In this paper, we investigate the output token probability information in the output embedding of language models. We find an approximate common log-linear encoding of output token probabilities within the output embedding vectors and empirically demonstrate that it is accurate and sparse. As a causality examination, we steer the encoding in output embedding to modify the output probability distribution accurately. Moreover, the sparsity we find in output probability encoding suggests that a large number of dimensions in the output embedding do not contribute to causal language modeling. Therefore, we attempt to delete the output-unrelated dimensions and find more than 30% of the dimensions can be deleted without significant movement in output distribution and sequence generation. Additionally, in the pre-training dynamics of language models, we find that the output embeddings capture the corpus token frequency information in early steps, even before an obvious convergence of parameters starts.
@article{arxiv.2406.01468,
title = {Understanding Token Probability Encoding in Output Embeddings},
author = {Hakaze Cho and Yoshihiro Sakai and Kenshiro Tanaka and Mariko Kato and Naoya Inoue},
journal= {arXiv preprint arXiv:2406.01468},
year = {2024}
}