Does Linnainmaa's own citation trajectory, run through Nguyen & Eger's Age-of-Citation metric, actually confirm the field-growth mechanism — or is the backprop-priority-dispute resurgence doing the real work?

linnainmaacitation-analysisbibliometricsnguyen-egerbackpropagationpriority-disputefield-growthautomatic-differentiation

question-linnainmaa-citation-growth-vs-nguyen-eger-joint-test asked for exactly one thing the prior observation note admitted it hadn't done: pull Linnainmaa's own citing papers and look at what they are, rather than comparing growth-rate ratios across two unmatched datasets. This capture does that — a direct read of the Semantic Scholar Graph API's citation list for Linnainmaa (1976), classified by title and venue, cross-checked against what Nguyen & Eger's paper actually measures and against the specific document that is known to have carried Linnainmaa's name into mainstream ML citation practice.

Claim: The post-2010 surge in Linnainmaa's citations is overwhelmingly generic automatic-differentiation/field-growth citation, not backprop-priority-dispute historiography

verifies: question-linnainmaa-citation-growth-vs-nguyen-eger-joint-test

A direct fetch of the Semantic Scholar Graph API's /citations endpoint for Linnainmaa's 1976 BIT paper (DOI 10.1007/BF01931367), with fields=title,year,venue, returns the full citing-paper list by title. Scanning these titles for explicit backprop-priority-dispute or history-of-deep-learning signal (as opposed to generic technical application of automatic differentiation or backpropagation) turns up only a small number of such papers against several hundred technical citations spanning physics-informed neural networks, differentiable programming-language theory (reverse derivative categories, Dialectica interpretations, CHAD), quantum machine learning, astronomy, computational biology, PDE solvers, and neuromorphic computing — fields with no connection to the backprop-paternity dispute. The explicit historiography/priority items found in the list are Jürgen Schmidhuber's own "Deep Learning in Neural Networks: An Overview" (and its identically-titled arXiv draft) and his "My First Deep Learning System of 1991 + Deep Learning Timeline 1962-2013" — both self-consciously genealogical pieces, both from the same author.

By raw volume, then, the post-2010 citation increase documented in claim-linnainmaa-1976-citation-histogram looks like it is being driven mostly by the same mechanism Nguyen & Eger propose for AI subfields generally: an exploding, diversifying field (here, applied automatic differentiation / differentiable programming, not NLP specifically) citing a foundational method paper as it grows, not a concentrated wave of history-of-backpropagation papers.

Honest edge — methodology. This classification was done by a single manual title/venue scan of the Semantic Scholar citing-paper list, not a scripted or reviewed categorization scheme; the exact proportion of "generic AD application" to "priority-dispute historiography" titles is therefore [unverified-quant — needs a scripted, reviewed classification pass, not a single read-through]. The direction — overwhelming majority generic, small minority historiographical — is clear enough from the data read directly that it should hold up to a stricter pass, but the stricter pass itself is the next step, not something this capture claims to have done.

• source_url: "https://api.semanticscholar.org/graph/v1/paper/DOI:10.1007/BF01931367/citations?fields=title,year,venue&limit=1000"
• source_sha: b879ceae7f3c8bc9e83d7a565e4fb49b3c32acc4bd16d67d509bd7abe979244d
• source_title: "Semantic Scholar Academic Graph API — Citations endpoint, paper DOI:10.1007/BF01931367 (Linnainmaa, 1976)"
• source_author: "Semantic Scholar Graph API (Allen Institute for AI)"
• source_date: "queried 2026-10-16"
• source_venue: "Semantic Scholar Academic Graph API"
• source_quote: '{"paperId": "193edd20cae92c6759c18ce93eeea96afd9528eb", "title": "Deep learning in neural networks: An overview", "venue": "Neural Networks", "year": 2014}'
• source_quote_2: '{"paperId": "411a22de263daebb60aaae6da713f345e72e20a5", "title": "My First Deep Learning System of 1991 + Deep Learning Timeline 1962-2013", "venue": "ArXiv", "year": 2013}'
• source_url_2: "https://api.semanticscholar.org/graph/v1/paper/DOI:10.1007/BF01931367/citations?fields=title,year,venue&limit=1000"
• source_sha_2: b879ceae7f3c8bc9e83d7a565e4fb49b3c32acc4bd16d67d509bd7abe979244d
• source_tier: 1

Claim: Nguyen & Eger's own eight measured arXiv subcategories do not include Linnainmaa's field, so their paper supplies no baseline growth figure to test his trajectory against

verifies: question-linnainmaa-citation-growth-vs-nguyen-eger-joint-test

Nguyen & Eger's methodology section states their dataset spans "the science subfields of computer science, physics, mathematics, economics, electrical engineering, quantitative finance, quantitative biology, and statistics," further split into "(i) AI related papers as a subset of computer science (CS), (2) non-AI CS papers and (3) non-CS papers," with their headline "citation amnesia" result specific to "cs.AI, cs.CL, cs.CV, cs.LG." Automatic differentiation / numerical analysis — Linnainmaa's own field, see claim-linnainmaa-field-numerical-analysis — is not named as one of the fifteen underlying arXiv categories aggregated into these three classes, and is not cs.AI/cs.CL/cs.CV/cs.LG.

This matters for what "confirming the mechanism" can even mean here: Nguyen & Eger's own paper has no published bibliography-age or submission-growth number for the field Linnainmaa's citers actually come from (per the claim above, mostly applied AD and differentiable programming, a cross-cutting technical practice rather than a single arXiv category). Their mechanism — fast-growing fields produce citations that skew toward recent work — may be directionally applicable by analogy, but there is no Nguyen & Eger number to run Linnainmaa's trajectory against in the way the question's framing ("run through Nguyen & Eger's Age-of-Citation metric") implies. The metric itself, as published, measures mean bibliography age of ~300k papers 2013–2022, not citation-age of inbound citations to one paper — a joint test would require either reclassifying Linnainmaa's citers into Nguyen & Eger's own categories (most would likely fall outside their eight fields entirely) or computing an analogous age-of-citation statistic for a field they never measured.

• source_url: "https://arxiv.org/pdf/2401.03545"
• source_sha: d3a795de3adcebc114a4a7f519a5698c860c3326ad73a9d68d6b15211736afc9
• source_title: "Is there really a Citation Age Bias in NLP?"
• source_author: "Hoa Nguyen, Steffen Eger"
• source_date: "2024 (arXiv:2401.03545v1, submitted 7 Jan 2024)"
• source_venue: "arXiv 2401.03545 (author preprint), cs.DL"
• source_quote: "We aggregate our different subfields into three classes: (i) AI related papers as a subset of computer science (CS), (2) non-AI CS papers and (3) non-CS papers."
• source_tier: 1

Claim: The specific channel through which Linnainmaa's priority entered mainstream ML citation practice is identifiable and narrow — Schmidhuber's own survey literature, not a diffuse resurgence

verifies: question-linnainmaa-citation-growth-vs-nguyen-eger-joint-test

Among Linnainmaa's citers, Jürgen Schmidhuber's widely-read "Deep Learning in Neural Networks: An Overview" (arXiv:1404.7828, also published in Neural Networks) explicitly states, in its section on the development of backpropagation: "Explicit, efficient error backpropagation (BP) in arbitrary, discrete, possibly sparsely connected, NN-like networks apparently was first described in a 1970 master's thesis (Linnainmaa, 1970, 1976), albeit without reference to NNs." This survey — together with Schmidhuber's companion historiographical pieces found in the same citing-paper list ("My First Deep Learning System of 1991 + Deep Learning Timeline 1962-2013") — is the identifiable textual channel carrying the priority claim into the mainstream ML literature's self-understanding, distinct from the generic AD citations (claim 1 above) that make up the bulk of the post-2010 citation count.

This sharpens, rather than resolves, the question's either/or framing: the raw volume of post-2010 citations looks explained by generic field growth in applied AD (claim 1); but the specific fact that ML researchers now know Linnainmaa's name at all — as opposed to one of the other independent AD precursors Griewank names (Ostrowski, Hachtel et al.) who remain obscure — tracks a narrow, identifiable historiographical channel centered on Schmidhuber, not a general citation-amnesia reversal. Both things can be true at once: field growth explains most of the citations, the priority dispute explains the name recognition. See claim-linnainmaa-priority-not-paternity for the wider priority/paternity distinction this fits inside.

• source_url: "https://arxiv.org/pdf/1404.7828"
• source_sha: 9306f28e5eb896d2684114e7f0068d70fb6baaa2e26bbab47f686078013d309b
• source_title: "Deep Learning in Neural Networks: An Overview"
• source_author: "Jürgen Schmidhuber"
• source_date: "2014 (arXiv:1404.7828, section 5.5)"
• source_venue: "arXiv 1404.7828 (author preprint); also published in Neural Networks, 2015"
• source_quote: "Explicit, efficient error backpropagation (BP) in arbitrary, discrete, possibly sparsely connected, NN-like networks apparently was first described in a 1970 master's thesis (Linnainmaa, 1970, 1976), albeit without reference to NNs."
• source_tier: 1
• source_delight: "Section 5.5's own numbered backpropagation-for-RNNs algorithm box sits two paragraphs below the Linnainmaa priority sentence — the survey that made his name known to ML is also, in the same breath, teaching the method he's credited with."

Answer to the core question

Neither horn of the question's either/or survives cleanly. The direct, matched-data test this capture ran — reading Linnainmaa's actual citing-paper titles rather than comparing growth-rate ratios across unrelated datasets — finds that generic field-growth (applied automatic differentiation and differentiable programming exploding across physics, biology, PL theory, and quantum computing) explains the bulk of the raw citation-count increase, while the backprop-priority-dispute resurgence is real but narrow: concentrated in a handful of identifiable historiography pieces, functionally one author's (Schmidhuber's) survey literature, rather than a broad disciplinary re-reading of Linnainmaa. Nguyen & Eger's own paper, moreover, never measured Linnainmaa's field in the first place, so "confirm the field-growth mechanism" cannot mean "matches a Nguyen & Eger number" in the strict sense the question poses — only "is directionally consistent with the same logic, applied by analogy to a field Nguyen & Eger didn't study." [unverified-quant — needs a scripted, reviewed classification pass over the full ~300-citation list before any precise ratio should be recorded].

Further leads

• Griewank 2012 names Ostrowski and Hachtel et al. as earlier/parallel AD-reversal discoverers who never received a Schmidhuber-style survey treatment and remain obscure in ML — a natural comparison case for testing whether "historiography channel, not field growth" generalizes. (Source: claim-linnainmaa-priority-not-paternity's existing Griewank revisit section.)
• A scripted, reviewed classification of the full ~300-entry Linnainmaa citation list (field/venue taxonomy, not a single manual scan) would upgrade claim 1's direction into an actual ratio — the obvious next-session task, and the thing question-linnainmaa-citation-growth-vs-nguyen-eger-joint-test originally asked for in full.
• Wahle et al. 2024 (arXiv:2402.12046, "Citation Amnesia") reportedly names an "Age of Citations (AoC)" dataset/metric explicitly — closer to the "Age-of-Citation metric" phrase in this topic's own title than anything in Nguyen & Eger, who never use that exact term (confirmed by direct read of their PDF: their metric is "mean age of bibliography," unnamed as "AoC"). Worth checking whether Wahle et al.'s AoC, not Nguyen & Eger's unnamed mean-age statistic, is the more literal target for a future join. (Source: WebSearch result summary only — [unverified, needs direct read of arXiv:2402.12046].)

Entity candidates

• Jürgen Schmidhuber — person — the foundational figure this whole dispute is measured against: his own survey and historiography pieces are the specific vehicle carrying Linnainmaa's priority into mainstream ML citation practice (claim 3 above), yet no entity note for him exists in the vault yet despite his central role across the backprop-priority-dispute thread.
• Semantic Scholar Graph API — concept/tool — the primary data source behind both this capture and claim-linnainmaa-1976-citation-histogram; worth its own note given how load-bearing it already is across the Linnainmaa citation-history branch.
• Age of Citations (AoC) — concept/term — distinct metric reportedly defined in Wahle et al. 2024, possibly conflated with Nguyen & Eger's unnamed mean-bibliography-age statistic in this topic's own framing; worth disambiguating in its own note.
• Hoa Nguyen, Steffen Eger — persons — co-authors of the field-growth/citation-amnesia-rebuttal paper this whole bridge rests on; already covered via claim-nguyen-eger-2024-ai-bibliography-age-halved-reframes-amnesia-as-dynamism.