Reverse-Mode Automatic Differentiation
1970Seppo Linnainmaa's 1970 MSc thesis (University of Helsinki, "The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors," in Finnish) introduced the reverse mode of automatic differentiation -- efficiently computing the derivative of a composite function represented as a graph by recursively applying the chain rule backward through it. General numerical technique, no neural-network framing at origin. Published as Linnainmaa, "Taylor expansion of the accumulated rounding error," BIT Numerical Mathematics 16(2):146-160, 1976 (OpenAlex W2018435387, 309 citations) -- the citable published version of the same thesis result. Split out from Backpropagation (2026-09-03) per BASIC_METHODOLOGY.md Tier 1 SS4 Option B, now that Basic has scaled past the 3-node POC that originally justified keeping this as one compromise-dated node: this is the clean, single-paper, unambiguous mathematical origin, distinct from Werbos's murkier 1974 thesis / 1982 concrete-application claim to have first applied the technique to a neural-network-style model (left as historical context on Backpropagation's own description, not modeled as a third node -- that claim is gradual/multi-source in the same way Many-Body Localization's lead-up was, not a single clean result to split off).
Originators
- Linnainmaa, S.
Landmark Paper
Lineage
Refined by:
- Backpropagation (1986)
Connections
No verified edges into the applied tree or elsewhere in Basic yet — never rendered as fabricated, just absent.