A native of Terre Haute, Indiana, Stuart E. Dreyfus is professor emeritus at

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

in the

Industrial Engineering Industrial engineering is an engineering profession that is concerned with the optimization of complex processes, systems, or organizations by developing, improving and implementing integrated systems of people, money, knowledge, information an ...

and

Operations Research Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve dec ...

Department. While at the

Rand Corporation The RAND Corporation (from the phrase "research and development") is an American nonprofit global policy think tank created in 1948 by Douglas Aircraft Company to offer research and analysis to the United States Armed Forces. It is financ ...

he was a programmer of the

JOHNNIAC The JOHNNIAC was an early computer built by the RAND Corporation (not Remington Rand, maker of the contemporaneous UNIVAC I computer) and based on the von Neumann architecture that had been pioneered on the IAS machine. It was named in honor of v ...

computer. While at Rand he coauthored ''Applied

Dynamic Programming Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. I ...

'' with

Richard Bellman Richard Ernest Bellman (August 26, 1920 – March 19, 1984) was an American applied mathematician, who introduced dynamic programming in 1953, and made important contributions in other fields of mathematics, such as biomathematics. He founde ...

. Following that work, he was encouraged to pursue a Ph.D. which he completed in

applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemat ...

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...

in 1964, on the

calculus of variations The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

. In 1962, Dreyfus simplified the

-based derivation of backpropagation (due to Henry J. Kelley and Arthur E. Bryson) using only the

chain rule In calculus, the chain rule is a formula that expresses the derivative of the Function composition, composition of two differentiable functions and in terms of the derivatives of and . More precisely, if h=f\circ g is the function such that h(x) ...

.Stuart Dreyfus (1990). Artificial Neural Networks, Back Propagation and the Kelley-Bryson Gradient Procedure. J. Guidance, Control and Dynamics, 1990.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
/ref>

Jürgen Schmidhuber Jürgen Schmidhuber (born 17 January 1963) is a German computer scientist most noted for his work in the field of artificial intelligence, deep learning and artificial neural networks. He is a co-director of the Dalle Molle Institute for Artifi ...

(2015). Deep Learning. Scholarpedia, 10(11):32832
Section on Backpropagation
/ref> He also coauthored ''Mind Over Machine'' with his brother Hubert Dreyfus in 1986.

Notes

References

Prof. Homepage of Stuart Dreyfus at UC Berkeley
*. Year of birth missing (living people) Living people American industrial engineers American operations researchers Harvard University alumni UC Berkeley College of Engineering faculty {{US-edu-bio-stub