# When Sample Selection Bias Precipitates Model Collapse

arXiv: https://arxiv.org/abs/2606.13732 · HTML: https://mlsanity.com/paper/2606.13732/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Model collapse from synthetic data, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 57 of its 86 references that are in the map.
- First posted on arXiv 11 Jun 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Model collapse from synthetic data](https://mlsanity.com/synth/model-collapse-from-synthetic-data/)

## Builds on (most cited first, 30 of 57)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [The Curse of Recursion: Training on Generated Data Makes Models Forget](https://mlsanity.com/paper/2305.17493/) (2023)
- [XL-Sum: Large-Scale Multilingual Abstractive Summarization for 44 Languages](https://mlsanity.com/paper/2106.13822/) (2021)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Self-Distillation Amplifies Regularization in Hilbert Space](https://mlsanity.com/paper/2002.05715/) (2020)
- [Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data](https://mlsanity.com/paper/2404.01413/) (2024)
- [BoNBoN Alignment for Large Language Models and the Sweetness of Best-of-n Sampling](https://mlsanity.com/paper/2406.00832/) (2024)
- [Theoretical Analysis of Domain Adaptation with Optimal Transport](https://mlsanity.com/paper/1610.04420/) (2016)
- [On the Stability of Iterative Retraining of Generative Models on their own Data](https://mlsanity.com/paper/2310.00429/) (2023)
- [Model Collapse Demystified: The Case of Regression](https://mlsanity.com/paper/2402.07712/) (2024)
- [Bias Correction of Learned Generative Models using Likelihood-Free Importance Weighting](https://mlsanity.com/paper/1906.09531/) (2019)
- [LAVA: Data Valuation without Pre-Specified Learning Algorithms](https://mlsanity.com/paper/2305.00054/) (2023)
- [Membership Inference Attacks against Synthetic Data through Overfitting Detection](https://mlsanity.com/paper/2302.12580/) (2023)
- [Strong Model Collapse](https://mlsanity.com/paper/2410.04840/) (2024)
- [Data Feedback Loops: Model-driven Amplification of Dataset Biases](https://mlsanity.com/paper/2209.03942/) (2022)
- [Will Large-scale Generative Models Corrupt Future Datasets?](https://mlsanity.com/paper/2211.08095/) (2022)
- [Fairness Feedback Loops: Training on Synthetic Data Amplifies Bias](https://mlsanity.com/paper/2403.07857/) (2024)
- [Collapse or Thrive? Perils and Promises of Synthetic Data in a Self-Generating World](https://mlsanity.com/paper/2410.16713/) (2024)
- [Beyond Model Collapse: Scaling Up with Synthesized Data Requires Verification](https://mlsanity.com/paper/2406.07515/) (2024)

## Built on by (most cited first, 1 of 1)

- [Screening Collapse under Recursive Synthetic Data](https://mlsanity.com/paper/2610.15617/) (2026)

## Abstract (arXiv)

The proliferation of recursive training on synthetic data can alleviate data scarcity but risks model collapse, where repeated training erodes distributional tails and homogenizes outputs. Data selection is widely viewed as a remedy, yet its reliability depends critically on the reference distribution used by the verifier. We show that in low-resource verification regimes, where each verifier observes only a small, fragmented, and biased slice of the target manifold, selection itself becomes biased. This situation naturally arises in low-resource data silos such as healthcare consortia or proprietary financial institutions, where raw data cannot be pooled and local references are inherently incomplete. As a result, selection preferentially retains samples aligned with the local manifold while pruning globally relevant tail modes, turning from a safeguard against collapse into a mechanism that precipitates it. We theoretically prove that such siloed selection accelerates collapse and induces power-law diversity decay. As an initial mitigation, we construct Wasserstein proxy references from multiple silos without sharing raw data. Empirical results confirm that local-reference selection fails on skewed distributions, whereas collaborative proxy references mitigate diversity degradation, suggesting that recursive synthetic-data pipelines require particular caution when real-data coverage is fragmented or scarce.