Fig. 2: Student feedback alters the language embedding according to a utility function.

a Principal Component Analysis (PCA) of the lower-dimensional messages of size K = 5 obtained from a language encoding without student feedback (eq. (4)) for all possible tasks in the 4 × 4 mazes with ≤1 walls (see “Methods” for a description of the tasks). i) Explained variance by principal component. ii)-iii) depicts the messages highlighted by the position of the single wall (gray refers to the maze with no walls) and by the position of the goal, respectively. b Result of the message encoding now including student feedback achieved by using eq. (1) for the loss function. i)-iii) depict the same concepts as in (a). iv) shows messages highlighted by the preferred first student action (step up or right). c PCA of the messages with student feedback from an example grid-world (depicted in ii)).