A qualia role-based entity-dependency graph (EDG) is proposed to represent and extract quantity relations for solving algebra story problems stated in Chinese. Traditional neural solvers use end-to-end models to translate problem texts into math expressions, which lack quantity relation acquisition in sophisticated scenarios. To address the problem, the proposed method leverages EDG to represent quantity relations hidden in qualia roles of math objects. Algorithms were designed for EDG generation and quantity relation extraction for solving algebra story problems. Experimental result shows that the proposed method achieved an average accuracy of 82.2% on quantity relation extraction compared to 74.5% of baseline method. Another prompt learning result shows a 5% increase obtained in problem solving by injecting the extracted quantity relations into the baseline neural solvers.

Natural language to structured query language (Text2SQL) is a critical task in intelligent question answering and database interaction. A fundamental challenge lies in achieving semantic symmetry between natural language expressions and database schemas, as well as behavioral symmetry between query generation and error correction. Traditional approaches often struggle with comprehending domain-specific concepts and dynamically adapting to user’s feedback, breaking the desired symmetry between system output and user intent. Thispaper presents EvoAgent-SQL as a lightweight engineering framework for private domain data querying based on low-cost lightweight models. The framework comprises three core agents: (1) the Schema Grounding Agent (SGA) establishes a symmetric mapping from natural language concepts to database fields; (2) the Execution Agent (EA) generates SQL queries; and (3) the Reflection Agent (RA) mirrors the EA’s outputs by analyzing errors and proposing corrections, forming a reflective symmetry loop. When ambiguity arises, user feedback is incorporated as a symmetry-breaking signal, which the RA uses to restore alignment through iterative evolution with a memory mechanism. We evaluate the framework on an education-domain dataset and provide a reproducibility plan for releasing sanitized schemas, natural language questions, and reference SQL while withholding confidential institutional records. Experimental results demonstrate that EvoAgent-SQL enhances query execution accuracy, achieving a $13.7\%$ reduction in the relative error residual after one evolution cycle and a $17.6\%$ cumulative reduction after two cycles, suggesting practical adaptability in domain-specific Text2SQL tasks.

Handwritten mathematical expression recognition (HMER) is a highly challenging task, as it involves not only distinguishing visually similar characters but also interpreting complex structures. Even for humans, it sometimes requires several rounds of confirmation to arrive at a recognition result. Iterative self-refinement is a strategy frequently employed by humans when tackling complex tasks. Inspired by this, we put forward a self-reflective, closed-loop feedback architecture for HMER. Specifically, a compatible Confidence-Guided Self-Correction Module (CGSCM) is proposed to endow existing end-to-end HMER models with self-correcting capabilities. CGSCM evaluates the semantic consistency between the preceding token predictions and the original handwritten image; it accordingly assigns confidence scores that reflect the visual consistency of each token. These scores guide the model in rethinking its previous predictions, placing greater emphasis on low-confidence tokens in the next refinement step. Furthermore, we incorporate self-correction into the training phase by introducing a token replacement strategy that forces the model to learn to distinguish between visually similar symbols. Extensive experiments conducted on the public CROHME, HME100K, and QA-HME datasets demonstrate that CGSCM can consistently enhance end-to-end HMER performance across different state-of-the-art model backbones, thus achieving new benchmark performance. Considering the expression level, the accuracy has achieved an average improvement of 1.01% across datasets and backbones, with the maximum improvement reaching 2.19%. Our work has verified the effectiveness of introducing the iterative self-refinement mechanism in the HMER task. The proposed CGSCM provides valuable insight for building robust self-refining models in complex tasks. The code is available at: https://github.com/Jzliu-dl/CGSCM