Yuzhu Chen

Yuzhu Chen, Tian Qin, Xinmei Tian et al.

Equivariant neural networks encode symmetry as an inductive bias and have achieved strong empirical performance in wide domains. However, their expressive power remains not well understood. Focusing on 2-layer ReLU networks, this paper investigates the impact of equivariance constraints on the expressivity of equivariant and layer-wise equivariant networks. By examining the boundary hyperplanes and the channel vectors of ReLU networks, we construct an example showing that equivariance constraints could strictly limit expressive power. However, we demonstrate that this drawback can be compensated via enlarging the model size. Furthermore, we show that despite a larger model size, the resulting architecture could still correspond to a hypothesis space with lower complexity, implying superior generalizability for equivariant networks.

Kenton Tang, Yuzhu Chen, Fengxiang He

Alignment and adaptation in large language models heavily rely on reinforcement learning from human feedback (RLHF); yet, theoretical understanding of its generalisability remains premature, especially when the learned reward could shift, and the KL control is estimated and clipped. To address this issue, we develop generalisation theory for RLHF that explicitly accounts for (1) \emph{reward shift}: reward models are trained on preference data from earlier or mixed behaviour policies while RLHF optimises the current policy on its own rollouts; and (2) \emph{clipped KL regularisation}: the KL regulariser is estimated from sampled log-probability ratios and then clipped for stabilisation, resulting in an error to RLHF. We present generalisation bounds for RLHF, suggesting that the generalisation error stems from a sampling error from prompts and rollouts, a reward shift error, and a KL clipping error. We also discuss special cases of (1) initialising RLHF parameters with a uniform prior over a finite space, and (2) training RLHF by stochastic gradient descent, as an Ornstein-Uhlenbeck process. The theory yields practical implications in (1) optimal KL clipping threshold, and (2) budget allocation in prompts, rollouts, and preference data.

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.

Shi Fu, Yuzhu Chen, Yingjie Wang et al.

Understanding the inner mechanisms of black-box foundation models (FMs) is essential yet challenging in artificial intelligence and its applications. Over the last decade, the long-running focus has been on their explainability, leading to the development of post-hoc explainable methods to rationalize the specific decisions already made by black-box FMs. However, these explainable methods have certain limitations in terms of faithfulness and resource requirement. Consequently, a new class of interpretable methods should be considered to unveil the underlying mechanisms of FMs in an accurate, comprehensive, heuristic, and resource-light way. This survey aims to review those interpretable methods that comply with the aforementioned principles and have been successfully applied to FMs. These methods are deeply rooted in machine learning theory, covering the analysis of generalization performance, expressive capability, and dynamic behavior. They provide a thorough interpretation of the entire workflow of FMs, ranging from the inference capability and training dynamics to their ethical implications. Ultimately, drawing upon these interpretations, this review identifies the next frontier research directions for FMs.

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.