  It is generally thought that transformer-based large language models benefit
from pre-training by learning generic linguistic knowledge that can be focused
on a specific task during fine-tuning. However, we propose that much of the
benefit from pre-training may be captured by geometric characteristics of the
latent space representations, divorced from any specific linguistic knowledge.
In this work we explore the relationship between GLUE benchmarking task
performance and a variety of measures applied to the latent space resulting
from BERT-type contextual language models. We find that there is a strong
linear relationship between a measure of quantized cell density and average
GLUE performance and that these measures may be predictive of otherwise
surprising GLUE performance for several non-standard BERT-type models from the
literature. These results may be suggestive of a strategy for decreasing
pre-training requirements, wherein model initialization can be informed by the
geometric characteristics of the model's latent space.
