Although the input and output tokens of a Large Language Model can technically be viewed as sub-sequences of a single, continuous sequence, it is common practice to employ separate variables—typically $\mathbf{x}$ for the input and $\mathbf{y}$ for the output. Adopting this distinct notation helps to clearly separate the given context from the generated text, resulting in mathematical formulations that closely resemble those used in other natural language processing text generation models, such as neural machine translation.