Seppo Linnainmaa

Seppo Ilmari Linnainmaa (born September 28, 1945 in Pori , Finland ) is a Finnish mathematician and computer scientist .

In 1974 he received the first computer science doctorate ever awarded by the University of Helsinki . In 1976 he became an assistant professor. From 1984 to 1985 he was visiting professor at the University of Maryland, USA. From 1986 to 1989 he was chairman of the Finnish Society for Artificial Intelligence. From 1989 to 2007 he was research professor at the Finnish Technical Research Center. He retired in 2007.

In 1970 Linnainmaa published the "backward mode" of automatic differentiation (AD) for the efficient calculation of the derivative of a differentiable composite function that can be represented as a graph or network. The central trick is the recursive application of the chain rule to the components of the function. This method is now used in numerous applications. In particular, backpropagation of errors in artificial neural networks is a special case of Linnainmaa's method.

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Individual evidence

↑ ^a ^b Andreas Griewank (2012). Who Invented the Reverse Mode of Differentiation ?. Optimization Stories, Documenta Matematica, Extra Volume ISMP (2012), 389-400.
^ Seppo Linnainmaa (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.
^ Seppo Linnainmaa (1976). Taylor expansion of the accumulated rounding error. BIT Numerical Mathematics, 16 (2), 146-160.
^ Andreas Griewank and A. Walther. Principles and Techniques of Algorithmic Differentiation, Second Edition. SIAM, 2008.
↑ Jürgen Schmidhuber (2015). Deep learning in neural networks: An overview. Neural Networks 61 (2015): 85-117. ArXiv

personal data
SURNAME	Linnainmaa, Seppo
ALTERNATIVE NAMES	Linnainmaa, Seppo Ilmari (full name)
BRIEF DESCRIPTION	Finnish mathematician and computer scientist
DATE OF BIRTH	September 28, 1945
PLACE OF BIRTH	Pori , Finland

[grie2012-1] Andreas Griewank (2012). Who Invented the Reverse Mode of Differentiation ?. Optimization Stories, Documenta Matematica, Extra Volume ISMP (2012), 389-400.

[lin1970-2] Seppo Linnainmaa (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.

[lin1976-3] Seppo Linnainmaa (1976). Taylor expansion of the accumulated rounding error. BIT Numerical Mathematics, 16 (2), 146-160.

[grie2008-4] Andreas Griewank and A. Walther. Principles and Techniques of Algorithmic Differentiation, Second Edition. SIAM, 2008.

[schmidhuber2015-5] Jürgen Schmidhuber (2015). Deep learning in neural networks: An overview. Neural Networks 61 (2015): 85-117. ArXiv