PAGE-RAG: Evidence-Grounded Adaptive Graph Retrieval for Long-Document Question Answering

GraphRAG improves long-document question answering by introducing structured representations beyond conventional retrieval. However, automatically constructed graphs are inherently incomplete projections of source documents, and treating them as independent knowledge sources may lead to unreliable retrieval and generation. We propose PAGE-RAG, a projection-aware adaptive graph retrieval framework for reliable long-document question answering. PAGE-RAG views graph structures as semantic skeletons that organize and navigate document knowledge, rather than replacing the original knowledge source. Based on this perspective, PAGE-RAG introduces a task-adaptive retrieval routing strategy that dynamically selects appropriate retrieval behaviors according to query requirements. Furthermore, PAGE-RAG incorporates strict knowledge boundary control, ensuring that generated responses remain grounded within available evidence and abstaining from unsupported information beyond the accessible knowledge scope. Experiments demonstrate that PAGE-RAG achieves competitive answer quality while improving retrieval efficiency and knowledge reliability, highlighting the importance of projection-aware graph modeling, adaptive retrieval, and explicit knowledge boundary control for trustworthy GraphRAG systems. The source code is publicly available at https://github.com/CXY0112/PAGE-RAG.

Symbolic Graph Networks for Robust PDE Discovery from Noisy Sparse Data

Data-driven discovery of partial differential equations (PDEs) offers a promising paradigm for uncovering governing physical laws from observational data. However, in practical scenarios, measurements are often contaminated by noise and limited by sparse sampling, which poses significant challenges to existing approaches based on numerical differentiation or integral formulations. In this work, we propose a Symbolic Graph Network (SGN) framework for PDE discovery under noisy and sparse conditions. Instead of relying on local differential approximations, SGN leverages graph message passing to model spatial interactions, providing a non-local representation that is less sensitive to high frequency noise. Based on this representation, the learned latent features are further processed by a symbolic regression module to extract interpretable mathematical expressions. We evaluate the proposed method on several benchmark systems, including the wave equation, convection-diffusion equation, and incompressible Navier-Stokes equations. Experimental results show that SGN can recover meaningful governing relations or solution forms under varying noise levels, and demonstrates improved robustness compared to baseline methods in sparse and noisy settings. These results suggest that combining graph-based representations with symbolic regression provides a viable direction for robust data-driven discovery of physical laws from imperfect observations. The code is available at https://github.com/CXY0112/SGN

KG-Augmented Executable CoT for Mathematical Coding

In recent years, large language models (LLMs) have excelled in natural language processing tasks but face significant challenges in complex reasoning tasks such as mathematical reasoning and code generation. To address these limitations, we propose KG-Augmented Executable Chain-of-Thought (KGA-ECoT), a novel framework that enhances code generation through knowledge graphs and improves mathematical reasoning via executable code. KGA-ECoT decomposes problems into a Structured Task Graph, leverages efficient GraphRAG for precise knowledge retrieval from mathematical libraries, and generates verifiable code to ensure computational accuracy. Evaluations on multiple mathematical reasoning benchmarks demonstrate that KGA-ECoT significantly outperforms existing prompting methods, achieving absolute accuracy improvements ranging from several to over ten percentage points. Further analysis confirms the critical roles of GraphRAG in enhancing code quality and external code execution in ensuring precision. These findings collectively establish KGA-ECoT as a robust and highly generalizable framework for complex mathematical reasoning tasks.