Tensor network theory

The theory was developed by Andras Pellionisz and Rodolfo Llinas in the 1980s as a geometrization of brain function (especially of the central nervous system) using tensors.

Much of the progress can be attributed to the work of Pellionisz and Llinas and their associates who developed the tensor network theory in order to give researchers a means to quantify and model central nervous system activities.

[1][2] In 1980, Pellionisz and Llinas introduced their tensor network theory to describe the behavior of the cerebellum in transforming afferent sensory inputs into efferent motor outputs.

Here, Pellionisz described the analysis of the sensory input into the vestibular canals as the covariant vector component of tensor network theory.

[10] The resulting metric tensor allowed for accurate predictions of the neuronal connections between the three intrinsically orthogonal vestibular canals and the six extraocular muscles that control the movement of the eye.

The flight computer's calculations and behavior was modeled as a metric tensor taking the covariant sensor readings and transforming it into contravariant commands to control aircraft hardware.

Metric tensor that transforms input covariant tensors into output contravariant tensors. These tensors can be used to mathematically describe cerebellar neuronal network activities in the central nervous system.
Neuronal network schematic. The sensory inputs get transformed by the hidden layer representing the central nervous system which in turn outputs a motor response.
Six rotational axes about which the extraocular muscles turn the eye and the three rotational axes about which the vestibular semicircular canals measure head-movement. According to tensor network theory, a metric tensor can be determined to connect the two coordinate systems.