The key to improving the readability and usage of educational resources is their orderly arrangement and integration. Knowledge graphs, which are a large-scale form of knowledge engineering, are an effective tool for managing and organizing educational resources. The water conservancy’s educational big data is separated into three tiers of objectives–courses–knowledge units based on the connotation level of self-directed learning. Combined with the idea of Outcome-based Education(OBE), the goal-oriented knowledge graph structure of water conservancy disciplines and graph creation method is proposed. The focus is the error accumulation problem brought about by the traditional relational extraction method of Named Entity Recognition based on rules or sequence labeling. We first complete this objective, and then the relationship classification is performed according to the water conservancy disciplines entity and relations joint extraction (WDERJE) model, on which the prompt mechanism design is based. Think of the entity-relationship extraction task as a sequence-to-sequence generation task, and take the structured extraction language to unify the coding entity extraction and relationship extraction structures. The evaluation results of the WDERJE model show that the F_0.5 value of each entity extraction is above 0.76, and the cumulative extraction relationship triple is nearly 180,000. The graph fully optimizes the organization and management of water conservancy education resources and effectively improves the readability and utilization rate of water conservancy teaching resources.

This paper proposes an interpretable geometry solution based on the formal language set of text and diagram. Geometry problems are solved using machines; however, machines encounter challenges in natural language processing and computer vision. Significant progress has improved existing methods in the extraction of geometric formal languages. However, the neglect of the graph structure information in the formal language and the lack of further refinement of the extracted language set can lead to poor theorem prediction and poor accuracy in problem solving. In this paper, a formal language graph is constructed using the extracted formal language set and applied to theorem prediction using a graph convolutional network. To better extract the relationship set of diagram elements, an improved diagram parser is proposed. The test results indicate that the improved method has good results when solving interpretable geometry problems.

This paper proposes an interpretable geometry solution based on the formal language set of text and diagram. Geometry problems are solved by machines, which still poses challenges in natural language processing and computer vision. Significant progress promotes existing methods in the extraction of geometric formal languages. However, the neglect of the graph structure information in the formal language and the lack of further refinement of the extracted language set can lead to the poor effect of the theorem prediction and affect the accuracy in problem solving. In this paper, the formal language graph is constructed by the extracted formal language set and used to theorem prediction by graph convolutional network. So as to better extract the relationship set of diagram elements, an improved diagram parser was proposed. The test results indicate that the improved method has good results in solving the problem with interpretability geometry.

Math Word Problems (MWP) solving involves language comprehension and mathematical reasoning. Most of the existing models are primarily based on deep learning methods. However, deep learning models often exhibit large model scales (e.g., large number of parameters), high feature dimensions, and an imbalance between accuracy and computational efficiency. To address these issues, We propose a novel dual-decoder model for solving Mathematical Word Problems (MWP), which is constructed using a Lie Group intrinsic mean feature matrix and named the Dual-Decoder Neural Symbolic Machine (DDNSM). This model projects data samples onto a Lie Group manifold to effectively reduce the output feature dimensions of the encoder through a feature matrix built around the Lie Group intrinsic mean, thereby reducing the computational load in the decoding stage and improving model inference efficiency. Additionally, we designed a dual-decoder system, comprising a decoder based on global and local attention mechanisms and another structured around a tree built from the Lie Group intrinsic mean. Extensive experiments on multiple challenging public datasets demonstrate that our model achieves competitive results in MWP tasks, achieving competitive results in MWP tasks with improved accuracy and computational efficiency.

Effective Automated Geometric Problem Solving (AGP) requires a deep integration of visual perception and textual comprehension. To address this, we propose a dual-stream fusion model that injects deep semantic understanding from a Pre-trained Language Model (PLM) into the geometric diagram parsing pipeline. Our core innovation is a Semantic-Guided Cross-Attention (SGCA) mechanism, which uses the global semantic intent of the problem text to direct attention toward key visual primitives. This yields context-enriched visual representations that serve as inputs to a Graph Neural Network (GNN), enabling relational reasoning that is not only perception-driven but also context-aware. By explicitly bridging the semantic gap between text and diagrams, our approach delivers more robust and accurate predictions. To the best of our knowledge, this is the first study to introduce a semantic-guided cross-attention mechanism into geometric diagram parsing, establishing a new paradigm that effectively addresses the cross-modal semantic gap and achieves state-of-the-art performance. This is particularly effective for parsing problems involving geometric symmetries, where textual cues often clarify or define symmetrical relationships not obvious from the diagram alone.