Transformers from scratch

I will assume a basic understanding of neural networks and backpropagation. If you'd like to brush up, this lecture will give you the basics of neural networks and this one will explain how these principles are applied in modern deep learning systems. A working knowledge of Pytorch is required to understand the programming examples, but these can also be safely skipped. The fundamental operation of any transformer architecture is the self-attention operation. Self-attention is a sequence-to-sequence operation: a sequence of vectors goes in, and a sequence of vectors comes out. The vectors all have dimension \(k\). The weight \(w_{\rc{i}\gc{j}}\) is not a parameter, as in a normal neural net, but it is derived from a function over \(\x_\rc{i}\) and \(\x_\gc{j}\). A few other ingredients are needed for a complete transformer, which we'll discuss later, but this is the fundamental operation. More importantly, this is the only operation in the whole architecture that propagates information between vectors. Every other operation in the transformer is applied to each vector in the input sequence without interactions between vectors. Despite its simplicity, it's not immediately obvious why self-attention should work so well.