The chain rule — how to trace influence through nested calculations
While building his calculus, Gottfried Wilhelm Leibniz arrived at a rule for the case where one quantity affects a second, which in turn affects a third: the overall rate of change is the product of the rates at each stage. This is what is now called the chain rule. A neural network is a stack of simple calculations nested many layers deep, so how much each connection is to blame for an error at the output can be found by applying this rule backwards from the output. That procedure came to be called backpropagation some 290 years later (see 1970 and 1986).
- Until it was used to train neural networks ~290 years
People and institutions: Gottfried Wilhelm Leibniz
NoteThe date 1676 follows Schmidhuber's survey (2022), which cites J. M. Child's English translation (1920). Leibniz published his calculus in 1684, and the chain rule took its textbook form later still. The manuscript itself has not been consulted.
- Annotated History of Modern AI and Deep Learning — arXiv:2212.11279 (2022), J. Schmidhuber
- The Early Mathematical Manuscripts of Leibniz (translated by J. M. Child) — Chicago: Open Court (1920); HathiTrust catalog record