Preventing Model Collapse via Contraction-Conditioned Neural Filters

TL;DR

This paper introduces a neural network filter based on contraction operators that prevents model collapse in generative models without increasing sample sizes, ensuring stable training and convergence.

Contribution

The paper proposes a novel neural filter architecture that learns contraction conditions to eliminate the need for increasing sample sizes in recursive training.

Findings

Neural filter effectively learns contraction conditions.

Prevents model collapse with fixed sample sizes.

Ensures convergence of estimation errors.

Abstract

This paper presents a neural network filter method based on contraction operators to address model collapse in recursive training of generative models. Unlike \cite{xu2024probabilistic}, which requires superlinear sample growth ($O(t^{1+s})$), 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., $\limsup_{t\to\infty}\mathbb{P}(\|\mathbf{e}_t\|>\delta)=0$ for any $\delta>0$. 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.