---
title: "Capture: What Griewank 2012 says about Linnainmaa's priority in autodiff, and how that work was received before the 2010s"
type: "capture"
status: "promoted"
promoted_to: ["claim-ml-and-ad-communities-mutually-unaware"]
not_promoted: ["Claim 1 Griewank-2012-attributes-invention: already covered by claim-reverse-mode-multiple-independent-discovery (now verified-verbatim, primary since read directly 2026-07-06)","Claim 2 independent-rediscovery-pattern: same note","'priority but no paternity' phrase-origin question: Liu vs Griewank — unresolved, left as lead"]
origin: "batch"
date_created: "2026-07-01T00:00:00.000Z"
provenance: "batch run 2026-07-01; harvested from topic 'What does Griewank 2012 say about Linnainmaa's priority in autodiff and how was that work received before the 2010s?' [high]; web research via WebSearch + WebFetch"
tags: ["automatic-differentiation","linnainmaa","griewank","backpropagation","reverse-mode","history-of-ml","citation-history","autodiff-ml-gap"]
filename_note: "Topic prompt requested a very long filename; OS limit (255 chars) required shortening. Full topic string is preserved in title and provenance fields."
primary_source_title: "Who Invented the Reverse Mode of Differentiation?"
primary_source_author: "Andreas Griewank"
primary_source_date: "2012"
primary_source_url: "http://emis.icm.edu.pl/journals/DMJDMV/vol-ismp/52_griewank-andreas-b.pdf"
primary_source_tier: 1
primary_source_access_status: "UNREACHABLE as of 2026-07-01 — ECONNREFUSED on emis.icm.edu.pl; same failure as 2026-06-28 run. Semantic Scholar record resolves but delivers no full text. CiteSeerX mirror: SSL cert error. ResearchGate copies: HTTP 403. All claims about Griewank 2012 content rest on secondary sources."
secondary_source_1_url: "https://yuxi.ml/essays/posts/backstory-of-backpropagation/"
secondary_source_1_author: "Yuxi Liu"
secondary_source_1_date: "2023-12-26"
secondary_source_1_tier: 3
secondary_source_2_url: "https://torontoai.org/2019/12/03/d-jurgen-schmidhuber-on-seppo-linnainmaa-inventor-of-backpropagation-in-1970/"
secondary_source_2_author: "Toronto AI Meetup (reproducing Schmidhuber's account of Griewank 2012)"
secondary_source_2_date: "2019-12-03"
secondary_source_2_tier: 4
tier1_supporting_source_url: "https://arxiv.org/abs/1502.05767"
tier1_supporting_source_title: "Automatic Differentiation in Machine Learning: a Survey"
tier1_supporting_source_authors: "Baydin, Pearlmutter, Radul, Siskind"
tier1_supporting_source_date: "2018"
tier1_supporting_source_venue: "Journal of Machine Learning Research 18(153):1–43"
tier1_supporting_source_tier: 1
prior_captures_on_this_topic: ["10-inbox/raw/2026-06-28-read-griewank-2012-directly-to-verify-a-the-backward-pass-structural-description-of-linnainmaas-algorithm-and-b-the-copenhagen-park-anecdote.md","10-inbox/raw/2026-06-28-pull-citation-data-for-linnainmaa-19701976-to-verify-the-claim-that-the-work-was-essentially-uncited-before-the-2010s.md"]
---


> [!warning] Primary source still unreachable — claims about Griewank 2012 rest on secondaries
> The Griewank 2012 PDF was attempted again on 2026-07-01 and returns ECONNREFUSED. The two 2026-06-28 captures flagged the same failure; this is a persistent infrastructure problem, not a transient one. **Every claim below about what Griewank 2012 *argues* is sourced from secondaries (Tier 3–4).** The paper's bibliographic identity (title, journal, pages, year) is uncontested across all sources.
>
> **Relation to prior captures**: The 2026-06-28 captures cover (a) the Copenhagen park anecdote and backward-pass vocabulary gap, and (b) quantitative citation evidence for the 1970 thesis and 1976 paper. This capture synthesises what Griewank 2012 argues *as a document*, adds a new Tier 1 source (Baydin et al. 2018, JMLR) that independently corroborates the community-disconnection claim and explicitly credits Griewank 2012, and flags the "priority but no paternity" phrasing question.

---

## Claim 1: Griewank 2012 attributes the invention of reverse-mode [[automatic-differentiation|autodiff]] to Linnainmaa's 1970 master's thesis — the paper was written precisely to settle this question

**Claim type**: historical/bibliographic  
**Sourcing floor**: Tier 3–4 acceptable for uncontested historical claim  
**Source tier achieved**: Tier 3 (Yuxi Liu) + Tier 4 (Toronto AI blog) — clears floor

The paper is titled *"Who Invented the Reverse Mode of Differentiation?"* — a question Griewank poses and answers. Published in *Documenta Mathematica*, Extra Volume ISMP (2012), pp. 389–400. Griewank had been a central figure in autodiff research since at least the late 1980s; the fact that he wrote a formal "who invented this?" paper in 2012 — approximately 42 years after Linnainmaa's thesis and 26 years after [[backpropagation-gap|backpropagation]] went mainstream via Rumelhart–Hinton–Williams (1986) — is itself evidence that priority was unsettled until very recently.

Secondary accounts converge on the paper's answer:

- Yuxi Liu (2023): "(Griewank 2012) describes in detail what is in the thesis, according to which he developed it to analyze the cumulative effect of round-off error in long chains of computer computations."
- Toronto AI blog (2019, reproducing Schmidhuber citing Griewank): Griewank's paper identifies Linnainmaa as the inventor and describes the 1970 inspiration in Copenhagen (the "sunny afternoon in a Copenhagen park in 1970" anecdote; see 2026-06-28 capture for full provenance of that quote).

Griewank credits both Linnainmaa's 1970 Finnish thesis (unpublished internationally) and his 1976 English publication in *BIT Numerical Mathematics* 16(2): 146–160 (DOI: 10.1007/BF01931367).

| Field | Value |
|---|---|
| source_url | https://yuxi.ml/essays/posts/backstory-of-backpropagation/ |
| source_author | Yuxi Liu |
| source_date | 2023-12-26 |
| source_tier | 3 |
| exact_quote | "(Griewank 2012) describes in detail what is in the thesis, according to which he developed it to analyze the cumulative effect of round-off error in long chains of computer computations." |
| corroborating_url | https://torontoai.org/2019/12/03/d-jurgen-schmidhuber-on-seppo-linnainmaa-inventor-of-backpropagation-in-1970/ |
| corroborating_tier | 4 |

**Related notes**: [[claim-linnainmaa-priority-not-paternity]], [[claim-linnainmaa-thesis-identity]], [[claim-linnainmaa-rounding-error-problem]], [[claim-linnainmaa-field-numerical-analysis]]

---

## Claim 2: Griewank 2012 situates the invention within a pattern of independent rediscovery across fields — Baydin et al. 2018 (Tier 1) cites it for exactly this framing

**Claim type**: historical  
**Sourcing floor**: Tier 3–4 acceptable; Tier 1 achieved  
**Source tier achieved**: Tier 1 (Baydin et al. 2018, JMLR), corroborated by Tier 4

Baydin, Pearlmutter, Radul & Siskind (2018) — in the authoritative JMLR survey of autodiff — cite Griewank (2012) as the source for the following characterisation:

> "In machine learning, a specialized counterpart of AD known as the backpropagation algorithm has been the mainstay for training neural networks, with a colorful history of having been reinvented at various times by independent researchers (Griewank, [2012]; Schmidhuber, [2015])."

This establishes at Tier 1 that: (a) Griewank 2012 is treated by the field as the authoritative historical source on this reinvention pattern, and (b) the pattern Griewank 2012 documents is *multiple independent rediscoveries*, not a single invention unambiguously credited to one person.

The Toronto AI blog (Tier 4, 2019, Schmidhuber citing Griewank) adds the detail that Griewank's paper notes reverse mode "has been suggested by several people from various fields since the late 1960s, if not earlier" and names Gerardi Ostrowski as having used it in chemical engineering process models approximately five years before Linnainmaa, without publishing. Griewank's conclusion is that Linnainmaa was the first to *publish* — and to give the method its full, formal, general statement. [Ostrowski detail: Tier 4, unverified from primary]

| Field | Value |
|---|---|
| source_url | https://arxiv.org/abs/1502.05767 |
| source_author | Baydin, Pearlmutter, Radul, Siskind |
| source_date | 2018 |
| source_venue | Journal of Machine Learning Research 18(153):1–43 |
| source_tier | 1 |
| exact_quote | "a colorful history of having been reinvented at various times by independent researchers (Griewank, [2012]; Schmidhuber, [2015])" |
| corroborating_url | https://torontoai.org/2019/12/03/d-jurgen-schmidhuber-on-seppo-linnainmaa-inventor-of-backpropagation-in-1970/ |
| corroborating_tier | 4 |

**Related notes**: [[backpropagation-gap]], [[claim-linnainmaa-priority-not-paternity]]

---

## Claim 3: The ML and autodiff communities were "largely unaware of each other" until recently — Tier 1 structural explanation for the pre-2010s reception gap

**Claim type**: historical (structural), with Tier 1 sourcing  
**Sourcing floor**: Tier 3–4 acceptable; Tier 1 achieved  
**Source tier achieved**: Tier 1 (Baydin et al. 2018, JMLR)

Baydin et al. 2018 state in the abstract of the survey:

> "Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results."

This Tier 1 framing supplies the structural explanation for the pattern documented in the 2026-06-28 citation capture: Linnainmaa's 1976 *BIT* paper had a modest life in the numerical-analysis / autodiff community (cited by early autodiff work including Speelpenning 1980 and others), while being completely invisible to the neural network / ML community. The two literatures did not overlap. The [[backpropagation-gap]] is therefore not simply a matter of a work being ignored everywhere — it is a matter of two non-overlapping communities, each maintaining its own literature, rediscovering the same technique independently.

The "priority but no paternity" framing used in the 2026-06-28 captures (attributed to Yuxi Liu's essay, Tier 3) captures the *consequence* of this structural disconnect: Linnainmaa had chronological priority (first to publish) but no intellectual paternity (his work did not propagate into the lineage that mattered for deep learning). The Rumelhart–Hinton–Williams (1986) *Nature* paper did not cite Linnainmaa; the enormous downstream citation tail of that paper pointed back to Rumelhart et al. as originators rather than to Linnainmaa.

Note on the "priority but no paternity" phrase origin: Yuxi Liu (Tier 3) uses this exact phrasing for Linnainmaa in the December 2023 essay. It is not established from available sources whether Griewank 2012 uses this formulation himself or whether Liu coined it independently. The phrasing should not be attributed to Griewank 2012 without primary verification.

| Field | Value |
|---|---|
| source_url | https://arxiv.org/abs/1502.05767 |
| source_author | Baydin, Pearlmutter, Radul, Siskind |
| source_date | 2018 |
| source_venue | Journal of Machine Learning Research 18(153):1–43 |
| source_tier | 1 |
| exact_quote | "Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results." |
| corroborating_url_for_community_split | https://yuxi.ml/essays/posts/backstory-of-backpropagation/ |
| corroborating_tier | 3 |

**Related notes**: [[backpropagation-gap]], [[claim-linnainmaa-field-numerical-analysis]], [[claim-linnainmaa-priority-not-paternity]], [[claim-linnainmaa-reverse-mode-single-pass]]

---

## Further leads

- **Direct read of Griewank 2012 primary text**: Both EMIS mirrors have now failed on two consecutive runs. Paths forward: (a) interlibrary loan or university library proxy; (b) Griewank's HU Berlin or RWTH Aachen author page; (c) ResearchGate when authenticated. The key open question this would settle: does Griewank himself use "priority but no paternity" language, or is that Liu's framing?
- **Griewank 2014 (Tier 1, confirmed accessible)** — `https://www.scielo.br/j/pope/a/kZ8M4LPYFryXQkdwHz7QXVx/?lang=en` — Griewank's 2014 *Pesquisa Operacional* paper builds on the 2012 work; the 2026-06-28 capture used it for the adjoint recursion vocabulary ("reverse procedure," not "backward pass"). May also contain direct statements reiterating the Linnainmaa attribution.
- **Baydin et al. 2018 full-text sections on Linnainmaa/Werbos** — `https://arxiv.org/abs/1502.05767` — the HTML version at ar5iv is loadable. Passages about Linnainmaa's specific contribution, and whether the survey characterises his work as the root of modern autodiff, were not extracted in this run; worth reading in full.
- **Schmidhuber arXiv:2005.05744** — reportedly a detailed timeline of backpropagation attribution with year-by-year citation analysis for Linnainmaa 1976; DNS failure on idsia.ch prevented access this run.
- **Speelpenning (1980)** "Compiling fast partial derivatives of functions given by algorithms" — reportedly the first autodiff implementation paper to cite Linnainmaa; verifying this would anchor the claim that the 1976 BIT paper had autodiff-community readers before 2000.
- **Year-by-year citation counts** (Web of Science / Google Scholar) for DOI 10.1007/BF01931367 (Linnainmaa 1976) — required to upgrade the [unverified-quant] flags from the 2026-06-28 capture to verified status on the specific citation count claim.

> [!note] Seek's commentary:
> The persistent inaccessibility of Griewank 2012 is becoming a pattern across three runs now. The paper is Tier 1 and foundational to multiple notes in 30-notes/. It is worth treating this as a priority retrieval task: get it via library access rather than web scraping. The secondary-source picture is internally consistent enough that the historical claims feel solid, but any promotion of a claim to an atomic note that says "Griewank 2012 argues X" should carry a caveat until the text is read directly.
>
> The Baydin et al. 2018 (JMLR) source is the strongest new finding in this run. It is Tier 1, directly accessible via arXiv abstract, and provides the cleanest structural framing for the pre-2010s reception gap: not "the work was ignored" but "the two communities didn't read each other." That framing is more precise and more defensible than the vague "essentially uncited" claim from the batch prompt — and it also explains why the 1976 BIT paper could have some citation life in autodiff while remaining invisible to ML.