Neural computing in four spatial dimensions

Relationships among near set theory, shape maps and recent accounts of the Quantum Hall effect pave the way to neural networks computations performed in higher dimensions. We illustrate the operational procedure to build a real or artificial neural network able to detect, assess and quantify a fourth spatial dimension. We show how, starting from two-dimensional shapes embedded in a 2D topological charge pump, it is feasible to achieve the corresponding four-dimensional shapes, which encompass a larger amount of information. Synthesis of surface shape components, viewed topologically as shape descriptions in the form of feature vectors that vary over time, leads to a 4D view of cerebral activity. This novel, relatively straightforward architecture permits to increase the amount of available qbits in a fixed volume.

Automated summary

The relationship among near set theory, shape maps, and recent accounts of the Quantum Hall effect opens up the possibility of neural networks computations in higher dimensions, enabling detection and quantification of a fourth spatial dimension. The operational procedure to build a real or artificial neural network to achieve this has been illustrated, showing that starting from two-dimensional shapes, it is possible to achieve corresponding four-dimensional shapes with more information content. The synthesis of surface shape components and topological view of shape descriptions leads to a 4D view of cerebral activity, allowing for an increase in the amount of available qbits in a fixed volume.