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Seppo Linnainmaa (born 1945 in Pori, Finland) is a Finnish mathematician and computer scientist. In 1974 he obtained the first doctorate ever awarded in computer science at the University of Helsinki.[1] In 1976, he became Assistant Professor. From 1984-1985 he was Visiting Professor at the University of Maryland, USA. From 1986-1989 he was Chairman of the Finnish Artificial Intelligence Society. From 1989-2007, he was Research Professor at the Technical Research Centre of Finland. He retired in 2007.

In 1970, Linnainmaa introduced the reverse mode of automatic differentiation (AD), to efficiently compute the derivative of a differentiable composite function that can be represented as a graph, by recursively applying the chain rule to the building blocks of the function.[1][2][3][4] This method is now heavily used in numerous applications. For example, Backpropagation of errors in multi-layer perceptrons, a technique used in machine learning, is a special case of reverse mode AD.


  1. ^ a b Griewank, Andreas (2012). Who Invented the Reverse Mode of Differentiation?. Optimization Stories, Documenta Matematica, Extra Volume ISMP (2012), 389-400.
  2. ^ Linnainmaa, Seppo (1970). The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors. Master's Thesis (in Finnish), Univ. Helsinki, 6-7.
  3. ^ Linnainmaa, Seppo (1976). Taylor expansion of the accumulated rounding error. BIT Numerical Mathematics, 16(2), 146-160.
  4. ^ Griewank, Andreas and Walther, A.. Principles and Techniques of Algorithmic Differentiation, Second Edition. SIAM, 2008.

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