For questions involving topology in any form in relation to Artificial Intelligence.

Topology is central to several fields of AI application.

  • In solid modelling, ray tracing, dynamic morphing, mechanical design, 3D printing, and numerically controlled (CNC) machining, topological analysis of surface adjacency and cornering is necessary to ensure reliable control.

  • In networking, the topology of a scalable network is often more important than the network's scale when projecting network behavior for capacity planning.

  • In machine learning designs, the interconnection of networks, such as feeding a CNN network used to recognize object movement into an RNN or LSTM, guiding Q-learning using a trained MLP, or using generative designs that involve oversight or balance between multiple networks all form a topology with the surroundings that is the most fundamental aspect to high level design.

  • In drawing electronic schematics or laying out printed circuit boards or integrated circuits, the topology of the circuit determines the ease and potential space and path efficiency of the layout. CAD software represents the circuit and its functioning as a directed or non-directed graph. Electronic and electrical CAD automation involves translating elementary components in a multidimensional space into two dimensions of a fixed set of circuitry and component layers.

  • In natural language recognition and authoring, the serial stream of sound or printed characters must be probabilistically parsed into a semantic network of objects and associations and the semantic network must be serialized into sound or printed characters. This is central to social AI, automation of call centers and chatbots, and the development of conversant robots.

  • Ontologies have a topology that is related to complexity and the features of line topology define the complexity of object design that represents the ontology and related operations.

  • The brains of people and animals contain topological structure in the division of brain regions, in the wiring of neurons, in the channels of chemical signaling, and the plastic structure of axons, dendrites, and synapses that are related to function and timing.

The Oxford Dictionary provides this definition:

to·pol·o·gy
/təˈpäləjē/
noun
1. the study of geometric properties and spatial relations unaffected by the continuous change of shape or size of figures.
2. the way in which constituent parts are interrelated or arranged: "the topology of a computer network"

The popularity of arrays, vectors, lists, loops, and tensors is a topological phenomenon in that computer machinery and language has evolved away from relay racks containing a rat's nest of relay wiring toward structures that are more rectilinear and easier to comprehend using tools of mathematics and language designed for orthogonal structures. The popular programming languages tend away from symbolic processing languages that handle arbitrary topology like LISP to languages that are heavily influenced by FORTRAN (formula translation to assembly language) with arrays and loops as the central parallel structure methodology.

Graph theory and graph software libraries support the representation of non-orthogonal structures, such as clusters of highly interrelated neurons found in brains that don't fit nicely into traditional tensor representation. A calculus of topological structure may or may not facilitate further and faster advancement of AI capabilities. Projections are divided and proposed process topology and data flow topology is varied.

In AI theory, many have proposed changes in computing topology away from the approach initiated by John von Neumann and others, which centralizes arithmetic and logical branch processing in a CPU. The argument points out that both processes and processors have topology and that a close alignment of the two produces greater efficiency in parallel processing in VLSI design, mother board design, and computer clustering. If this principle is generally true, energy efficiency, speed of computation, reliability, weight (for launch application), and conservation of space are all related to topology.

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