Y. T. Zhang

Yuanhe Zhang, Fanghui Liu, Yudong Chen

This paper explores how theory can guide and enhance practical algorithms, using Low-Rank Adaptation (LoRA, Hu et al. 2022) in large language models as a case study. We rigorously prove that, under gradient descent, LoRA adapters align with specific singular subspaces of the one-step full fine-tuning gradient. This result suggests that, by properly initializing the adapters using the one-step full gradient, subspace alignment can be achieved immediately and applicable to both linear and nonlinear models. Building on our theory, we propose a theory-driven algorithm, LoRA-One, where the linear convergence (as well as generalization) is built and incorporating preconditioners theoretically helps mitigate the effects of ill-conditioning. Besides, our theory reveals connections between LoRA-One and other gradient-alignment-based methods, helping to clarify misconceptions in the design of such algorithms. LoRA-One achieves significant empirical improvements over LoRA and its variants across benchmarks in natural language understanding, mathematical reasoning, and code generation. Code is available at: https://github.com/YuanheZ/LoRA-One.

Yuanhe Zhang, Ilja Kuzborskij, Jason D. Lee et al.

Large Language Models (LLMs) demonstrate strong performance on mathematical problems when prompted with Chain-of-Thought (CoT), yet it remains unclear whether this success stems from search, rote procedures, or rule-consistent reasoning. To address this, we propose modeling CoT as a certain rule-based stochastic process over directed acyclic graphs (DAGs), where nodes represent intermediate derivation states and edges encode rule applications. Within this framework, we introduce logical closeness, a metric that quantifies how well a model's CoT trajectory (i.e., the LLM's final output) adheres to the DAG structure, providing evaluation beyond classical PASS@k metrics. Building on this, we introduce the DAG-MATH CoT format and construct a benchmark that guides LLMs to generate CoT trajectories in this format, thereby enabling the evaluation of their reasoning ability under our framework. Across standard mathematical reasoning datasets, our analysis uncovers statistically significant differences in reasoning fidelity among representative LLM families-even when PASS@k is comparable-highlighting gaps between final-answer accuracy and rule-consistent derivation. Our framework provides a balance between free-form CoT and formal proofs systems, offering actionable diagnostics for LLMs reasoning evaluation. Our benchmark and code are available at: https://github.com/YuanheZ/DAG-MATH-Formatted-CoT.

Yuanhe Zhang, Fangzhou Xie, Zhenhong Zhou et al.

Large Language Diffusion Models (LLDMs) exhibit comparable performance to LLMs while offering distinct advantages in inference speed and mathematical reasoning tasks.The precise and rapid generation capabilities of LLDMs amplify concerns of harmful generations, while existing jailbreak methodologies designed for Large Language Models (LLMs) prove limited effectiveness against LLDMs and fail to expose safety vulnerabilities.Successful defense cannot definitively resolve harmful generation concerns, as it remains unclear whether LLDMs possess safety robustness or existing attacks are incompatible with diffusion-based architectures.To address this, we first reveal the vulnerability of LLDMs to jailbreak and demonstrate that attack failure in LLDMs stems from fundamental architectural differences.We present a PArallel Decoding jailbreak (PAD) for diffusion-based language models. PAD introduces Multi-Point Attention Attack, which guides parallel generative processes toward harmful outputs that inspired by affirmative response patterns in LLMs. Experimental evaluations across four LLDMs demonstrate that PAD achieves jailbreak attack success rates by 97%, revealing significant safety vulnerabilities. Furthermore, compared to autoregressive LLMs of the same size, LLDMs increase the harmful generation speed by 2x, significantly highlighting risks of uncontrolled misuse.Through comprehensive analysis, we provide an investigation into LLDM architecture, offering critical insights for the secure deployment of diffusion-based language models.