Bilevel optimization underpins many machine learning applications, including hyperparameter optimization, meta-learning, neural architecture search, and reinforcement learning. While hypergradient-based methods have advanced significantly, a gap persists between theoretical guarantees and practical single-loop implementations required for efficiency. We bridge this gap by establishing sharper convergence results for single-loop approximate implicit differentiation (AID) and iterative differentiation (ITD) methods, leveraging our proposed analytical framework, decoupled norm analysis (DNA). For AID, we improve the convergence rate from $\mathcal{O}(\kappa^6/K)$ to $\mathcal{O}(\kappa^5/K)$, where $\kappa$ is the condition number of the inner-level problem. For ITD, we prove that the asymptotic error is $\mathcal{O}(\kappa^2)$, exactly matching the known lower bound and improving upon the previous $\mathcal{O}(\kappa^3)$ guarantee. Numerical experiments on synthetic and real tasks corroborate our theoretical findings.
Ensuring the accuracy of financial documents is critical for economic analysis, regulatory compliance, and corporate decision-making. Several studies have shown that Large Language Models (LLMs) perform well in many financial tasks, such as stock price movements and financial analytics. However, a critical task remains unexplored: the ability of LLMs to identify errors in financial documents. In this paper, we introduce \textbf{FinED-Bench}, the first publicly \textbf{Bench}mark for \textbf{Fin}ancial \textbf{E}rror \textbf{D}etection across three levels of cognitive complexity. FinED-Bench covers nine real-world financial scenarios, and includes over 900 documents reported in 2025 that are unseen by existing language models. We detail the benchmark construction process and evaluate several advanced LLMs (e.g., GPT-4o, Qwen3-14B) on this tasks, which requires both financial domain knowledge and reasoning capabilities. Experimental results show that current LLMs still struggle with this task, especially in high-complexity cases. Besides, supervised fine-tuning can significantly improve the performance of weaker LLMs on this task. Our data and code are available at https://github.com/hedyHe/FinED-Bench.
Ying He, Zhouhong Gu, Zhecheng Hu et al.· Annual Meeting of the Associ...· 2 citations
