David E. Rumelhart, Geoffrey E. Hinton, and Ronald J. Williams published “Learning representations by back-propagating errors” in Nature, volume 323, on 9 October 1986, beginning on page 533. The verified copy hosted on Hinton’s own university page reproduces the original Nature article, confirming the title, authors, journal, volume, and date.
The paper described a learning procedure that repeatedly adjusts the connection weights of a network to minimize the difference between its actual output and the desired output. Crucially, it showed how networks with hidden units, whose desired states are not specified by the task, could learn useful internal representations of the problem on their own, overcoming a limitation that had stalled earlier perceptron-style methods.
Although the underlying mathematics had appeared earlier, including in Werbos’s 1974 thesis, this clear and accessible Nature paper is what brought backpropagation into the mainstream. It became the standard training algorithm for neural networks and remains the foundation of how essentially all deep learning models are trained today.