The intuition behind the model is that the probability of a word appearing at day t depends on the background log-frequencies, the deviation coefficients of the word at previous timesteps β 1:t−1 , and the similarity of current conditions of the world (based on observable features x) to previous timesteps through f (x t , x k ).
f is a function that takes ddimensional feature vectors at two timesteps x t and x k and returns a similarity vector f (x t , x k ) ∈ R M (see §6.1.1 for an example of f that we use in our experiments).