A knowledgeable user graciously submitted this edit for the topology tag, but the scope of the content is such that I wanted to bring it to the community for discussion:
USAGE GUIDANCE Topology is the study of geometric constructs and whether they can or cannot arise from other geometric constructs solely from stretching, contracting, bending, or twisting. In the context of AI, the topology correlates closely with the categorical capabilities of the system.
TAG WIKI Topology is the study of geometric constructs as to whether they can or cannot arise from other geometric constructs solely from stretching, contracting, bending, or twisting. See the Miriam-Webster online dictionary definition of topology below.
In the context of AI, the topology correlates closely with the categorical capabilities of the system.
The feedback of signals from the output of a network or a layer to a previous point in signal flow is a topological feature involving splitting and joining which matches the use of the term in mechanics, mathematics, semantic web analysis, and IT network provisioning.
Gating and Attention organelles are topological.
The signal paths that create the adversarial balance between generative and discriminative networks in the GAN design create a topology that is unique to collaborative circuit pairing.
Although the term topology has been used in relation to the number of activation elements in a neural network layer, there is an undeniable semantic flaw with that usage:
Neural networks form a geometry of discrete elements without meaningful size attributes. Activations and input attenuation parameters cannot be stretched, contracted, bent, or twisted meaningfully. Moving a vertex with the edges still attached in the graphic representation also lacks functional meaning.
The only possible meaning of morphing a neural network layer is to change the quantity of its array elements, which means that the artificial neuron counts in the layers CANNOT be part of a network's topology if the word topology is to delineate anything at all.
Only Possible Logical Conclusion
If topology is to be applied to AI design, only features that cannot be changed solely by modifying the dimensionality of one or more arrays in the design can qualify as topological features.
a : 1. a branch of mathematics concerned with those properties of geometric configurations (such as point sets) which are unaltered by elastic deformations (such as a stretching or a twisting) that are homeomorphisms 2. the set of all open subsets of a topological space b : configuration — topology of a molecule topology of a magnetic field