Building Quantum Field Theories Out of Neurons
- URL: http://arxiv.org/abs/2112.04527v1
- Date: Wed, 8 Dec 2021 19:05:36 GMT
- Title: Building Quantum Field Theories Out of Neurons
- Authors: James Halverson
- Abstract summary: An approach to field theory is studied in which fields are comprised of $N$ constituent random neurons.
Gaussianity is exhibited at large-$N$, potentially explaining a feature of field theories in Nature.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: An approach to field theory is studied in which fields are comprised of $N$
constituent random neurons. Gaussian theories arise in the infinite-$N$ limit
when neurons are independently distributed, via the Central Limit Theorem,
while interactions arise due to finite-$N$ effects or non-independently
distributed neurons. Euclidean-invariant ensembles of neurons are engineered,
with tunable two-point function, yielding families of Euclidean-invariant field
theories. Some Gaussian, Euclidean invariant theories are reflection positive,
which allows for analytic continuation to a Lorentz-invariant quantum field
theory. Examples are presented that yield dual theories at infinite-$N$, but
have different symmetries at finite-$N$. Landscapes of classical field
configurations are determined by local maxima of parameter distributions.
Predictions arise from mixed field-neuron correlators. Near-Gaussianity is
exhibited at large-$N$, potentially explaining a feature of field theories in
Nature.
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