Is the Widrow–Hoff LMS rule established as a stochastic gradient descent method by a Tier 1–2 primary source, not just Wikipedia?
claim-amari-stochastic-descent-and-widrow-hoff-lms-are-sgd-siblings rests one of its two legs on a Tier-4 Wikipedia characterization: "It is a stochastic gradient descent method in that the filter is only adapted based on the error at the current time" ("Least mean squares filter"). Characterizing how LMS relates to gradient descent is a technical-mechanism claim, which under the sources.md sourcing floor requires Tier 1–2 — Wikipedia here is a pointer to a primary, not the source itself. Until that grounding is in the vault, the sibling note stays seedling.
What would answer it.
- Widrow & Hoff, "Adaptive switching circuits," 1960 IRE WESCON Convention Record — the original LMS/ADALINE paper. Confirm the rule is the instantaneous-error (single-sample) update it is later called an SGD method for.
- Widrow & Stearns, Adaptive Signal Processing (Prentice-Hall, 1985) — the standard text that derives LMS explicitly as an instantaneous-gradient stochastic approximation to steepest descent (E[gradient] = true gradient; single-sample estimate). A verbatim quote from its LMS derivation would clear the mechanism floor at Tier 1.
- Either confirms the technical framing already asserted from the vault's Tier-1 Amari side (claim-amari-1968-saito-experiment-primary-read) and the SGD-family root (claim-robbins-monro-1951-stochastic-approximation).
Why it matters. LMS is the hinge node in moc-backpropagation-origins connecting neural-net history to Ted Hoff and the Intel 4004 (claim-ted-hoff-widrow-phd-student-architected-intel-4004). If "LMS is SGD" is going to carry weight across that cluster, it should not rest on an aggregator. Related but distinct open thread: question-lucky-widrow-adaptive-filter-mutual-awareness.
Next move. Pull the Widrow & Stearns LMS derivation (or the 1960 WESCON paper) and lift the exact phrase; on success, upgrade the sibling note past seedling and record the primary quote there.
Progress log
- 2026-08-15 — answered yes, at the mechanism level, by three Tier 1 primaries read directly this session: claim-bottou-2010-classifies-widrow-hoff-lms-as-sgd-matching-original-algorithm (Bottou's own 2010 paper classifies LMS/Adaline as SGD, matching the original algorithm), claim-widrow-hoff-1960-original-paper-describes-lms-as-stochastic-steepest-descent (the inventors' own 1960 paper calls the error surface 'stochastic' and describes single-pattern steepest descent), and claim-widrow-lehr-1990-lms-instantaneous-gradient-unbiased-estimate (Widrow's own 1990 retrospective proves the instantaneous gradient is an unbiased estimate of the true gradient — the defining mathematical property of SGD). What settled it: every piece of the SGD mechanism is present in Widrow's own words across 1960–1990, though the compound phrase 'stochastic gradient descent' itself never appears in his papers — that label is Bottou's 2010 application from outside. Answered as a mechanism claim, which is what the sourcing floor asks for; the terminology nuance is recorded in the three claim-notes rather than treated as a blocker.
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