# A Knowledge and Semantic Fusion Method for Automatic Geometry Problem Understanding
## 2 Related Work
### Machine-Learning-Based Methods  
In recent years, machine learning methods have been widely applied in geometry intelligence and can be further categorized into large-scale deep learning methods and lightweight machine learning methods. With advancements in computational power and massive data accumulation, large language models (LLMs), BERT [18], and Transformer [19] have demonstrated strong capabilities in various text-parsing tasks, and these models are gradually being adopted in the geometry domain. AlphaGeometry employs a Transformer-based language model for text processing [20], while the upgraded AlphaGeometry2 combines a Gemini-architecture neural language model with symbolic reasoning engines [21,22]. FGeo-Parser utilizes a T5 model to convert problem texts into text CDL and target CDL, optimized via enhanced training sets and cross-entropy loss [23,24]. UniGeo constructs a multimodal encoder based on the VL-T5 model [25,26]. PGPSNet uses a masked language model (Masked LM) task structure and semantic pretraining method to handle the text modality [27], while [PERSON] et al. proposed an end-to-end deep learning method that uses feature learning to extract the features of geometry problem text [28]. [PERSON] et al. utilized the BERT model and domain knowledge graphs to convert entities and relationships in problem text into equivalent equation representations [29]. MagicGeo leverages the zero-shot capabilities of LLMs for geometry text formalization [30]. TongGeometry builds an Olympiad-level problem solver using two fine-tuned LLMs [31]. These studies employ highly complex deep learning models with millions to billions of parameters. These models heavily depend on data, requiring training data ranging from millions to billions of samples. The computational resource demands during training and inference are high, limiting the applicability and promotion of lightweight methods. In contrast, lightweight machine learning methods typically use fewer parameters and smaller datasets, enabling effective learning under resource-constrained conditions. For example, GeoQA constructs a text encoder using a single-layer unidirectional LSTM [32; 33], while upgraded GeoQA+ combines RoBERTa and Bi-LSTM to address varying text lengths [34; 35]. [PERSON] et al. employed BiLSTM-CRF with triple-level normalization and template mapping to convert directly mentioned information in problem text into knowledge graph representations [36; 37]. [PERSON] et al. proposed a knowledge-guided Sequence-to-General Tree (S2G) model, which builds an encoder using GRU [38; 39]. [PERSON] proposed a stacked long short-term memory network (Stacked LSTM) method to parse 3D analytic geometry problem texts [40; 41]. [PERSON] et al. adopted LSTM with RoBERTa as a text encoder [42]. [PERSON] et al. proposed a supervised learning method based on feature extraction and an SVM classifier to extract geometry relationships from problem texts [43]. [PERSON] et al. used a discriminative model to identify relationships in texts [2]. Lightweight machine learning methods face performance bottlenecks, including the strong dependence on manual feature engineering, leading to coverage gaps and long-tail issues, limited contextual awareness, and poor performance in handling scenarios with nested, hidden, and large gaps in information. From the perspective of technology transfer applications, works like asGeoRE and MLLMs validate that models performing well on conventional general-domain datasets suffer a significant performance drop when applied to the geometry domain, and their experiments also indicate the challenges of adapting machine learning models to the geometry field [44; 45]. Moreover, both large-scale deep learning and lightweight models face common challenges in GPU: first, the inherent bias of neural network probabilistic outputs conflicts with the requirement for precise semantic parsing in geometry problem understanding. Second, heavy reliance on data and computational resources hinders lightweight deployment.