  Conceptual spaces represent entities in terms of their primitive semantic
features. Such representations are highly valuable but they are notoriously
difficult to learn, especially when it comes to modelling perceptual and
subjective features. Distilling conceptual spaces from Large Language Models
(LLMs) has recently emerged as a promising strategy, but existing work has been
limited to probing pre-trained LLMs using relatively simple zero-shot
strategies. We focus in particular on the task of ranking entities according to
a given conceptual space dimension. Unfortunately, we cannot directly fine-tune
LLMs on this task, because ground truth rankings for conceptual space
dimensions are rare. We therefore use more readily available features as
training data and analyse whether the ranking capabilities of the resulting
models transfer to perceptual and subjective features. We find that this is
indeed the case, to some extent, but having at least some perceptual and
subjective features in the training data seems essential for achieving the best
results.
