Foundations of Computational Mathematics

, Volume 10, Issue 1, pp 67–91

Mathematics of the Neural Response


  • S. Smale
    • Toyota Technological Institute at Chicago and University of California
  • L. Rosasco
    • CBCL, McGovern Institute, MIT & DISIUniversità di Genova
    • CBCL, Brain and Cognitive SciencesMassachusetts Institute of Technology
  • A. Caponnetto
    • Department of MathematicsCity University of Hong Kong
  • T. Poggio
    • CBCL, McGovern Institute, CSAIL, BCSMassachusetts Institute of Technology

DOI: 10.1007/s10208-009-9049-1

Cite this article as:
Smale, S., Rosasco, L., Bouvrie, J. et al. Found Comput Math (2010) 10: 67. doi:10.1007/s10208-009-9049-1


We propose a natural image representation, the neural response, motivated by the neuroscience of the visual cortex. The inner product defined by the neural response leads to a similarity measure between functions which we call the derived kernel. Based on a hierarchical architecture, we give a recursive definition of the neural response and associated derived kernel. The derived kernel can be used in a variety of application domains such as classification of images, strings of text and genomics data.


Unsupervised learningComputer visionKernels

Mathematics Subject Classification (2000)


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© SFoCM 2009