We introduce GeoDANO, a geometric vision-language model (VLM) with a domain-agnostic vision encoder, for solving plane geometry problems. Although VLMs have been employed for solving geometry problems, their ability to recognize geometric features remains insufficiently analyzed. To address this gap, we propose a benchmark that evaluates the recognition of visual geometric features, including primitives such as dots and lines, and relations such as orthogonality. Our preliminary study shows that vision encoders often used in general-purpose VLMs, e.g., OpenCLIP, fail to detect these features and struggle to generalize across domains. We develop GeoCLIP, a CLIP based model trained on synthetic geometric diagram-caption pairs to overcome the limitation. Benchmark results show that GeoCLIP outperforms existing vision encoders in recognizing geometric features. We then propose our VLM, GeoDANO, which augments GeoCLIP with a domain adaptation strategy for unseen diagram styles. GeoDANO outperforms specialized methods for plane geometry problems and GPT-4o on MathVerse.

Graph-based models have become increasingly important in various domains, but the limited size and diversity of existing graph datasets often limit their performance. To address this issue, we propose EPIC (Edit Path Interpolation via learnable Cost), a novel interpolation-based method for augmenting graph datasets. Our approach leverages graph edit distance to generate new graphs that are similar to the original ones but exhibit some variation in their structures. To achieve this, we learn the graph edit distance through a comparison of labeled graphs and utilize this knowledge to create graph edit paths between pairs of original graphs. With randomly sampled graphs from a graph edit path, we enrich the training set to enhance the generalization capability of classification models. We demonstrate the effectiveness of our approach on several benchmark datasets and show that it outperforms existing augmentation methods in graph classification tasks.