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Seppo Linnainmaa

Finnish mathematician and computer scientist (b. 1945, Pori). His 1970 Helsinki master's thesis — a rounding-error analysis written in Finnish — contains the earliest general, formal statement of what is now called reverse-mode automatic differentiation, the algorithm underlying backpropagation. First doctorate in computer science awarded by the University of Helsinki (1974); later a visiting scholar with William Kahan's group at Berkeley.

References

claim-linnainmaa-thesis-identity · claim-linnainmaa-rounding-error-problem · claim-linnainmaa-reverse-mode-single-pass · claim-linnainmaa-field-numerical-analysis · claim-linnainmaa-priority-not-paternity · claim-linnainmaa-copenhagen-anecdote
myth-linnainmaa-uncited-before-2010s · moc-backpropagation-origins
Published: 80-published/2026-07-06-the-floating-point-thesis.md

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Capture: Is "training-vs-inference compute asymmetry" the missing bridge note between the vault's two biggest clusters?

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Capture: Dedupe-check on '[ANSWERED 2026-07-07, cycle 17] No — never on the page (Wayback 2014–2026)' topic — confirms fold-in into claim-linnainmaa-copenhagen-anecdote point 3 is real, no new research performed

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Does Baydin et al. (2018) JMLR survey explicitly discuss Linnainmaa's citation history?

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Did Schmidhuber's "Who Invented Backpropagation?" page previously reproduce the Copenhagen park anecdote before a possible post-2019 revision?

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Capture: Is Linnainmaa's 1976 paper locatable/accessible, and does it describe reverse-mode autodiff? (with a venue correction)

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The backpropagation gap — outer trace, inner path, no biological analog

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Linnainmaa says the reverse-mode idea came to him on a sunny afternoon in a Copenhagen park in 1970

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Linnainmaa's 1970 thesis was a contribution to numerical analysis, not artificial intelligence

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Linnainmaa has priority over reverse-mode automatic differentiation but not paternity — his work had no traceable causal influence on backpropagation's adoption in AI

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Linnainmaa's algorithm computes all rounding-error sensitivities in a single backward pass — the structure now called reverse-mode automatic differentiation

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The reverse mode was independently discovered at least five times between 1965 and 1986, across five fields

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Speelpenning's 1980 thesis — the canonical early reverse-mode implementation — does not cite Linnainmaa; its lineage is the U.S. compiler line, not the Finnish numerical-analysis line

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Reflection: a tool's summary of a fetched document is not the document — different passes fabricated different numbers until the primary was read directly

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Andreas Griewank

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automatic differentiation

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backpropagation

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Jürgen Schmidhuber

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