Why Are Positional Encodings Nonessential for Deep Autoregressive Transformers? A Petroglyph Revisited

Do autoregressive Transformer language models require explicit positional encodings (PEs)?The answer is 'no' provided they have more than one layer-they can distinguish sequences with permuted tokens without the need for explicit PEs.This follows from the fact that a cascade of (permutation invariant) set processors can collectively exhibit sequence-sensitive behavior in the autoregressive setting.This property has been known since early efforts (contemporary with GPT-2) adopting the Transformer for language modeling (Irie et al., 2019).However, this result does not appear to have been well disseminated, leading to recent rediscoveries.This may be partially due to a sudden growth of the language modeling community after the advent of GPT-2/3, but perhaps also due to the lack of a clear explanation in prior work, despite being commonly understood by practitioners in the past.Here we review the long-forgotten explanation why explicit PEs are nonessential for multi-layer autoregressive Transformers (in contrast, one-layer models require PEs to discern order information of their inputs), as well as the origin of this result, and hope to re-establish it as a common knowledge.