pathways, perform batch effect correction, interactively annotate cell types, and identify pathway variation with treatment over time.