Triple equivalence for the emergence of biological intelligence

TL;DR

This paper reveals a fundamental equivalence between neural networks, Bayesian inference, and Turing machines, explaining how biological intelligence emerges through evolution and Helmholtz energy minimisation.

Contribution

It introduces a novel theoretical framework linking neural networks, Bayesian inference, and Turing machines via Helmholtz energy, explaining the emergence of biological intelligence.

Findings

Neural networks, Bayesian inference, and Turing machines are mathematically equivalent.

Biological intelligence can be characterized by Bayesian model selection and belief updating.

Numerical simulations support the theoretical propositions.

Abstract

Characterising the intelligence of biological organisms is challenging. This work considers intelligent algorithms developed evolutionarily within neural systems. Mathematical analyses unveil a natural equivalence between canonical neural networks, variational Bayesian inference under a class of partially observable Markov decision processes, and differentiable Turing machines, by showing that they minimise the shared Helmholtz energy. Consequently, canonical neural networks can biologically plausibly equip Turing machines and conduct variational Bayesian inferences of external Turing machines in the environment. Applying Helmholtz energy minimisation at the species level facilitates deriving active Bayesian model selection inherent in natural selection, resulting in the emergence of adaptive algorithms. In particular, canonical neural networks with two mental actions can separately memorise transition mappings of multiple external Turing machines to form a universal machine. These propositions were corroborated by numerical simulations of algorithm implementation and neural network evolution. These notions offer a universal characterisation of biological intelligence emerging from evolution in terms of Bayesian model selection and belief updating.