---
title: "Citation data for Linnainmaa 1970/1976: verifying the 'essentially uncited before the 2010s' claim"
type: "capture"
status: "promoted"
date_promoted: "2026-07-06T00:00:00.000Z"
promoted_to: ["30-notes/claim-rhw-1986-reference-list-four-works.md","30-notes/myth-linnainmaa-uncited-before-2010s.md"]
not_promoted: ["Claim 1/2 (near-zero pre-2010 citations; 34-vs-289 totals): [unverified-quant] honored — quantitative core routed to the myth entry as `unresolved`, not asserted as a claim-note; primary Scholar/WoS pull still blocked (question-verify-linnainmaa-citation-count stays open)","Claim 4 (Griewank 2012 as earliest formal priority attribution): superseded by the 2026-07-06 direct read — the paper is a multiple-discovery account and does not attribute sole priority; corrected framing lives in myth-werbos-invented-backpropagation and the revisit note on claim-linnainmaa-priority-not-paternity"]
origin: "batch"
date_created: "2026-06-28T00:00:00.000Z"
provenance: "batch run 2026-06-28; web research via WebSearch + WebFetch"
tags: ["backpropagation","automatic-differentiation","Linnainmaa","citation-history","history-of-AI","uncited-work"]
primary_sources_consulted: [{"url":"https://yuxi.ml/essays/posts/backstory-of-backpropagation/","author":"Yuxi Liu","date":"2023-12-26","tier":3},{"url":"https://people.idsia.ch/~juergen/who-invented-backpropagation.html","author":"Jürgen Schmidhuber","date":"retrieved 2026-06-28 (updated periodically)","tier":3},{"url":"https://link.springer.com/article/10.1007/BF01931367","author":"Seppo Linnainmaa","date":"1976","tier":1,"note":"URL resolves but access-gated (Springer paywall); publication confirmed via multiple secondary sources"},{"url":"https://www.semanticscholar.org/paper/Who-Invented-the-Reverse-Mode-of-Differentiation-Griewank/8ff0c546aff84566635f0a9a2e01feb3d6588c1c","author":"Andreas Griewank","date":"2012","tier":1,"note":"Semantic Scholar record confirmed; full text at emis PDF was unreachable during this run"}]
access_failures: ["ACM DL (doi/10.1007/BF01931367) → 403 Forbidden","ResearchGate Griewank PDFs → 403 Forbidden","Semantic Scholar API → 429 Too Many Requests","emis.icm.edu.pl Griewank PDF → connection refused"]
---


**Topic question:** Does the citation record support the claim that Linnainmaa's backpropagation work was *essentially* uncited before the 2010s?

**Short answer the claims below support:** Partially true, with an important split. The 1970 Finnish thesis was indeed essentially uncited in any community before the 2010s. The 1976 English BIT paper achieved modest citation traction in the [[claim-linnainmaa-field-numerical-analysis|automatic differentiation]] community before 2000, but was not cited by neural network researchers. The [[backpropagation-gap]] is real but must be stated precisely: it is total for the thesis and community-specific for the 1976 paper.

---

## Claim: Linnainmaa's 1970 MSc thesis attracted essentially no citations before the 2010s

**Claim type:** Historical (uncontested biographical) with quantitative component (near-zero citations before 2010).

The thesis — titled *"Algoritmin kumulatiivinen pyöristysvirhe yksittäisten pyöristysvirheiden Taylor-kehitelmänä"* (University of Helsinki, 1970) — was written in Finnish and was never formally published as a journal article. It was therefore inaccessible to non-Finnish readers and absent from standard bibliographic databases. Per [[claim-linnainmaa-thesis-identity]], these are the same physical work referenced as "Linnainmaa 1970" and "Linnainmaa 1976" in the secondary literature.

Yuxi Liu, in a detailed bibliographic essay (December 2023), states: *"his thesis were basically never cited before the 2010s"* and characterises it as *"one of those papers that people cite for ritual completion only."* Liu's framing of [[claim-linnainmaa-priority-not-paternity]] captures the result: *"He has priority but no paternity."*

**Sourcing floor check:** The historical claim (what was cited, when) rests at Tier 3. Acceptable for uncontested historical claims. **However**, the implicit quantitative claim — that citations before 2010 were at or near zero — requires Tier 1–2. Primary citation-database data (Google Scholar, Web of Science, Semantic Scholar year-by-year counts) was *not accessible during this run* due to authentication walls and rate limits. **Flag: [unverified-quant — needs primary]** on the near-zero citation count before 2010.

| 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 | "his thesis were basically never cited before the 2010s" |
| exact_quote_2 | "one of those papers that people cite for ritual completion only" |
| exact_quote_3 | "He has priority but no paternity" |

---

## Claim: The 1976 BIT paper received some autodiff-community citations before 2000, but was ignored by neural network researchers

**Claim type:** Historical with quantitative component (some / non-negligible citations in one community, zero in another).

Linnainmaa's English-language journal publication — *"Taylor expansion of the accumulated rounding error,"* BIT Numerical Mathematics 16(2): 146–160, 1976 (DOI: 10.1007/BF01931367) — is the work recorded in standard databases. Yuxi Liu, reviewing "all his English papers during the 1970s," found *"only ([Linnainmaa 1976]) has been cited non-negligibly before 2000,"* while immediately hedging: *"may have had some impact on automatic differentiation, but I cannot tell by how much."*

Secondary sources consistently confirm that early reverse-mode AD papers — Speelpenning (1980), Griewank & Corliss (1991 edited volume), Berz, Bischof, Corliss & Griewank (1996 edited volume) — cited the 1976 BIT paper within the automatic differentiation community. However, the Rumelhart–Hinton–Williams 1986 *Nature* paper, the work that brought [[claim-linnainmaa-reverse-mode-single-pass|backpropagation]] to wide attention in neural networks, did not cite Linnainmaa (see Claim 3).

A search-engine snippet from the ACM Digital Library characterised the paper's *total lifetime citation count* as 34. This figure could not be verified by direct database access during this run. **Flag: [unverified-quant — needs primary]** on both (a) the specific "34 total citations" figure and (b) the pre-2000 citation count in the autodiff community.

| 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 | "only ([Linnainmaa 1976]) has been cited non-negligibly before 2000" |
| exact_quote_2 | "may have had some impact on automatic differentiation, but I cannot tell by how much" |
| secondary_url | https://link.springer.com/article/10.1007/BF01931367 |
| secondary_tier | 1 (publication record confirmed; full citation list not accessed) |
| unverified_figure | "34 total citations" (ACM DL snippet, could not verify directly) |

---

## Claim: Rumelhart, Hinton & Williams (1986) — the paper that popularised backpropagation for neural networks — did not cite Linnainmaa

**Claim type:** Historical, uncontested.

The 1986 *Nature* paper "Learning representations by back-propagating errors" (DOI: 10.1038/323533a0) is the work that placed backpropagation on the map for the neural-network community. Multiple independent sources — Yuxi Liu (2023), Schmidhuber (ongoing), and multiple historical surveys — state or imply that this paper contained no citation to [[claim-linnainmaa-rounding-error-problem|Linnainmaa's prior work]]. Schmidhuber characterises Rumelhart as having reinvented the method independently: *"he didn't cite previous work because they were so obscure."* (Source: Yuxi Liu essay paraphrasing Rumelhart's own retrospective statements.)

The practical consequence: the enormous downstream citation tail of the 1986 paper — which became one of the most-cited papers in the history of machine learning — pointed back to Rumelhart et al. as originators rather than to Linnainmaa. This is why the thesis has "priority but no paternity."

This is a historical claim with no credible dissent. Tier 3 sourcing is acceptable here.

| 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 | "he didn't cite previous work because they were so obscure" (Rumelhart, paraphrased via Liu) |
| corroborating_url | https://people.idsia.ch/~juergen/who-invented-backpropagation.html |
| corroborating_tier | 3 |
| corroborating_quote | "It took 4 decades until the backpropagation method of 1970 got widely accepted as a training method for deep NNs" |

---

## Claim: Griewank (2012) "Who Invented the Reverse Mode of Differentiation?" appears to be the earliest sustained scholarly effort to formally attribute priority to Linnainmaa in the peer-reviewed literature

**Claim type:** Historical, partially contested (Schmidhuber makes similar claims from roughly the same era).

Andreas Griewank published a retrospective in *Documenta Mathematica*, Extra Volume ISMP (2012), titled "Who Invented the Reverse Mode of Differentiation?" This paper is indexed on Semantic Scholar and explicitly credits Seppo Linnainmaa with the invention of reverse-mode automatic differentiation. Multiple secondary sources describe Griewank 2012 as the key scholarly effort to document Linnainmaa's priority.

This paper's existence is itself evidence that the historical record was not settled until ~2012: a major autodiff researcher (Griewank had been central to the field since the late 1980s) felt it necessary to write a formal "who invented this?" paper forty years after the fact.

Note: Schmidhuber's active campaign to credit Linnainmaa appears roughly contemporaneous (accelerating after ~2012–2015, with arXiv papers appearing from 2019 onwards). Neither Griewank nor Schmidhuber's efforts are the same as widespread *citation* of Linnainmaa — they are efforts to retroactively establish the record.

Full text of Griewank 2012 was not accessed during this run (EMIS server connection refused). The claim rests on Semantic Scholar metadata and multiple secondary descriptions.

| Field | Value |
|---|---|
| source_url | https://www.semanticscholar.org/paper/Who-Invented-the-Reverse-Mode-of-Differentiation-Griewank/8ff0c546aff84566635f0a9a2e01feb3d6588c1c |
| source_author | Andreas Griewank |
| source_date | 2012 |
| source_tier | 1 (peer-reviewed, Documenta Mathematica) — but full text not accessed; flag as [unverified-mechanism — needs primary] on the specifics of what the paper argues |
| publication | Documenta Mathematica, Extra Volume ISMP, 2012 |
| corroborating_url | https://people.idsia.ch/~juergen/who-invented-backpropagation.html |
| corroborating_tier | 3 |

---

## Further leads

- **Year-by-year citation data from Google Scholar or Web of Science** for DOI 10.1007/BF01931367 — not accessible this run (auth walls, rate limits); this is the single most important gap for promoting the quant claims above to verified status.
- **Griewank 2012 full text** (try mirror at https://www.math.uni-bielefeld.de/documenta/vol-ismp/ or through library access) — would supply Tier 1 exact quotes on Linnainmaa priority and the autodiff reception.
- **Speelpenning (1980)** "Compiling fast partial derivatives of functions given by algorithms" — reportedly the first autodiff implementation paper to cite Linnainmaa; fetching this would confirm the pre-2000 autodiff citation claim.
- **Schmidhuber arXiv:2005.05744** — contains a timeline of backpropagation attribution; HTML version at ar5iv returned a redirect loop this run.
- **Werbos (1974/1981)** thesis and follow-up: did Werbos cite Linnainmaa? Search results say he did study Linnainmaa but this needs verification from the primary text.
- **Baydin et al. (2018)** "Automatic Differentiation in Machine Learning: a Survey" — JMLR, Tier 1; HTML version at ar5iv reportedly mentions backpropagation as a "colorful history of reinventions" but the portion about Linnainmaa specifically was not in the excerpt retrieved.

> [!note] Seek's commentary:
> The "essentially uncited" claim is true for the 1970 thesis in any community, and true for the 1976 paper specifically *in the neural network community*. But the framing is imprecise if applied globally: the 1976 BIT paper had a real (if modest) life in the numerical analysis / autodiff world from the late 1970s onward. The important historical point is that the *neural network* research program — the one that became modern deep learning — rediscovered backpropagation entirely independently and only began formally crediting Linnainmaa decades later. The [[backpropagation-gap]] is real, but its precision matters: it's a gap between *communities* as much as between *time periods*.
>
> Quantitative claims here are all flagged [unverified-quant — needs primary]. Promoting these to verified claim-notes requires running the same DOI through Web of Science or Google Scholar and capturing actual year-by-year citation counts. Until then the qualitative pattern (thesis ~ uncited; 1976 paper ~ modest autodiff presence, zero neural-network presence) is well-supported at Tier 3 from multiple consistent secondary sources.