The Curse of Dimensionality Problem: How Can the Brain Solve It?

The notion of "Curse of Dimensionality" was coined by Richard Bellman (1961). It refers to the exponential increase in computing a task of interest when extra dimensions are added to an associated mathematical space. For example, it arises in solving dynamic programming and optimal control problems when the dimension of the state vector is large. It also arises in solving learning problems when a finite number of data samples is used to learn a "state of nature, the distribution of which is infinitely large."

Much has been written on the curse of dimensionality problem in the mathematics and engineering literature. In contrast, little is known on how the human brain solves problems of this kind with relative ease. The key question is: How does the brain do it? To address this basic problem, it may be that we can learn from the mathematics and engineering literature, reformulated in the context of neuroscience.