Self-Organized Cognitive Algebraic Neural Network

A multi-layered multi-dimensional Self-Organized Cognitive Algebraic Neural Network (“SCANN”) – our proprietary learning method – is formulated, in accordance with the dynamic proactive-retroactive learning method and self-organized learning method. This is required to arrange information and determine undefined rules based on a cognitive structure for the individual (or the subject matter). This may include choices and maximum likelihood estimation of each choice for the activity of the individual. A set of data in activity, for example, is determined for each individual (n) and more individuals are added to the activity content that form choices and different choice sets. The features (or attributes) of these choices and choice-sets may or may not be causal factors that influence a choice.

Intelligence, like all bounded living cell or a group of cells acting together, is the information machine in small world networks to:  

1. perform functions themselves – self-organized – to maintain themselves, and to reproduce themselves

2. evolutionary, starting with blank or empty memory and evolves through a process of natural selections

3. leads to better designed intelligent (and living) entities without having a designer;

Intelligence has multi-layered-multi-dimensional networks of – cognitive – structure to assimilate information:

Layer I (Foundation): form sensory (look-and-feel, attributes, latent features), rational (causal reasoning, importance, trade-offs) and emotion (deep belief cues, attitudes, signals of values, etc.) – Believing passionately that what makes companies succeed is brands, not products, he set out to make the world appreciate how brands appeal not only by what they do, but by what they mean.;

[Stephen King (JWT), Paul E. Green]

Layer 2 (Objective): set lattices to plan or “manage probable” (forecast), “satisfice” factors and weights (optimization), “lead possibilities” (options and choices) and build capability (allocation/assignment);               

[Paul Erdős-Alfréd Rényi combinatorics]


Layer 3 (Controls): occupy or signal a low-density position (state) in decision momentum variables, execute “to do” (action), expect others’ “to do” (response) and find the end-result (reward) in phase transitions;

[Bose-Einstein Statistics]

Layer 4 (Inference): forage dynamic inferences on choice-sets – the decisions that an individual makes as a member of an organization are quite distinct from his or her personal choices. Both are bounded rational;

[Herbert Simon]

In the formation of a group with different clusters, based on activity and/or factors thereof, each choice set becomes a function of activity and interactions within a group, where the individual is a member. The features (or attributes) of these choices and choice-sets may or may not be causal factors that influence a choice. A choice set attribute may comprise one or more attributes, for example, of the item such as combination of sensory attributes, (taste, looks, etc.), rational (price, ingredients, etc.) and emotional (feel good, lifestyle, etc.). In the formation of a group with different clusters, based on activity and/or factors thereof, each choice set becomes a function of activity and interactions within a group, where the individual is a member. One or more common contact individual and/or individual’s activity content between individuals may exist in a group. Further, this indicates a “hub” contact with “cross” features and attributes for individual and/or individual’s activity content between individuals in a group, thus forms a graph structure of the network.

Many naturally occurring multi-layered multi-dimensional networks (Erdös, and Renyi), as represented in the figure above, explicitly incorporate multiple channels of connectivity and constitute the natural environment to describe systems interconnected through different categories of connections: each activity content module (signals, states, actions, responses and rewards) may be represented by a layer and the same node or entity may have different kinds of interactions (set of nearest-neighbors in each layer).

The latent feature structure, as depicted in above, is abstracted from variables to render microstate probabilities of each (dis)satisfied individual’s choice-set attributes and latent causal variables, accessible by mere combinatorial, (im)perfect and (in)complete information conditions much in the same way as graph probabilities, become accessible in random graph. At an atomic level, for each individual, the structure finds the optimal choice-set of latent variables that has causal effect on the expected outcome or reward or pay-off. The interaction variables that are available for individuals to exercise preference, or any variable involving an interaction of the individual for a good or service.

Mathematical Construct: SCANN

The coefficients are predetermined and represented a diminishing level of satisfaction, for example, over time. In addition, the latent learning represents that, in cognitive decision, despite their non-equilibrium and irreversible nature, the evolving network is mapped into an equilibrium Bose-Einstein (“BE”) condensation nodes corresponding to energy levels, and links representing the individual’s activity contents, as particles (Bianconi and Barabási). The mapping to a Bose gas and the possibility of Bose-Einstein condensation in random networks predicts the existence of three distinct phases characterizing the dynamical properties of evolving networks: (a) a scale-free phase, (b) a fit-get-rich phase and (c) a Bose-Einstein condensate. The active strand of the study in this direction is to study individualized ensembles with fixed degree sequences, or degree distributions following, for instance, a power-law. This is the probability that a randomly chosen node in the network has exactly 𝑙 links, is proportional to 𝑙-y for some y  (2, ) This describes the phenomenon of a phase transition that is an abrupt, discontinuous change in the properties of a system. We have set several examples of a phase transition like Bose-Einstein condensation for multi-layered later in the section Objective-Driven Construct. In those cases, we looked fairly closely to see the discontinuity: it was lurking in the derivative of the heat capacity. In other phase transitions — many of them already familiar — the discontinuity is more manifest.

There are also many conditions where the individual and/or individuals in a group choose actions without fully knowing with whom they will interact and what would be their response. Instead of a fixed network, individuals are now unsure about the network that will be in place in the future, but have some idea of the number of interactions that they will have. To fix ideas, the individual and/or a group where individual is a member and their action data may choose to find expected response that is only useful in interactions with other individuals who has the same product as well, but without being sure of with whom one will interact in the future.

Intelligence is free to expand or contract – algebraic – in computing like elasticity based on dynamic inferences of the situation and selectively forget (either retained in “deep” or recollect only as “salient” and “preferential attachment”) information.

In the solid phase, the molecules form a crystal. They are arranged in a regular pattern that repeats over and over again. In the liquid phase, the molecules no longer form any repeating pattern. They are still densely packed together, but they are in constant motion, breaking bonds and forming new ones as they move around. In the gas phase, the molecules are no longer packed together. They spread apart to fill whatever space is available to them. 

In-between solid-liquid transition phase – a phase that looks like both a liquid and a solid at the same time: the glass phase. On the outside the material behaves like a solid, but inside it appears as disorderly as a liquid. Glassy systems are a class of disordered systems that share a common phenomenology, characterized by a very slow dynamics in the low temperature phase. In-between the liquid-gas transition phase is probably a rather dramatic thing to watch. The coexistence curve only goes so far, then comes to an end. The point at which it ends is called a critical point. Beyond that point, there are no longer separate liquid and gas phases.

These layers in networks are bounded in a multi-dimensional structure of Voronoi geometry – as in the principles of Cliques and Cavities – to learn optimal (Mahalanobis) distance metrics in networks. First, plan or be “proactive” – based on connected (or complete or Clique) information. Second, add new information to disconnected dots, (or incomplete or Cavity), and change in “retroactive” the previously held information. For example: Time 1: Apple is a red colored round-shape fruit, Time 2: Apple is also a green and wood colored round-shape fruit. In another example: Day 1: hurricane X category 4 will hit the island, Day 2: hurricane X category 2 will move away from the island. (“Aha! I did not know this before” moments). More on this in the Synchronized Graph Machine section.