Amari's 1967 stochastic descent and the 1960 Widrow–Hoff LMS rule are sibling members of the SGD family, about seven years apart

Two adaptive learning rules from the 1960s are members of the same stochastic-gradient-descent family, separated by roughly seven years. The Widrow–Hoff least-mean-squares (LMS) rule (1960), co-invented by Bernard Widrow and Ted Hoff for the ADALINE (claim-ted-hoff-widrow-phd-student-architected-intel-4004), is described in settled textbook usage as "a stochastic gradient descent method in that the filter is only adapted based on the error at the current time" — it updates weights on the instantaneous single-sample error rather than on a full-batch gradient. Amari's 確率的降下法 (stochastic descent method), introduced in his 1967–68 work and read directly from the 1968 book (claim-amari-1968-saito-experiment-primary-read), is the same instantaneous-error family applied to discriminant learning, introduced explicitly as converging where the perceptron rule does not. Both descend from the statistical root of the family, claim-robbins-monro-1951-stochastic-approximation — LMS and Amari's rule are cousins of that 1951 method, one repurposing noisy sequential root-finding into weight adaptation.

This sibling relationship is the load-bearing point. An embedding hop had suggested a direct resemblance between the Amari-SGD-MLP myth and Faggin's anti-computationalist argument. That direct edge is superficial — a shared note-shape (a computing pioneer plus a single-witness contested claim), not a connection in the world. The real connective tissue runs Amari → (SGD family) → Widrow–Hoff LMS → Ted Hoff → the Intel 4004 silicon → Faggin. The vault already held the Hoff-to-Faggin end of that chain; the previously-undrawn link was Amari into the LMS/adaptive-filter lineage — the same lineage that also produced Lucky's 1965 steepest-descent equalizer (claim-lucky-1965-adaptive-equalizer-steepest-descent-transversal-filter). Cluster: moc-backpropagation-origins.