Fig. 1: Clone-structured cognitive graph.

a Sketch explaining dynamic Markov coding. A first-order Markov chain shown as a graph between nodes representing its states, modeling observation sequences A → C → E (purple arrows) and B → C → D (green arrows) will also assign high probability to the sequence A → C → D because higher-order information is lost at state C. (Middle) Higher-order information can be recovered by cloning the state C for different contexts, and then relearning their outgoing connections (blue) to result in the graph on the right. b Cloning structure of dynamic Markov coding can be represented in an HMM with a structured emission matrix, the cloned HMM. c Probabilistic graphical model for CSCG which extends cloned HMMs in b by including actions. d Neural implementation of cloned HMM. Arrows are axons, and the lateral connections implement the cloned HMM transition matrix. Different sequences are in different colors, e.g., A → C → E in purple. Neurons in a column are clones of each other that receive the bottom-up input (blue arrows) from the same observation. e Inference dynamics in the cloned HMM neural circuit. Neural activations strengths are represented in shades of red. Activations that propagate forward are the ones that have contextual (lateral) and observational (bottom-up) support. f Replay within the circuit for the sequence A → B → (C, D) → E → E.