The increasing reliance on generative AI models is rapidly increasing the volume of synthetic data, with some projections suggesting that most available new data for training could be machine-generated by 2030. This shift to a mainly synthetic content presents a critical challenge: repeated training in synthetic data leads to a phenomenon known as model collapse, where model performance degrades over generations of training, eventually rendering the models ineffective. While the causes of model collapse are increasingly understood, effective mitigation strategies remain scarce. We address this challenge by leveraging a key insight: auto-regressive models tend to generate text sequences to which they assign high confidence (i.e., high log-likelihood). Based on this observation, we introduce the Truncated-Cross-Entropy (TCE) loss function. TCE mitigates collapse by selectively ignoring high-confidence tokens during training, effectively filtering out likely machine-generated artifacts from the learning process. Our experiments demonstrate that models trained with TCE not only learn effectively but also exhibit significantly increased resilience, tolerating over 2.3x more synthetic data before the onset of collapse. In addition, we provide an open-source benchmark for collapse dynamics in mixed-data settings. Our results demonstrate that confidence-aware training objectives can substantially delay collapse onset, offering a practical and generalizable tool for model robustness under synthetic-data exposure.
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