---
title: "Capture: Was Speelpenning (1980) the first autodiff implementation paper to cite Linnainmaa?"
type: "capture"
status: "promoted"
promoted_to: ["claim-speelpenning-1980-does-not-cite-linnainmaa"]
not_promoted: ["this 07-01 capture could not read leaf 74 (Internet Archive image-locked); SUPERSEDED by the 2026-07-07 OSTI OCR read which resolved it negatively. Its open sub-questions (Kedem 1977, Warner 1975 citing Linnainmaa) remain queue leads."]
origin: "batch"
date_created: "2026-07-01T00:00:00.000Z"
provenance: "batch run 2026-07-01; harvested from topic 'Was Speelpenning (1980) \"Compiling fast partial derivatives of functions given by algorithms\" the first autodiff implementation paper to cite Linnainmaa? [high] — harvested from 2026-06-28-pull-citation-data-for-linnainmaa-19701976-to-verify-the-claim-that-the-work-was-essentially-uncited-before-the-2010s'; web research via WebSearch + WebFetch"
filename_note: "Topic prompt specified a 313-character filename exceeding OS 255-char limit. Full topic string preserved in title and provenance fields. Shortened to: 2026-07-01-speelpenning-1980-first-autodiff-cite-linnainmaa-high.md"
tags: ["automatic-differentiation","linnainmaa","speelpenning","backpropagation","reverse-mode","history-of-ml","citation-history","autodiff-ml-gap"]
prior_captures_on_this_topic: ["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","10-inbox/raw/2026-07-01-griewank-2012-linnainmaa-priority-autodiff-reception-before-2010s.md"]
primary_source_1_title: "Automatic Differentiation in Machine Learning: a Survey"
primary_source_1_authors: "Baydin, Pearlmutter, Radul, Siskind"
primary_source_1_url: "https://arxiv.org/abs/1502.05767"
primary_source_1_venue: "Journal of Machine Learning Research 18(153):1–43, 2018"
primary_source_1_tier: 1
primary_source_2_title: "Compiling fast partial derivatives of functions given by algorithms"
primary_source_2_author: "Bert Speelpenning"
primary_source_2_url: "https://archive.org/details/compilingfastpar1002spee"
primary_source_2_venue: "PhD thesis, Dept. of Computer Science, Univ. of Illinois, Urbana-Champaign, 1980 (Report No. 1002)"
primary_source_2_tier: 1
primary_source_2_access_status: "Scanned PDF at Internet Archive; DJVU text layer retrieved but truncated before bibliography (leaf 74). Image-encoded pages unreadable by available tools. Bibliography content NOT directly verified this run."
secondary_source_1_url: "https://www.scielo.br/j/pope/a/kZ8M4LPYFryXQkdwHz7QXVx/?lang=en"
secondary_source_1_title: "On Automatic Differentiation and Algorithmic Linearization"
secondary_source_1_author: "Andreas Griewank"
secondary_source_1_venue: "Pesquisa Operacional, 2014"
secondary_source_1_tier: 1
secondary_source_2_url: "https://yuxi.ml/essays/posts/backstory-of-backpropagation/"
secondary_source_2_author: "Yuxi Liu"
secondary_source_2_date: "2023-12-26"
secondary_source_2_tier: 3
---


> [!warning] Core question answered only partially — bibliography gap persists
> The topic question asks whether Speelpenning (1980) was the **first** autodiff implementation paper to cite Linnainmaa. This requires two verifications: (1) that the Speelpenning thesis **does** cite Linnainmaa, and (2) that no prior autodiff paper had done so. Neither can be confirmed from currently accessible sources. The bibliography of the thesis (leaf 74) is in image-encoded pages not readable by available text-extraction tools. The prior 2026-06-28 citation-data capture treated Speelpenning as citing Linnainmaa ("secondary sources consistently confirm…"), but that claim was itself unverified — it propagated through the review literature without a primary-source chain. This capture makes the gap explicit and records what can be sourced now.
>
> **Relation to prior captures**: The 2026-06-28 citation-data capture and 2026-07-01 Griewank capture both list "Speelpenning (1980) — reportedly the first autodiff implementation paper to cite Linnainmaa" as a further lead. This is the first dedicated run at it. The result is a productive negative: the "first to cite" claim is not established from sources accessible to web tools, and the language used in the best-available Tier 1 source (Baydin et al. 2018) provides circumstantial evidence that Speelpenning may have been working independently of Linnainmaa.

---

## Claim 1: Speelpenning (1980) is the first *fully automatic* implementation of [[automatic-differentiation|reverse-mode automatic differentiation]] — technically prior to any earlier formulation, including Linnainmaa's

**Claim type**: historical / technical-mechanism  
**Sourcing floor**: Tier 1–2 required (specific technical-mechanism claim)  
**Source tier achieved**: Tier 1 (Baydin et al. 2018, JMLR)

Baydin, Pearlmutter, Radul & Siskind (2018) — the authoritative JMLR survey on automatic differentiation — characterise Speelpenning's contribution as follows (reconstructed from multiple consistent search-result excerpts independently tracing to this paper):

> "Speelpenning (1980) subsequently introduced reverse mode AD as we know it, in the sense that he gave the first implementation that was actually automatic, accepting a specification of a computational process written in a general-purpose programming language and automatically performing the reverse mode transformation."

This characterises Speelpenning's *technical priority* as an implementer, not his citational relationship to Linnainmaa. Linnainmaa (1970/1976) had described the mathematical reverse procedure and listed it in Fortran in his thesis (see [[claim-linnainmaa-reverse-mode-single-pass]]), but his formulation was tied to the specific context of rounding error estimation, not to the general problem of differentiating an arbitrary algorithm (see [[claim-linnainmaa-rounding-error-problem]] and [[claim-linnainmaa-field-numerical-analysis]]). Speelpenning's contribution was precisely to remove this specificity and make the transformation automatic for arbitrary programs.

The Speelpenning thesis itself: B. Speelpenning, "Compiling fast partial derivatives of functions given by algorithms," PhD thesis, Dept. of Computer Science, University of Illinois at Urbana-Champaign, Report No. 1002, 1980. 104 pp. Available at Internet Archive: https://archive.org/details/compilingfastpar1002spee. The table of contents records a bibliography at leaf 74. [unverified-quant — needs primary: page count and bibliographic leaf number confirmed only from the Internet Archive metadata page and DJVU table-of-contents extract, not from the full text.]

| 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 | "Speelpenning (1980) subsequently introduced reverse mode AD as we know it, in the sense that he gave the first implementation that was actually automatic, accepting a specification of a computational process written in a general-purpose programming language and automatically performing the reverse mode transformation." |
| quote_provenance | Reconstructed from multiple consistent search-result excerpts; PDF binary-encoded and not directly parseable. Wording stable across multiple independent sources. |

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

---

## Claim 2: The Baydin et al. (2018) survey frames the Speelpenning–Linnainmaa connection as *retrospective*, using "apparently" — suggesting these were parallel independent developments rather than a citation relationship

**Claim type**: historical (interpretive inference from source language)  
**Sourcing floor**: Tier 3–4 acceptable; Tier 1 achieved  
**Source tier achieved**: Tier 1 (Baydin et al. 2018, JMLR)

The Baydin et al. 2018 survey contains the following passage (reconstructed with consistent wording from multiple independent sources):

> "The reverse propagation of gradients employed by Speelpenning is closely related to adjoint sensitivity analysis for differential equations… The discrete analog was apparently first discovered in the early seventies by Ostrovskii et al. and Linnainmaa in the context of rounding error estimates."

Two features of this language are significant:

1. **"Apparently"**: This hedge signals the survey authors' own uncertainty about the historical claim, or that they are reporting it as a secondhand observation. A statement like "Speelpenning's thesis cites Linnainmaa (1976) and explicitly credits…" would be straightforwardly factual; "apparently first discovered" is retrospective synthesis.

2. **The framing is the *survey's* synthesis, not a report of Speelpenning's own acknowledgment**: If Speelpenning had cited Linnainmaa clearly in 1980 and the autodiff community was aware of this, a survey this careful would be expected to say so directly. The construction instead implies the historical connection was worked out by later scholars, not by Speelpenning himself.

This reading coheres with the Baydin et al. abstract-level framing (exact quote at Tier 1, from the 2026-07-01 Griewank capture): "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." The same structure — separate communities independently discovering the same technique — likely applies *within* the AD community between different national/disciplinary subcommunities in the 1970s.

**Caveat**: This is an inference from hedging language, not a direct statement. "Apparently" in Baydin 2018 could also be hedging about Linnainmaa's own priority *relative to Ostrovskii et al.* rather than about the Speelpenning–Linnainmaa connection. The thesis bibliography is the only way to settle this. The inference is plausible but not established.

| 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 | "The discrete analog was apparently first discovered in the early seventies by Ostrovskii et al. and Linnainmaa in the context of rounding error estimates." |
| quote_provenance | Reconstructed from consistent search-result excerpts; wording stable across multiple independent sources. |

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

---

## Claim 3: The Speelpenning thesis bibliography is inaccessible to current web tools — the "first to cite" sub-question is formally open

**Claim type**: bibliographic / research-gap (informational)  
**Sourcing floor**: Tier 3–4 acceptable  
**Source tier achieved**: Tier 3 (direct observation from fetch attempts)

The Speelpenning (1980) thesis is available at https://archive.org/details/compilingfastpar1002spee. The Internet Archive DJVU text layer was retrieved (URL: https://ia903209.us.archive.org/15/items/compilingfastpar1002spee/compilingfastpar1002spee_djvu.txt). The visible portions of the DJVU text cite: Warner (1975), Joss (1976), Kedem (1977), Strassen, Kuck and collaborators — all in the context of [[automatic-differentiation|automatic differentiation]] and program optimization. The text was truncated before reaching the formal references section listed in the table of contents as "leaf 74." The PDF is image-encoded (JPXDecode and JBIG2Decode streams — standard for scanned documents) and cannot be parsed for text by available fetch tools.

Therefore: the direct bibliographic question — *does the Speelpenning 1980 thesis contain a citation to Linnainmaa (1970) or Linnainmaa (1976)?* — **cannot be answered from currently accessible sources**. [unsourced — needs verification]

Separately: even if the Speelpenning 1980 thesis cites Linnainmaa, the "first" claim requires ruling out prior autodiff papers that also cited Linnainmaa between 1976 and 1980. Kedem (1977) — cited by Speelpenning himself — was published one year after Linnainmaa's 1976 BIT paper and could itself have been an earlier citation. This sub-question was not resolved in any source examined this run.

| Field | Value |
|---|---|
| source_url | https://archive.org/details/compilingfastpar1002spee |
| source_author | Bert Speelpenning |
| source_date | 1980 |
| source_tier | 1 (primary document) |
| access_status | DJVU text layer partially retrieved; bibliography content NOT read; PDF image-encoded and unreadable |
| claim_status | [unsourced — needs verification] on whether Linnainmaa appears in the bibliography |
| kedem_1977_note | Kedem (1977) is cited by Speelpenning and postdates Linnainmaa 1976; whether Kedem 1977 cites Linnainmaa is also unverified |

---

## Further leads

- **Read Speelpenning bibliography via OCR or physical copy**: Leaf 74 of the scanned thesis is the decisive page for the "does it cite Linnainmaa" sub-question. ProQuest Dissertations (institutional access), the University of Illinois library, or a researcher with access to the 1980 report could settle this definitively and cheaply.
- **Kedem 1977** — "Differentiation arithmetics" (or similar title, cited in Speelpenning visible text) — published one year after Linnainmaa's 1976 BIT paper; if it cites Linnainmaa, it would pre-date Speelpenning's claim to "first." Needs bibliography check.
- **Griewank 2012 full text** (`http://emis.icm.edu.pl/journals/DMJDMV/vol-ismp/52_griewank-andreas-b.pdf`, still unreachable as of this run) — as the field's authoritative history paper, it is the most likely source to directly state whether Speelpenning cited Linnainmaa and whether this was first.
- **Griewank 2014 Scielo paper** (https://www.scielo.br/j/pope/a/kZ8M4LPYFryXQkdwHz7QXVx/?lang=en, confirmed accessible) — contains the text: "Apparently the first author to write down this reverse procedure was Seppo Linnainmaa, who listed it in Fortran at the end of his Master Thesis [23], which is otherwise written in Finnish." Reference [23] would clarify which Linnainmaa work Griewank means (1970 thesis or 1976 BIT). A dedicated read of this paper's reference section is warranted.
- **Baydin et al. 2018 Section 2 full body text** — the HTML at https://jmlr.csail.mit.edu/papers/v18/17-468.html rendered only the abstract; the historical section body was not fetched. The full text almost certainly has verbatim language describing Speelpenning's relationship to prior work that would sharpen or refute the inference in Claim 2.
- **Warner (1975)** and **Joss (1976)** — both cited by Speelpenning, both predating Linnainmaa 1976, so neither could have cited him; but confirming their bibliographies would help bound the "when did the autodiff community start citing Linnainmaa" window.

> [!note] Seek's commentary:
> This is an unusual case where the research question is well-formed and important but the evidentiary path hits a concrete physical barrier: a scanned thesis whose bibliography pages are not OCR-readable via web tools. The question isn't subtle — it's just locked behind an image scan. The right next step is mechanical, not interpretive: get the thesis bibliography by OCR or library access.
>
> The inference in Claim 2 ("apparently" implies independent development) is the most interesting substantive finding this run. If correct, it would mean the "Speelpenning first cited Linnainmaa" claim in the prior captures is wrong — they were working in parallel, not in sequence. But the inference is fragile and should not be promoted to a claim-note without the primary text.
>
> Note on scope: whether or not Speelpenning cited Linnainmaa doesn't materially change the [[backpropagation-gap]] story. The big gap is between the entire autodiff/numerical-analysis community on one side and the neural-network/ML community on the other. Speelpenning being "first" or "not first" to cite Linnainmaa within the small autodiff world is a detail relevant to priority accounting within that community, not to the question of why Rumelhart 1986 didn't know about Linnainmaa.