Yuzhu Chen

Shi Fu, Yingjie Wang, Yuzhu Chen et al.

High-quality data is essential for training large generative models, yet the vast reservoir of real data available online has become nearly depleted. Consequently, models increasingly generate their own data for further training, forming Self-consuming Training Loops (STLs). However, the empirical results have been strikingly inconsistent: some models degrade or even collapse, while others successfully avoid these failures, leaving a significant gap in theoretical understanding to explain this discrepancy. This paper introduces the intriguing notion of recursive stability and presents the first theoretical generalization analysis, revealing how both model architecture and the proportion between real and synthetic data influence the success of STLs. We further extend this analysis to transformers in in-context learning, showing that even a constant-sized proportion of real data ensures convergence, while also providing insights into optimal synthetic data sizing.

Yuzhu Chen, Yingjie Wang, Shunyu Liu et al.

Autoregressive pre-trained models combined with decoding methods have achieved impressive performance on complex reasoning tasks. While mainstream decoding strategies such as beam search can generate plausible candidate sets, they often lack provable coverage guarantees, and struggle to effectively balance search efficiency with the need for versatile trajectories, particularly those involving long-tail sequences that are essential in certain real-world applications. To address these limitations, we propose \textsc{CoVeR}, a novel model-free decoding strategy wihtin the conformal prediction framework that simultaneously maintains a compact search space and ensures high coverage probability over desirable trajectories. Theoretically, we establish a PAC-style generalization bound, guaranteeing that \textsc{CoVeR} asymptotically achieves a coverage rate of at least $1 - α$ for any target level $α\in (0,1)$.

Yuzhu Chen, Yingjie Wang, Shi Fu et al.

This paper studies the crucial impact of initialization in Low-Rank Adaptation (LoRA). Through theoretical analysis, we demonstrate that the fine-tuned result of LoRA is highly sensitive to initialization, which is likely to lead suboptimal low-rank results. While this issue can be mitigated by adjusting the initial direction towards the main singular vectors of the target $ΔW$, which is, however, typically unknown in real-world scenarios. To approximate this initial direction, we propose High-Rank Preheating (HRP), which first trains LoRA with a higher preheating rank for a few steps, then uses the main singular vectors of the derived $BA^\top$ as initialization for the main fine-tuning process. With only a modification in the initial direction, we prove that HRP makes LoRA achieve better fine-tuned results than random initialization in expectation, and the enhancement grows with the preheating rank. We validate our theoretical findings through extensive experiments in various models and tasks, where HRP significantly enhances LoRA's effectiveness and outperforms other initialization strategies and other LoRA variants.