Fig. 5: Illustration of how to assess whether feedforward- and feedback-dominated interactions involve the same population activity patterns.

a Canonical dimensions identified during a feedforward-dominated period in the trial (red dimensions). These are putative “Feedforward” (FF) canonical dimensions. Open red circles denote activity during the feedforward-dominated period. Solid red circles denote the projection onto the FF canonical dimensions. b We can then ask whether these FF canonical dimensions generalize to a feedback-dominated period. One possibility is that the interaction structure (defined using the canonical dimensions) remains stable across the two periods. In this case, the FF canonical dimensions (red dimensions) capture a similar level of correlation during the feedback-dominated period as the canonical dimensions identified during this period, the putative “Feedback” (FB) canonical dimensions (blue dimensions). As a result, the normalized correlation, the ratio of the population correlation for the FF canonical dimensions to that for the FB canonical dimensions (both computed in a cross-validated manner; see Methods), is close to 1. Open blue circles denote activity during the feedback-dominated period. Solid purple circles denote the projection of activity during the feedback-dominated period onto the FF canonical dimensions. Solid blue circles denote the projection onto the FB canonical dimensions. c Alternatively, the interaction structure might change across the two periods. In this case, the FF dimensions capture only a small fraction of the population correlation during the feedback-dominated period. Same conventions as in b.