Before revision:  We then show that these neuronal dynamics approximate natural gradient descent, a well-known optimisation algorithm from information geometry that prescribes locally optimal belief updates. Lastly, numerical simulations suggest that both schemes perform equally well on average. The performance of belief updating is scored in terms of information length , a measure of the distance traveled in information space , which has a direct interpretation in terms of metabolic efficiency.
After revision:  We then show that these neuronal dynamics approximate natural gradient descent, a well-known optimisation algorithm from information geometry that follows the steepest descent of the objective in information space. We compare the information length of belief updating is scored in terms of information length , a measure of the distance traveled in information space , which has a direct interpretation in terms of metabolic efficiency.