mlsanityData to 7 Oct 2026

Theoretical Proof that Auto-regressive Language Models Collapse when Real-world Data is a Finite Set

arXiv 2412.14872 ↗First posted 19 Dec 2024cs.CLcited by 4

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Abstract (arXiv)

Auto-regressive language models (LMs) have been widely used to generate data in data-scarce domains to train new LMs, compensating for the scarcity of real-world data. Previous work experimentally found that LMs collapse when trained on recursively generated data. This paper presents a theoretical proof: once a corpus (such as a subset of the World Wide Web) begins to incorporate generated data and no new real-world data is added to the corpus, then no matter how small the amount of data each LM generates and contributes to the corpus, LM collapse is inevitable after sufficient time. This finding suggests that attempts to mitigate collapse by limiting the quantity of synthetic data in the corpus are fundamentally insufficient. Instead, avoiding collapse hinges on ensuring the quality of synthetic data.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 11 of its 18 references that are in the map. First posted on arXiv 19 Dec 2024.

Builds on

11 of 18 references.

References · 11

  1. 2022Self-Instruct: Aligning Language Models with Self-Generated Instructionscited by 2,674
  2. 2023WizardLM: Empowering large pre-trained language models to follow complex instructionscited by 1,116
  3. 2023Self-Consuming Generative Models Go MADcited by 239
  4. 2024Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Datacited by 143
  5. 2024A Tale of Tails: Model Collapse as a Change of Scaling Lawscited by 127
  6. 2023On the Stability of Iterative Retraining of Generative Models on their own Datacited by 98
  7. 2024Model Collapse Demystified: The Case of Regressioncited by 80
  8. 2024How Bad is Training on Synthetic Data? A Statistical Analysis of Language Model Collapsecited by 75
  9. 2022Data Feedback Loops: Model-driven Amplification of Dataset Biasescited by 59
  10. 2024Collapse or Thrive? Perils and Promises of Synthetic Data in a Self-Generating Worldcited by 49
  11. 2024Self-Consuming Generative Models with Curated Data Provably Optimize Human Preferencescited by 35

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 2.

4 papers.

  1. 2025Epistemic diversity across language models mitigates knowledge collapsecited by 2
  2. 2025Deep Graph Learning for Industrial Carbon Emission Analysis and Policy Impactcited by 1
  3. 2026Is Convergence Inevitable? Tracing Output Homogeneity Back to Base Modelscited by 1
  4. 2026Bridging the Stability-Expressivity Gap: Synthetic Data Scaling and Preference Alignment for Low-Resource Spoken Language Modelscited by 0