# Preventing Model Collapse via Contraction-Conditioned Neural Filters

arXiv: https://arxiv.org/abs/2512.00757 · HTML: https://mlsanity.com/paper/2512.00757/

## Key facts

- No citing papers in the map yet (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 4 of its 6 references that are in the map.
- First posted on arXiv 30 Nov 2025.

## 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, 4 of 4)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [A Probabilistic Perspective on Model Collapse](https://mlsanity.com/paper/2505.13947/) (2025)

## Abstract (arXiv)

This paper presents a neural network filter method based on contraction operators to address model collapse in recursive training of generative models. Unlike citexu2024probabilistic, which requires superlinear sample growth (O(t1+s)), our approach completely eliminates the dependence on increasing sample sizes within an unbiased estimation framework by designing a neural filter that learns to satisfy contraction conditions. We develop specialized neural network architectures and loss functions that enable the filter to actively learn contraction conditions satisfying Assumption 2.3 in exponential family distributions, thereby ensuring practical application of our theoretical results. Theoretical analysis demonstrates that when the learned contraction conditions are satisfied, estimation errors converge probabilistically even with constant sample sizes, i.e., limsupt→∞mathbbP(|et|>δ)=0 for any δ>0. Experimental results show that our neural network filter effectively learns contraction conditions and prevents model collapse under fixed sample size settings, providing an end-to-end solution for practical applications.