Seppo Ilmari Linnainmaa (born 28 September 1945) is a

Finnish Finnish may refer to: * Something or someone from, or related to Finland * Culture of Finland * Finnish people or Finns, the primary ethnic group in Finland * Finnish language, the national language of the Finnish people * Finnish cuisine See also ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and computer scientist. He was born in Pori. In 1974 he obtained the first doctorate ever awarded in computer science at the

University of Helsinki The University of Helsinki ( fi, Helsingin yliopisto, sv, Helsingfors universitet, abbreviated UH) is a public research university located in Helsinki, Finland since 1829, but founded in the city of Turku (in Swedish ''Åbo'') in 1640 as the ...

. In 1976, he became Assistant Professor. From 1984 to 1985 he was Visiting Professor at the

University of Maryland The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public land-grant research university in College Park, Maryland. Founded in 1856, UMD is the flagship institution of the University System of M ...

, USA. From 1986 to 1989 he was Chairman of the Finnish Artificial Intelligence Society. From 1989 to 2007, he was Research Professor at the VTT Technical Research Centre of

Finland Finland ( fi, Suomi ; sv, Finland ), officially the Republic of Finland (; ), is a Nordic country in Northern Europe. It shares land borders with Sweden to the northwest, Norway to the north, and Russia to the east, with the Gulf of B ...

. He retired in 2007. Explicit, efficient error

backpropagation In machine learning, backpropagation (backprop, BP) is a widely used algorithm for training feedforward artificial neural networks. Generalizations of backpropagation exist for other artificial neural networks (ANNs), and for functions gener ...

in arbitrary, discrete, possibly sparsely connected, neural networks-like networks was first described in a 1970 master's thesis (Linnainmaa, 1970, 1976), albeit without reference to NNs,Jürgen Schmidhuber, (2015)
Who Invented Backpropagation?
/ref> when Linnainmaa introduced the reverse mode of

automatic differentiation In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation, computational differentiation, auto-differentiation, or simply autodiff, is a set of techniques to evaluate the derivative of a function s ...

(AD), in order to efficiently compute the

derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...

of a

differentiable In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its ...

composite function that can be represented as a

graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...

, by recursively applying the

chain rule In calculus, the chain rule is a formula that expresses the derivative of the 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)=f(g(x)) for every , ...

to the building blocks of the function.Griewank, Andreas and Walther, A.. Principles and Techniques of Algorithmic Differentiation, Second Edition. SIAM, 2008. Linnainmaa published it first, following Gerardi Ostrowski who had used it in the context of certain process models in chemical engineering some five years earlier, but didn't publish. With faster computers emerging, the method has become heavily used in numerous applications. For example,

of errors in multi-layer perceptrons, a technique used in

machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...

, is a special case of reverse mode AD.

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External links

* {{DEFAULTSORT:Linnainmaa, Seppo Living people 1945 births People from Pori Finnish mathematicians Finnish computer scientists University of Helsinki alumni Academic personnel of the University of Helsinki