Why is positional encoding essential in the Transformer architecture, and what limitation does it address?

Positional encoding is essential in the Transformer architecture because the self-attention mechanism is inherently permutation-invariant, meaning it doesn't inherently consider the order of words in the input sequence. The self-attention mechanism calculates attention weights based on the relationships between words, but it doesn't have any built-in awareness of their position in the sequence. This is a limitation because word order is crucial for understanding the meaning of a sentence. For example, "the dog chased the cat" has a different meaning than "the cat chased the dog." Without positional information, the Transformer would treat these two sentences as having the same meaning because the relationships between the words are the same, only the order differs. Positional encoding addresses this limitation by adding information about the position of each word to its embedding. This positional information is added to the word embeddings before they are fed into the self-attention mechanism. This allows the model to consider both the meaning of the words and their position in the sequence when calculating attention weights. There are different ways to implement positional encoding, such as using sinusoidal functions or learned embeddings, but the key idea is to provide the model with information about the absolute or relative position of words in the input sequence. Without positional encoding, the Transformer would be unable to distinguish between sentences with different word orders, severely limiting its ability to understand language.