What is the primary function of positional encoding in a Transformer architecture?

Positional encoding serves the primary function of providing information about the position of words in a sequence to the Transformer architecture. Transformers, unlike recurrent neural networks (RNNs), do not inherently process words in a sequential order. Because of this, they treat all words in a sentence as if they appear at the same time. This is fast, but it also means the model doesn't automatically know the order of the words. To address this, positional encodings are added to the word embeddings, which are numerical representations of the words. These encodings are mathematical functions that assign a unique vector (an array of numbers) to each position in the sequence. The specific values in the positional encoding vector depend on the position of the word. By adding this positional information to the word embeddings, the Transformer can understand the relationships between words based on their position in the sequence. Different mathematical functions, like sine and cosine functions of varying frequencies, are commonly used to create these unique positional vectors. These functions ensure that each position has a distinct encoding and that nearby positions have encodings that are similar, allowing the model to learn relationships based on proximity. Without positional encoding, the Transformer would lack the ability to distinguish between different word orders, significantly impacting its ability to understand language.