According to Schmidhuber's 2014 overview, explicit, efficient error backpropagation in arbitrary, discrete, possibly sparse NN-like networks was apparently first described in Linnainmaa's 1970 master's thesis, without reference to neural networks.
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Deep Learning in Neural Networks: An Overview → attributes to → The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors (master's thesis, University of Helsinki)
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