Claim LD09-SL-C31 (v1.0)

In laboratory experiments, replacing real training data with each generation’s synthetic data tends towards model collapse, but accumulating synthetic data alongside the original real data avoids it; for a sequence of linear models, the authors prove that test error then has a finite upper bound however many generations pass.

Provenance and status

Claim type: ESTIMATE (as printed: “ESTIMATE”)
Publication status: ELIGIBLE (PREPRINT) (as printed: “ELIGIBLE WITH PREPRINT QUALIFIER”)
Verification state: CONTENT_VERIFIED_PRIMARY (PREPRINT) (as printed: “CONTENT VERIFIED PREPRINT”; verified by: UNKNOWN)
Does not license: Anything about the flow of new human-written data, which the setup holds fixed
Source (field 6, as printed): Gerstgrasser, Schaeffer, Dey, Rafailov, Sleight, Hughes et al., “Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data,” arXiv:2404.01413, 2024
Source type (field 7): PREPRINT (as printed: “Preprint”)
Institutional position: Academic, Stanford University-led, with co-authors at non-academic organisations (Constellation, Sequoia Capital)
Maturity (claim evidence / publication maturity): CONTESTED (as printed: “CONTESTED”)
Recorded date: 2026-10-15
Currentness / correction: This is the current version. No correction or concern relation is recorded on its Sources.

Version

Pinned version v1.0 (entry LD09-SL-C31--v1.0) — this page never floats to newer evidence.

This pinned version is also the current version.

Versions:v1.0 · current

Pinned Sources (field 6, version-specific)

“Gerstgrasser, Schaeffer, Dey, Rafailov, Sleight, Hughes et al., “Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data,” arXiv:2404.01413, 2024” → SRC-SL-GERSTGRASSER-ET-AL-ARXIV-2404-01413--v1.0 — Gerstgrasser, Schaeffer, Dey, Rafailov, Sleight, Hughes et al., “Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data,” arXiv:2404.01413, 2024; class PREPRINT (explicit public provenance pin)

All 25 canonical Claim fields (raw values and normalized values)

#	Canonical field	Canonical value (verbatim)	Normalized (Claim Value Vocabulary v1.0.2)
1	CLAIM ID	LD09-SL-C31	—
2	PUBLIC-FACING CLAIM	In laboratory experiments, replacing real training data with each generation’s synthetic data tends towards model collapse, but accumulating synthetic data alongside the original real data avoids it; for a sequence of linear models, the authors prove that test error then has a finite upper bound however many generations pass.	—
3	CLAIM TYPE	ESTIMATE	base_types: ESTIMATE
4	RESEARCH STRAND	C — Systems, decisions and shared knowledge	—
5	MATURITY	CONTESTED	states: CONTESTED
6	SOURCE	Gerstgrasser, Schaeffer, Dey, Rafailov, Sleight, Hughes et al., “Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data,” arXiv:2404.01413, 2024	source_ids: SRC-SL-GERSTGRASSER-ET-AL-ARXIV-2404-01413
7	SOURCE TYPE	Preprint	classes: PREPRINT
8	INSTITUTIONAL POSITION	Academic, Stanford University-led, with co-authors at non-academic organisations (Constellation, Sequoia Capital)	—
9	SCOPE	Generative models trained recursively, in the laboratory	—
10	DESIGN	Experiments and theory comparing data replacement with data accumulation	—
11	SAMPLE / DATASET	Several model types; not recorded in detail for this version	—
12	MODEL / TOOL / VERSION	Language, diffusion and other generative models	—
13	COMPARATOR	Replacement of real data by synthetic data	—
14	MAIN RESULT	Replacement “does indeed tend towards model collapse”; accumulation “avoids model collapse”; with accumulation, “the test error has a finite upper bound independent of the number of iterations”	—
15	INFERENTIAL TARGET	Whether model collapse is inevitable	—
16	DOES NOT LICENSE	Anything about the flow of new human-written data, which the setup holds fixed	—
17	VERIFICATION STATE	CONTENT VERIFIED PREPRINT	state: CONTENT_VERIFIED_PRIMARY · qualifiers: PREPRINT · verified_by: UNKNOWN
18	LIMITATIONS	Preprint, checked against the full text of arXiv version 2; venue not confirmed; laboratory result; the bound is proved for linear models	—
19	CONTRADICTORY / SUPPORTING SOURCES	Collapse under replacement: LD09-SL-C30	—
20	GEOGRAPHY / LANGUAGE	Not applicable / English	—
21	DISTRIBUTIONAL LEDGER	Not recorded	—
22	R01 / FIELD-MAP LINKS	LD-09, D3	—
23	WHAT WOULD CHANGE THIS CLAIM?	Evidence on how real training pipelines mix human and model data	—
24	PUBLICATION STATUS	ELIGIBLE WITH PREPRINT QUALIFIER	state: ELIGIBLE · qualifiers: PREPRINT
25	RECORDED DATE	2026-10-15	—

Field 22 references resolved against Field Map v0.2: LD-09 (LIVING_DEBATE); D3 (DOMAIN)

Cited by Living Debate versions

LD-09 v0.1

Research-of-record provenance

Materialized by sociolens-materializer 0.6.0 at 2026-09-28T20:00:00.000Z; normalization contract SocioLens — Claim Value Vocabulary v1.0.2 — Pre-Spike Materialization Contract (v1.0.2). Content seal SHA-256 52b69e84ed5256561ec334f6e7d2309bfb2d81a30ee00333dc8be52410531f3e.

Repository-authored inputs (not Drive exports)

SocioLens claim — LD09-SL-C31 v1.0 (v1.0) — written in the SocioLens repository by Project Lead (Claude, AI) on 2026-10-15; no Drive identity exists. Authority: AGENTS.md "Authority" (the Project Lead decides research content within the research-integrity rules) and the Owner's choice in the SocioLens project chat on 15 October 2026 to build the LD-09 debate; a new Claim, first version, written from the project's LD-09 source notes, checked against full texts or official abstracts. Block “ENTRY 31 — LD09-SL-C31” SHA-256 148a3986c848500b3014f0cb8404f0d874d429d99a81415af6906ca8138c04e9; fixture fixtures/authored/claims/LD09-SL-C31--v1.0.

Builder decisions (not Drive data)

VERSION = v1.0 — basis: Claim version taken from the repository-authored claim fixture version (SocioLens claim — LD09-SL-C31 v1.0); the first version of a new Claim of the LD-09 debate
CURRENT_POINTER = true — basis: repository-authored claim "SocioLens claim — LD09-SL-C31 v1.0" (Project Lead (Claude, AI), 2026-10-15); basis: AGENTS.md "Authority" (the Project Lead decides research content within the research-integrity rules) and the Owner's choice in the SocioLens project chat on 15 October 2026 to build the LD-09 debate; a new Claim, first version, written from the project's LD-09 source notes, checked against full texts or official abstracts
FIELD_6_SOURCE_REFERENCE = SRC-SL-GERSTGRASSER-ET-AL-ARXIV-2404-01413--v1.0 — basis: field 6 of ENTRY 31 — LD09-SL-C31 cites "Gerstgrasser, Schaeffer, Dey, Rafailov, Sleight, Hughes et al., “Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data,” arXiv:2404.01413, 2024"; the only field-6 segment of this ClaimVersion's repository-authored ledger block.
SOURCE_PROVENANCE_PIN = SRC-SL-GERSTGRASSER-ET-AL-ARXIV-2404-01413--v1.0 — basis: explicit version-pinned public provenance of this ClaimVersion (Amendment v1.2 §6): the pinned field-6 Source record "Gerstgrasser, Schaeffer, Dey, Rafailov, Sleight, Hughes et al., “Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data,” arXiv:2404.01413, 2024".