ResearchLearning and high-order statistics

How might brains learn the statistical regularities of the world?

Clearly these go well beyond second order. Here we show that a third-order statistic of edge distributions is reminiscent of curve and texture geometry:

The original paper relating endstopping to curvature is:

In general, it supports the hypothesis that differential geometry can serve as a surrogate for very high-order statistical relationships. As required, brains can learn them.
Here is a generalization of Hebbian learning:

Of course, connections to diffusion geometry exist: