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., $\limsup_{t\to\infty}\mathbb{P}(\|\mathbf{e}_t\|>δ)=0$ 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.

翻译：本文提出一种基于收缩算子的神经网络滤波方法，以解决生成模型递归训练中的模型崩溃问题。与\\cite{xu2024probabilistic}需要超线性样本增长（$O(t^{1+s})$）不同，我们的方法通过设计能够学习满足收缩条件的神经滤波器，在无偏估计框架内完全消除了对递增样本量的依赖。我们开发了专门的神经网络架构和损失函数，使滤波器能够主动学习满足指数族分布中假设2.3的收缩条件，从而确保理论结果的实际应用。理论分析表明，当学习到的收缩条件满足时，即使样本量恒定，估计误差也能以概率方式收敛，即对于任意$δ>0$，有$\\limsup_{t\\to\\infty}\\mathbb{P}(\\|\\mathbf{e}_t\\|>δ)=0$。实验结果表明，我们的神经网络滤波器能够有效学习收缩条件，并在固定样本量设置下防止模型崩溃，为实际应用提供了端到端的解决方案。