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Stuart Dreyfus

A native of Terre Haute, Indiana, Stuart E. Dreyfus is Professor Emeritus at University of California, Berkeley in the Industrial Engineering and Operations Research Department. While at the Rand Corporation he was a programmer of the JOHNNIAC computer. While at Rand he was coauthor, with Richard Bellman, of Applied Dynamic Programming. Following that work, he was encouraged to pursue a Ph.D. which he completed in applied mathematics at Harvard University in 1964, on the calculus of variations. In 1962, Dreyfus simplified the Dynamic Programming-based derivation of backpropagation (due to Henry J. Kelley and Arthur E. Bryson) using only the chain rule.[1][2][3][4] He also coauthored Mind Over Machine with his brother Hubert Dreyfus in 1986.


  1. ^ Stuart Dreyfus (1962). The numerical solution of variational problems. Journal of Mathematical Analysis and Applications, 5(1), 30-45. Online
  2. ^ Stuart Dreyfus (1990). Artificial Neural Networks, Back Propagation and the Kelley-Bryson Gradient Procedure. J. Guidance, Control and Dynamics, 1990.
  3. ^ Eiji Mizutani , Stuart Dreyfus, Kenichi Nishio (2000). On derivation of MLP backpropagation from the Kelley-Bryson optimal-control gradient formula and its application. Proceedings of the IEEE International Joint Conference on Neural Networks (IJCNN 2000), Como Italy, July 2000. Online
  4. ^ Jürgen Schmidhuber (2015). Deep Learning. Scholarpedia, 10(11):32832. Section on Backpropagation