  This paper reveals a novel linear characteristic exclusive to transformer
decoders, including models such as GPT, LLaMA, OPT, BLOOM and others. We
analyze embedding transformations between sequential layers, uncovering a
near-perfect linear relationship (Procrustes similarity score of 0.99).
However, linearity decreases when the residual component is removed due to a
consistently low output norm of the transformer layer. Our experiments show
that removing or linearly approximating some of the most linear blocks of
transformers does not affect significantly the loss or model performance.
Moreover, in our pretraining experiments on smaller models we introduce a
cosine-similarity-based regularization, aimed at reducing layer linearity. This
regularization improves performance metrics on benchmarks like Tiny Stories and
SuperGLUE and as well successfully decreases the linearity of the models. This
study challenges the existing understanding of transformer architectures,
suggesting that their operation may be more linear than previously assumed.
