White paper on Quasi Artifactual Intelligence

D R A F T   D O C U M E N T

quasiArtifactualIntelligence —a perception from the edge

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  About ∞ White paper ∞ QuasiMatrix Code ∞ QAT Code ∞ Data Examples ∞ Scatter-Gather Explained ∞ The Plow Share ∞

Developing 911 era category theory as a front-end quasi-relational perceptive envelope

for machine learning and control

a plowpoint project.

Introduction

The Quasi Axiomatic Theory (QAT) was developed as a big-data tool to discover significant events in the live-edge of the expanding world-corpus —Cyberspace: 2000

As a category theory, a sampling of the world corpus, would contain a sampling of most of the categories of interest.  

As an investigatory tool, The QAT could isolate category trends and waves of change in large data samples, planet sized, by taking a sparse sample of the information-routes of the expanding world corpus, recorded in internet router logs.  

The QAT paradigm was implemented as an in-memory data engine of records retrieved by a sparse sampling of the world data, such that when categories of significance were discovered by visual examination.  With discovery of category-frequency-trends in communication IP router logs, the cause of the change-wave may be reverse-searched from category, to data-event, by a category-link explorer, made to step through smaller sets of significant categories —toward discovery of individual internet routes as the causative determinant.  The butterfly.  

These algorithmic approaches are termed, 'categorical abstraction' (a scatter-gather visual map), and 'eventChemistry' as the category explorer.

Here we explore the QAT algorithms to expose how machine learning can be afforded a place within the quasi-axiomatic analysis loop. With the processing of value categories, the QAT and paradigm affords a perception of relational dynamics, evidenced by the occurrence-density of the simultaneity of related dynamics shared between two channels of measurement, about the same event, measured as different aspects. 

The machine learning, of an AI in training, can witness the quasi-artifact of measured reality. This examines the development of quasiArtifactualIntelligence  

The Architecture of the QAT Algorithms

Visual Abstraction —mapping cross-category coincidence-frequency dynamics

The Quasi Axiomatic Theory SLIP browser showing the structures of coincedence within an internet router log file.

The visual abstraction of the random-scatter mapping appears as points (representing value categories) that move on a mapping, which map the category-points were randomly scattered upon.

The 'magic' ingredient of the QAT algorithms that afford a visual categorical abstraction (cA) of relational events is the Cartesian product of the value categories found in the data stream sample for analysis. The magic is conjured by a tight iteration (programmatic loop) that moves two points slightly closer together upon the map.

Moving random point-pairs in the vA by micro-movements toward each the other, produces a clustering of categories upon the vA mapping.  The coincedent-proportionality subset of a,b permutations of the Cartesian product is established by the occurrence-frequency of members in a category as sampled from the data stream.

With an animated spectrum of motion-activated groups of map-points moving, an operator of this technology, typically an NSA analyst, could partition the categorical-dynamics with a sub-selection of the time-windows sampled for analysis.

This describes the Category Abstraction (cA) portion of the Quasi Axiomatic Theory and Paradigm (QAT).

Event Chemistry

The QAT eventChemistry browser, as a navigable classic graph (mouse click navigation), through the 'compounds' of categories of coincidence.

A further affordance of the QAT is an inference technique availed by the displayed cross-channel emergent-relationships, termed Event Chemistry (eC).

Once interesting groups of categories within the data-stream are isolated by category abstraction mapping, groupings of interest are selected from the clusters on the cA mapping.

Browsing an isolation of small groups from a world of information

Event chemistry abstraction, as a interactive classical graph of circles connected with lines, allowed inference techniques to sleuth the chemistry of categorical interactions. Prueitt's formal QAT applied Mill's logic of inferences with an overlaid knowledge-management framework of annotation and reporting.

Along with all of the contributions nationally, during the 911 response era, aiding in the global cause, were also the data structures of the QAT visual abstraction, navigable with event chemistry, providing access back to the source-moment of any categorical trend. A basic butterfly hunter.

QAT Theory in principle of emergent processing of causal artifact within chaos

The QAT is a map maker.  

If points on a map are linked with value-categories, and randomized onto a circle as a random radial distribution, then purely random operation on pairs of these distributed map points would continue to randomize the points in radial positions.

The QAT used a grouping-motion on two random points on the map, on each iteration.  Five hundred thousand very small grouping movements between random map points were used to produce the spikes, as illustrated, on the circular gather map.  This 'grouping' is the 'emergence' in this implementation of emergent computing.

A simpler way to conceive of emergence of pattern from chaos

If a simultaneity map were made between two channels, and both channels held identical data, duplicates, then the motion test would always be true, and the fuzzy circle would be endlessly re-randomized, pair by pair. However, when variation between the two channels occurs, then the randomality of the fuzzy circle is injected with a determinance, in this case, the grouping determinant of moving a pair closer together. After many small movements in a tight loop, the grouping determinant gathers clusters. These clusters are causal artifacts of a relationship between the dual, synchronous measurements.

Emergency lexicon (footnotes?)

a stratification of category-frequency density of inter-relational coincidence 'tween two channels of measurement

Tween —a made-up term
A categorical stratification process that groups  over time a category-map as a random-pair selection in a tight-loop. Tweening is the act of emergent computing, in a general sense. Usage of the term:  The spikes on the circle illustrated were 'tweened' from the fuzzy halo of the other fuzzy circle illustration.

Implementation of QAT Data Structures

What for the oddness of cross-channel simultaneity dynamics upon a QAT cluster map over time, the data structures to produce emergent processing of the QAT are yet redundantly simple.

The gather method is supported by three lists:

1) UniqueList-A: A list of the unique values within the sample block from a data stream of channel-A. (Category theory term: atoms)

Term: 'Atom value categories'

2) UniqueList-B: A similar list of channel-B. (Category theory term: links)

Term: 'Link value categories'

3) ExpandedList-A: A list of all the combinations that can be expanded from the UniqueList-A, e.g.:

Term: 'Pairs' as a list of all of the combinations of any two categories from the UniqueList-A)

The eventChemistry methods operate with two more lists

4) Link Index-List by Atom: An index per each unique category value within the channel-A data sample block as a list of all the coincidental categories of Channel-B, per each unique category value of Channel-A.

5) Atom Index-list by Link: An identical index for Channel-B, listing coincidental Channel-A categories.

These lists 4) and 5) are created from a sub-set of the sampling data, bracketed by an operator.

In 2001, the 'bracketing operator' was a human

In 2024, the 'bracketing operator' is machine intelligence —quasiArtifactualIntelligence  

Simplification

While the original QAT proof was written to perform in steps (Prueitt, et al. BAA 2000), the data structures were also broken out in steps and largely duplicated in steps, and that complicated with the bracketing being represented by recursive storage folder access.

The notational-burden of time-synchronization between five lists broken into recursive sub-sections, while lists must remain synchronous, was a large part of the DARPA proof's notational challenge.

Solution Harvesting

An optimal solution for big data information access is for the data to get loaded once, never moved, indexed in place, and structured in place for binary-tree access, implemented as an indexed array.

The QAT foundation lists of Atoms and Links are afforded by the binary tree, which is a linking-structure of categories of values, as sampled from a data stream.

The data of every measurement-event (a row of multiple data channels) remains loaded in memory in natural order. Each repeat value of the same data value, is linked together in the natural order of the sampling measurements. By definition, the head of a linked list of equivalent values in this scheme is the category node. Big(O) binary access to the category node, then provides immediate access to every member of the value category, in order of occurrence.

With Big(0) category access to a data value, and direct access from the category node to the set of category members, all foundation lists needed for QAT emergent processing and cross-category visual membership browsing is not only fast, but this ontologizing process, per se, slows down very little with huge data sampling sets. World scale.

The solution is harvested by algorithmic-navigation from the root of the binary tree, through the tree on a least-distance navigation, and the solution is assembled, linearly, along the path of the solution excursion.

The array-based binary-tree / linked-list hybrid

The minimum pointer-set to implement a binary-tree combined with a linked list of tree-node members is stored as an array of integers, one integer to point to the data, and four more integers to point to data elements earlier in the data sample:

a) data pointer

b) lesser value pointer

c) greater value pointer

d) previous equivalent value pointer

e) next equivalent value pointer [Note: the next eq. pointer will be zero for a new data node, as 'next' is in the future for a new append.]

Use for comparison redundance

The binary comparator that builds a binary-tree data structure has two outcomes used in tree construction —a lesser or greater comparative result.

A third result, of any comparison, is from a comparison of equivalent values, neither lesser or greater.

When an equivalence is discovered while building the binary-tree, another link is appended to the linked-list of equivalent data members, headed from each category node hosting equivalence.

As a design application may allow, the node of each binary tree can also cache the equivalence-count of that node, which is the length of the linked-list of equal-values.

All of the five tables of the formal QAT solution are accessible directly, or from a cached table directly built from this fast, hybrid solution.

However, as application may dictate, even the cached tables can be resolved without the cache table by calculating for the one instance what the pre-cached table does for all instances.

Moreover, each inline-calculation may be cached in-place within the time-synchrous hybrid structure with little loss to real-time processing throughput. This describes a cached JIT solutions that is only a bit slower with the advent of novel category events.

Additionally, as a time-series data block, the hybrid tree/list structure is implicitly a time-line addressable mini-ontology. [Jargon sanity-check request]

By structuring the data-sample stream, or some sparse selection of samples over time, into a structure including all members in an accessible structure, the tree/list composite becomes a rudimentary ontology of the data-stream structured by value-comparisons against a data-relationship, and time-reversible (or re-build-able to any certain event on the time line). Anything programmatically comparable can be ontologized.

below here be dragons

Two measurement channels provide one QAT dimension of analysis^QAT.I-RIB providing visual abstraction of relationships in the cross-comparison. This occurs by randomly scattering onto a visual map the set of points representing all existing pairs within dual channels of measurement in the data ontology widget. The gather process accesses the proportionality map to animate the category-mapping- wherein this is a visual abstraction of dynamic relationships translated to a stratification of motions within the category-scatter-map.

• I-RIB: In-memory Referential Information Base. A term coined by P. S. Prueitt. Foundational Paper on Referential Bases, Paul S Prueitt Ph.D, October 31, 2006
• http://www.bcngroup.org/beadgames/TaosDiscussion/referentialBases.htm
• http://www.bcngroup.org/area1/2005beads/GIF/RoadMap.htm and
• Event Detection and categorical Abstraction 2002, Paul S. Prueitt PhD, OntologyStream URL: http://www.ontologystream.com/cA/papers/EventDetection.htm
• File:Foundational Paper on Referential Bases 2006, Paul S. Prueitt, Ph.D October 31, 2006

A question on nomenclature

Is a data structure of a tree-of-categories sharing indices with a linked-list headed with each category node, with the list comprising as pointers to all members of a value category —then may the pointer matrix be properly termed an ontology?  An ontological primitive?

future development notes

• Implement a QAT analysis on a basis of duration invariance

—QATNAP N-Dimensional Timing Variance on a Toroidal NMR continuous-wave group-resonance.

• Implement a video-frame-rate capability of gather processes on a random-scatter map, providing a gather-process that stratifies category-frequency-dynamics of a data-stream sample AS compared to another data-stream. I.e., dual-channel-expansion of category-frequency dynamics of unknown data.

Known </> Unknown ==> meaningful results to a domain expert, where '</>' represents a cluster-process (tweening) based on a determinant.

Known </> Known ==> machine intelligence training scenario

Unknown </> Unknown ==> interesting patterns which can be traced back to the causal instances of a value-category-occurrence in the sampled data stream/log

• Trace-back to root causality of existing unknown category dynamics is available to adjust sampling resolution.

• This affords in principles of an applicable domain a domestication of Maxwell's demon over events of chaotic environment, capable of isolating causal-determinants in ongoing apparent chaos.

• Massive parallel circuits on FPGA configurations customized for UI customized/calibrated to units and measures of the data stream for analysis. —Chaos Domestication Project

• Implement N-Dimensional quasiAI analysis —The Perceptorium