---
title: "The \"Wengert list\" tape is named for the inventor of the other mode — Wengert 1964 published forward accumulation; automatic reverse mode arrived with Speelpenning 1980"
type: "claim"
status: "budding"
audit_status: "verified-verbatim (both Tier-1 sources read directly as PDFs at capture level, 2026-07-06; Griewank 2012 checked from queen cache 2026-07-07 — it never mentions Wengert, so the naming point rests on Baydin/Innes, not on the reverse-mode historian)"
source_url: "https://jmlr.org/papers/volume18/17-468/17-468.pdf"
source_author: "Baydin, Pearlmutter, Radul & Siskind, 'Automatic Differentiation in Machine Learning: a Survey' (JMLR 18, 2018)"
source_date: 2018
source_tier: 1
source_quote: "Forward mode AD as a general method for evaluating partial derivatives was essentially discovered by Wengert (1964)."
provenance: "Promotion from 10-inbox/raw/2026-07-06-what-is-the-wengert-list-tape-and-how-it-underlies-autograd-in-pytorch-jax-tensorflow.md, 2026-07-07, queen cycle 19"
origin: "batch"
derived_from: "10-inbox/raw/2026-07-06-what-is-the-wengert-list-tape-and-how-it-underlies-autograd-in-pytorch-jax-tensorflow.md"
date_created: "2026-07-07T00:00:00.000Z"
tags: ["wengert-list","automatic-differentiation","forward-mode","reverse-mode","history-of-computation","naming"]
audits: ["2026-07-07 unknown-model"]
---


A Wengert list is the evaluation trace: the recorded sequence of elementary
operations a composite function decomposes into — "also called a Wengert
list (Wengert, 1964)" (Baydin et al., read directly); "often referred to as
a Wengert list, tape or graph" (Innes 2020, MLSys, read directly), the
substrate "that all reverse-mode ADs use at a minimum."

The naming irony, load-bearing and Tier-1-grounded: **Wengert's 1964 CACM
paper (7(8):463–464) described forward-mode differentiation.** Baydin et
al.: "Forward mode AD as a general method for evaluating partial derivatives
was essentially discovered by Wengert (1964)." The automatic reverse mode —
the mode whose implementations actually carry a "tape" — they credit
separately: "Speelpenning (1980) subsequently introduced reverse mode AD as
we know it, in the sense that he gave the first implementation that was
actually automatic." Innes's opening sentence draws the same split:
"forward (Wengert, 1964) and later reverse (Speelpenning, 1980) modes."

So the reverse-mode tape wears the forward-mode inventor's name — a
mislabeling gentler than, but structurally akin to, the attribution drift
tracked across [[moc-backpropagation-origins]]. Checked and worth recording:
Griewank's 2012 reverse-mode history (queen-cached full text) never mentions
Wengert at all, so this naming observation cannot be pushed onto the
lineage's principal historian; it rests on the two surveys above.

The mechanism the tape implements is Linnainmaa's reverse accumulation
([[claim-linnainmaa-1976-algorithm-t-reverse-sweep]],
[[claim-linnainmaa-reverse-mode-single-pass]]); the canonical first
implementation is Speelpenning's
([[claim-speelpenning-1980-does-not-cite-linnainmaa]]); how today's
frameworks reify it: [[claim-autograd-three-reifications-of-the-tape]].

> [!note] Seek's commentary:
> This is attribution drift in its purest, motive-free form — which is exactly what makes it instructive. The reverse-mode tape is named for Wengert, who invented *forward* mode; the mode that actually uses a tape came later (Speelpenning 1980). There's no ego here, no credit worth fighting over, nothing to gain from misnaming a data structure — and it drifted anyway. Which suggests the mechanism behind even the high-stakes misattributions the vault tracks might be this banal: names stick by momentum, not merit. "Wengert list" got attached early and held, correctness be damned. If a label drifts when nobody benefits, greed and ego aren't required to explain the ones that drift when someone does — linguistic inertia is enough on its own.
> — Seek