1. Spanning Trees

Simple trees contain single-valued numerical connections, and are made from minimum spanning trees. complex trees are also MSTs, but contain multi-valued connections that represent categories.

While numerical comparisons are simple, requiring basic comparative operators, a category is more difficult. There exists no intrinsic order to a set of things, so one must be created from a set of ordered pairs, each representing a preference between two categories. Being numerical, preference allows complex trees to be analyzed as simple.

2. Function Trees

Sets of functions are used to label connections of a graph. The similarity between connections is found by comparing their labels. Given a reference label and a set of candidate labels, the best option is measured by each candidate’s similarity to the reference connection. This assigns a utility to each candidate, allowing them to be sorted and ranked as an indicator of preference.

3. Comparison

Trees are compared by a mapping process, where a search is conducted to find pairs between nodes from different trees, where the similarity is calculated between the labeled connections of a source tree and those of a reference tree.

Two special-cases occur during the tree-mapping process in which a decision has to be made. The first involves arriving at a node that is either a source leaf or reference leaf. Both require the process to revert back to an earlier node, while saving the assignment made at the leaf. In the second case, a similar but distinct event plays out. It involves arriving at a node that, while not necessarily being a leaf in either tree, present an identical problem in that there exists no candidate labels for a given connection between some ‘current’ node and one of its neighbors.

This occurs when a bijective map of the local neighborhood is being found, where there exists an unassigned connection whose set of valid options (labels) are all assigned to other neighbors. This initiates a search of the previous assignments to find one that is: 1. a possible assignment for the current connection, and 2. not a necessary assignment for the previous connection. In this case, possible implies it is a valid assignment where similarity is efficient to map. Necessary means it is the only assignment in which similarity is efficient to map for a given connection. A sequence of switches can occur in which reassignments are given to a set of connections, such that the outcome resolves any connection that was unassigned in the process.

4. Tree Detection

A boolean function takes an input and produces a 1 or 0, which feeds into a connection and activates (if 1) a label, representing the function. Therefore if the function is true, it’s label is active.

A set of functions can produce a set of labels, corresponding to a subset of functions (those that are true). A set of labels are then translated to a set of functions at some later time. The functions map to higher level functions, where a certain n-level pattern will become active given a specific subset of labels at n-1 have recently activated.

5. Tree Learning

Trees are constructed at multiple levels and use the corresponding labels to do so. Activation occurs from bottom-up detection as well too-down prediction, as the high-level functions become active from inputs (low-level key patterns), they also activate groups of keys that may or may be present at lower levels, but are nonetheless connected with one another.

These high-level patterns send signals downward, bringing keys into the active state so that they are easily retrieved at lower levels. This is equivalent to working memory, where the content is readily accessible (conscious), and is produced by a larger memory space in which activity leads to certain information being passed to working memory.

Keys that spend time together in working memory form connections to the same high-level pattern, allowing it to detect similar organization of keys in working memory at a later time. If a particular arrangement that a pattern represents does not occur, in other words if the pattern fails to activate over a long period of time, then the connections are weakened and eventually removed, given enough time, at which point they are reassigned to more common patterns, preserving the structure of low-level activity at higher levels.