White paper on Quasi Artifactual Intelligence

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 ∞

A development of 911 era category theory applied as a front-end category engine for machine learning and control —a plowpoint project, presenting:

Developing a perceptive envelope of reckoning for an artifactual intelligence —quasiAI: the perceptor

Editors note:  Wow!  The QAT is fascinating to revisit after a couple of decades!  When re-examined and documented, the example concept-soup below will redact in an attempt to reveal the fascinating things from the mind of Dr. Prueitt.

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 in the analysis loop —a keen plowpoint

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 visual abstraction (vA) 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

in severe edit XenoEngineer (talk) 12:51, 21 July 2023 (UTC)

Allow an attempt to express the feature of a deep category theory learned from a very deep mind that influenced in some fashion the beginning of the domestic spy agency over two decades ago.

Template:Img data scatter-gather 122x124

The QAT is a map maker.  

If points on a mapped 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. Perhaps hundreds of thousands of very small grouping movements between random map points were used to produce the spikes illustrated on the circular gather map.

The QAT only moves random points closer if the categories the two points represent were ever coincidental between the two columns of measured data. I.e., did the two values of the categories selected for movement ever occur simultaneously? If simultaneity had occurred within the sample block, move the points closer, else leave them alone, select another pair of points and continue in the tight loop hundreds of thousands of times. The loops were in big numbers, but computers were fast, and only seconds were needed to produce dual-channel simultaneity clusters.

Simpler to conceive, 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.

[animated fuzzy circle morphing into a spiky circle illustration goes here | hang right]

Emergency lexicon (footnotes?)

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

What's a tween?

A categorical stratification process over time 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 are 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.

2) UniqueList-B

A similar list of channel-B.

3) ExpandedList-A

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

The eventChemistry methods that provide user-interactive graphical navigation of the cross-time structure of inter-channel relational groupings required two additional data lists.

4) An index per each unique category value channel-A as a list of all the coincidental categories of Channel-B.

5) An identical index for Channel-B, listing all of channel-A's simultaneities per unique value category.

Simplification

While a original QAT proof was written to perform in steps, 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 recursed sub-sections and all synchronous was a large part of the DARPA proof's notational challenge.

Solution harvesting

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, explained by their monikers:

a) data pointer

b) lesser value pointer

c) greater value pointer

d) previous equivalent value pointer

e) next equivalent value pointer

All of the five tables of the formal QAT solution are accessible directly, or from a cached table directly built from the 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 the time-synchrous hybrid structure with little loss to real-time processing throughput. Cached JIT solutions that are only slower with the advent of novel category events.

Additionally, as a time-series data block, there is implicitly a time-line addressable ontology.

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.

fragment

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?    

Rigorous loose thoughts

In this notational paradigm of measurement and category frequency trending, the data is a recording and remains immutable.

A binary tree implementation for data access has no need to balance an immutable log.

A delete function for a tree node isn't needed, moreover, the data element tree/list nodes are each a demarcation of their category membership, in order on the time-line.

In the category theory implementation, the data may be sparsely sampled with the same results, within limits.

Should a data-access excursion on the tree-list structure get lengthy (as an unbalanced binary-tree) in any certain data sample, it is simply rejected as part of the un-sampled, dis-obviating any need for binary tree balancing.

The outcome of the paradigm rendered to notation is a binary-tree/linked-list data widget where all members of a category value are linked as a chain, as category-member-chains attached to each binary tree node.

The binary-tree nodes each have a chain of equivalent values indexed in natural order as a linked list. The fully structured data widget affords any data by relational-path-access, including lower_category, higher_category, next_member, previous_member, with all index values anywhere within the structure also indicating relative age by natural order, i.e., the magntitude of the access-index is a relative age value in a time-line sampling.

With structured historical data access of a measured channel, a second structure is referenced holding a second channel of measurements.  These two structures provide the prismatic affordance of the proportionality map of their implicit relational dynamics across a sampling of events within a time line.

Future Development

• Hyper-accelerating quasiAI category-perception with the Cartesian product sub-set on high-speed data-streams as a running-recent-average analysis window (or any previous history of the data-stream)
• 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 an unknown data-stream. I.e., dual-channel-expansion of how category-frequency dynamics of unknown data.

Known </> Unknown ==> meaningful results to a domain expert, where '</>' represents a cluster-process 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.
• Implement N-Dimensional QAT analysis, with an N-quasiAI