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.

SocioLens project,

Claim LD09-SL-C31 (v1.0)

Provenance and status

Claim type: Estimate
Publication status: Eligible for publication, with qualifiers: preprint
Verification state: Checked against the primary source; the source is a preprint. Who checked this claim is not recorded for it; claim checks so far were AI-led, and no person has checked claims against their sources.
Does not license: Anything about the flow of new human-written data, which the setup holds fixed
Limitations: Preprint, checked against the full text of arXiv version 2; venue not confirmed; laboratory result; the bound is proved for linear models
Source (as cited): 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: Preprint (recorded as “Preprint”)
Institutional position: Academic, Stanford University-led, with co-authors at non-academic organisations (Constellation, Sequoia Capital)
Maturity of the evidence: Contested evidence
Recorded date: 15 October 2026
Currentness / correction: This is the current version. No correction or concern is recorded on its sources.

Sources this version 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 (Preprint)
Read the original

Version

This is the current version, v1.0. Earlier versions stay available, and their records never change.

Versions: v1.0 · current

Raw record: every recorded field, with its coded values

All 25 canonical Claim fields, verbatim, with the coded values derived from them. The plain-language labels above are read from these.

Claim type (coded): ESTIMATE (as printed: “ESTIMATE”)
Publication status (coded): ELIGIBLE (PREPRINT) (as printed: “ELIGIBLE WITH PREPRINT QUALIFIER”)
Verification state (coded): CONTENT_VERIFIED_PRIMARY (PREPRINT)
Source type (coded): PREPRINT
Maturity (coded): CONTESTED

#	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)

The sources as recorded, with their record IDs and coded source types:

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” → Gerstgrasser et al. (2024), “Is Model Collapse…” (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)

Cited by Living Debate versions

Individual gain, collective narrowing? Does AI make science, creative work and shared knowledge more alike? (v0.1) LD-09

Cite this page

SocioLens project. (2026, October 15). 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 [Claim LD09-SL-C31, version v1.0]. SocioLens. https://sociolens-web.pages.dev/claims/ld09-sl-c31/v1.0/

@misc{sociolens_ld09_sl_c31_v1_0,
  author = {{SocioLens project}},
  title = {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.},
  year = {2026},
  date = {2026-10-15},
  howpublished = {\url{https://sociolens-web.pages.dev/claims/ld09-sl-c31/v1.0/}},
  note = {Claim LD09-SL-C31, version v1.0}
}

The link points to this version, whose record never changes. For a finding, cite the original study as well: SocioLens summarizes research and does not replace it.

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".