Neurons are potential statisticians

Humans and animals can predict what will happen in the future and act appropriately by inferring how the sensory inputs were generated from underlying hidden causes. The free-energy principle is a theory of the brain that can explain how these processes occur in a unified way. However, how the fundamental units of the brain, such as the neurons and synapses, implement this principle has yet to be fully established. Here, we have mathematically shown that neural networks that minimise a cost function implicitly follow the free-energy principle and actively perform statistical inference. We have reconstructed a biologically plausible cost function for neural networks based on the equation of neural activity and shown that the reconstructed cost function is identical to variational free energy, which is the cost function of the free-energy principle. This equivalence speaks to the free-energy principle as a universal characterisation of neural networks, implying that even at the level of the neurons and synapses, the neural networks can autonomously infer the underlying causes from the observed data, just as a statistician would. The proposed theory will advance our understanding of the neuronal basis of the free-energy principle, leading to future applications in the early diagnosis and treatment of psychiatric disorders, and in the development of brain-inspired artificial intelligence that can learn like humans.