  Recent advances in language modeling consist in pretraining highly
parameterized neural networks on extremely large web-mined text corpora.
Training and inference with such models can be costly in practice, which
incentivizes the use of smaller counterparts. However, it has been observed
that smaller models can suffer from saturation, characterized as a drop in
performance at some advanced point in training followed by a plateau. In this
paper, we find that such saturation can be explained by a mismatch between the
hidden dimension of smaller models and the high rank of the target contextual
probability distribution. This mismatch affects the performance of the linear
prediction head used in such models through the well-known softmax bottleneck
phenomenon. We measure the effect of the softmax bottleneck in various settings
and find that models based on less than 1000 hidden dimensions tend to adopt
degenerate latent representations in late pretraining, which leads to reduced
evaluation performance.
