Why Are Positional Encodings Nonessential for Deep Autoregressive Transformers? Revisiting a Petroglyph

Do autoregressive Transformer language models require explicit positional encodings (PEs)? The answer is "no" as long as they have more than one layer -- they can distinguish sequences with permuted tokens without requiring explicit PEs. This property has been known since early efforts (those contemporary with GPT-2) adopting the Transformer for language modeling. However, this result does not appear to have been well disseminated and was even rediscovered recently. This may be partially due to a sudden growth of the language modeling community after the advent of GPT-2, but perhaps also due to the lack of a clear explanation in prior publications, despite being commonly understood by practitioners in the past. Here we review this 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 input tokens). We also review the origin of this result, and hope to re-establish it as a common knowledge.