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.
Author Information
Simon Haykin (Mc Master University)
Terrence J Sejnowski (Salk Institute)
Steven W Zucker (Yale University)
More from the Same Authors

2018 Poster: Gradient Descent for Spiking Neural Networks »
Dongsung Huh · Terrence J Sejnowski 
2014 Poster: Feedforward Learning of Mixture Models »
Matthew Lawlor · Steven W Zucker 
2014 Oral: Feedforward Learning of Mixture Models »
Matthew Lawlor · Steven W Zucker 
2013 Session: Oral Session 3 »
Terrence J Sejnowski 
2012 Posner Lecture: Suspicious Coincidences in the Brain »
Terrence J Sejnowski 
2011 Session: Opening Remarks and Awards »
Terrence J Sejnowski · Peter Bartlett · Fernando Pereira 
2010 Placeholder: Opening Remarks »
Terrence J Sejnowski · Neil D Lawrence 
2010 Talk: Opening Remarks and Awards »
Richard Zemel · Terrence J Sejnowski · John ShaweTaylor 
2009 Invited Talk: Cognitive Dynamic Radio »
Simon Haykin 
2008 Workshop: Cortical Microcircuits and their Computational Functions »
Tomaso Poggio · Terrence J Sejnowski 
2006 Workshop: Decoding the neural code »
Eric Thomson · Bill Kristan · Terrence J Sejnowski