Jincheng Ren

Jincheng Ren, Hong-lin Liao, Jiwei Zhang et al.

Due to the intrinsically initial singularity of solution and the discrete convolution form in numerical Caputo derivatives, the traditional $H^1$-norm analysis (corresponding to the case for a classical diffusion equation) to the time approximations of a fractional subdiffusion problem always leads to suboptimal error estimates (a loss of time accuracy). To recover the theoretical accuracy in time, we propose an improved discrete Grönwall inequality and apply it to the well-known L1 formula and a fractional Crank-Nicolson scheme. With the help of a time-space error-splitting technique and the global consistency analysis, sharp $H^1$-norm error estimates of the two nonuniform approaches are established for a reaction-subdiffusion problems. Numerical experiments are included to confirm the sharpness of our analysis.

Dingling Zhang, He Zhu, Jincheng Ren et al.

Deep Research Agents (DRAs) aim to automatically produce analyst-level reports through iterative information retrieval and synthesis. However, most existing DRAs were validated on question-answering benchmarks, while research on generating comprehensive reports remains overlooked. Worse, current benchmarks for report synthesis suffer from task complexity and subjective metrics -- this fails to reflect user demands and limits the practical utility of generated reports. To address these gaps, we present Fine-grained DEepResearch bench (FINDER), an enhanced benchmark consisting of 100 human-curated research tasks with 419 structured checklist items that standardize report structure, analytical depth, and factual grounding. Based on approximately 1,000 reports produced by mainstream DRAs, we further propose Deep rEsearch Failure Taxonomy (DEFT), the first failure taxonomy for deep research agents. DEFT contains 14 fine-grained failure modes across reasoning, retrieval, and generation, and is built upon grounded theory with human-LLM co-annotating and inter-annotator reliability validation. Our experimental findings reveal that current DRAs struggle not with task comprehension but with evidence integration, verification, and reasoning-resilient planning.