The Role of Word Length in Semantic Topology

A topological argument is presented concering the structure of semantic space, based on the negative correlation between polysemy and word length. The resulting graph structure is applied to the modeling of free-recall experiments, resulting in predictions on the comparative values of recall probabilities. Associative recall is found to favor longer words whereas sequential recall is found to favor shorter words. Data from the PEERS experiments of Lohnas et al. (2015) and Healey and Kahana (2016) confirm both predictons, with correlation coefficients $r_{seq}= -0.17$ and $r_{ass}= +0.17$. The argument is then applied to predicting global properties of list recall, which leads to a novel explanation for the word-length effect based on the optimization of retrieval strategies.