  A recent body of work has demonstrated that Transformer embeddings can be
linearly decomposed into well-defined sums of factors, that can in turn be
related to specific network inputs or components. There is however still a
dearth of work studying whether these mathematical reformulations are
empirically meaningful. In the present work, we study representations from
machine-translation decoders using two of such embedding decomposition methods.
Our results indicate that, while decomposition-derived indicators effectively
correlate with model performance, variation across different runs suggests a
more nuanced take on this question. The high variability of our measurements
indicate that geometry reflects model-specific characteristics more than it
does sentence-specific computations, and that similar training conditions do
not guarantee similar vector spaces.
