A research paper on language models presents the probability of an output token y given an input context x in two different ways:

Expression 1: p(y | x; W, θ) Expression 2: p(y | x)

Assuming both expressions refer to the same underlying model where W and θ are the model's parameters, what is the most accurate interpretation of the relationship between them?

Interpreting Model Notation in a Research Context

In the context of parameterized machine learning models, the mathematical expression p(y|x) indicates that the probability of output y given input x is calculated without relying on any learned model parameters.