Symbol eta

The passage around this formula

evaluated using only the fixed start and end conditions — the equation has no term for how the system got to its starting point, because it does not need one. An adaptive walk is a statement about one step from one place: $x_{i+1} = x_i + \eta\,\nabla W(x_i)$. a new position built only from the previous position and the local slope of fitness W at that exact point, with no access to the global shape of the landscape and no way to undo $x_i$ once it is fixed. In optimization-theory terms, the first rule is global by construction; the second is a greedy local rule that can only report the best it found from where it started. Physics gets to run the first kind of rule because a photon and a planet have no history…

Read this part in the article →