Fig. 4: Learning temporal order and paths.

In all experiments, CSCG learned the optimal model for prediction, and the learned circuits matched neurobiological observations. a Modified T maze from¹⁶ with an overlapping segment between the blue and red paths. A, B, ⋯ , N are the observations at different locations in the maze. b CSCG learns route-differentiated clones for the overlapping segment. (The redundant clones on the non-overlapping segments are identical, and due to the learning algorithm not always using the minimal number of clones). c Activity of the clones for the right trial, and the left trial. Similar to the observations in¹⁶, the activity of clones in this overlapping segment will indicate whether the agent is going to turn left or right. Distinct neurons are active in the overlapping segment for left-turn trials vs right-turn trials although the observations in the overlapping segment are identical for both trials. Note that clones are not limited to one time step. CSCG learning is able to propagate clones backward into multiple time steps to unravel long overlapping paths. d Overlapping odor sequences from⁷⁴ e Full circuit learned by the CSCG shows that it has learned distinct paths in the overlap, as in⁷⁴. f A complex maze in which the agent takes two stochastic paths indicated in magenta and green. Observations in the maze are marked by numbers and, as before, the same observation can be sensed in many parts of the maze. The green and magenta paths overlap in up to seven locations in the middle segment (observations 4-5-11-12-13-5-17). The stochasticity of the paths and the long overlaps make this a challenging learning problem. In contrast to mazes in a and d, the two paths in this maze lead to the same destination as in²⁰ g. Transition graph learned by the CSCG shows that two different chains are learned for the two routes in f, similar to the observation that place cells encode routes, not destinations²⁰. h Paths replayed from the CSCG after it was trained on sequences from f. As they pass through the overlapping segment, the green and magenta routes maintain the higher-order history of where they originated, showing that the learned graph compactly represents the stochasticity and directionality of each route while separating the two routes by appropriately merging and splitting the clones.