Towards a Mathematical Theory of Cortical Micro-circuits
(A) Structure of the reference node, with five coincidence patterns and two Markov chains. This is an HTM node that has finished its learning process. It is assumed that this is the first node at level 2 of a network and is therefore labeled as . Each coincidence pattern represents a co-occurrence of the Markov chains of the children. This node has 2 children. Child 1 has 3 Markov chains and child 2 has 4 Markov chains – hence there are seven elements in each coincidence pattern. The portions of the coincidence pattern coming from the first and second child are shown in different shades of gray. (B) Information flow in the reference node for the computation of the belief propagation equations shown in Table 1. The rectangles inside the node are processing units for the equations in the rows corresponding to the number displayed in each rectangle. We will use ‘feed-forward’ or ‘bottom-up’ to qualify messages received from children and messages sent up to the parent of this node. We will use ‘feedback’ or ‘top-down’ to qualify messages received from the parent and messages sent to the child nodes of this node. The node shown in the figure has two bottom-up input messages coming from the two children and has two top-down outputs which are the messages sent to these children. The arrows show vectors of inputs, outputs, and intermediate computational results. The number of components of each vector is represented using an array of boxes placed on these arrows.