  How are the meanings of linguistic expressions related to their use in
concrete cognitive tasks? Visual identification tasks show human speakers can
exhibit considerable variation in their understanding, representation and
verification of certain quantifiers. This paper initiates an investigation into
neural models of these psycho-semantic tasks. We trained two types of network
-- a convolutional neural network (CNN) model and a recurrent model of visual
attention (RAM) -- on the "most" verification task from \citet{Pietroski2009},
manipulating the visual scene and novel notions of task duration. Our results
qualitatively mirror certain features of human performance (such as sensitivity
to the ratio of set sizes, indicating a reliance on approximate number) while
differing in interesting ways (such as exhibiting a subtly different pattern
for the effect of image type). We conclude by discussing the prospects for
using neural models as cognitive models of this and other psychosemantic tasks.
