Widrow's 1990 retrospective (with Lehr) proves the LMS per-sample 'instantaneous gradient' is an unbiased estimate of the true gradient — the defining mathematical property of stochastic gradient descent

widrowhofflmsadalinesgdstochastic-gradient-descenthistory-of-mlbackpropagation-origins

In "30 Years of Adaptive Neural Networks: Perceptron, Madaline, and Backpropagation" (Widrow & Lehr, Proceedings of the IEEE, 1990), Widrow derives the μ-LMS algorithm as approximate steepest descent on the mean-square-error surface, substituting "an instantaneous gradient based upon the square of the instantaneous linear error" for the true gradient "because it is readily available from a single data sample" — computing the true gradient "would involve averaging the instantaneous gradients associated with all patterns in the training set" and is "usually impractical." The paper states plainly: "It is shown in [30] that the instantaneous gradient is an unbiased estimate of the true gradient" (reference [30]: Widrow & Stearns, Adaptive Signal Processing, Prentice-Hall, 1985 — unread in this vault; see Further leads below).

A rule that substitutes a single-sample, unbiased estimate of the expected gradient for the true gradient, and iterates on that estimate, is stochastic gradient descent by mathematical definition — this is the property the name refers to. Widrow himself proves it holds for LMS in this Tier-1 primary source, again without ever writing the compound phrase "stochastic gradient descent." Together with the 1960 original paper and Bottou's 2010 outside classification, this closes question-verify-lms-is-stochastic-gradient-descent-primary: every piece of the SGD mechanism — a stochastic surface, single-sample steepest descent, and now the unbiasedness proof — is established in Widrow's own words across thirty years, even though the label itself arrived from elsewhere. Cluster: moc-backpropagation-origins.

Further leads. Widrow & Stearns, Adaptive Signal Processing (Prentice-Hall, 1985) — the book this quote cites as reference [30], and the text question-verify-lms-is-stochastic-gradient-descent-primary originally named as the strongest possible single source. No PDF or full-text excerpt was locatable this session; would be worth a library/archive.org pass if a future session wants the derivation itself rather than a citation to it.