Exploratory Data Analysis and Feature Extraction

The workflow begins by loading the amphora/ResearchMath-14k dataset, which contains research-level mathematics problems from arXiv. Initial processing involves filtering for meaningful text length and performing a distribution analysis across mathematical fields (taxonomy_level_1) and problem status (open_status). To understand the thematic composition of these fields, the tutorial uses a TfidfVectorizer to extract the top 8 keywords per mathematical category, providing a clear view of the terminology that defines different research areas.

Semantic Search and Predictive Modeling

Moving beyond keyword matching, the tutorial leverages the sentence-transformers/all-MiniLM-L6-v2 model to generate semantic embeddings for the problem statements. This enables two primary capabilities:

• Semantic Search: By calculating cosine similarity between a user query and the dataset embeddings, the system retrieves the most relevant research problems, allowing for conceptual search rather than simple keyword matching.
• Status Classification: Using the generated embeddings as features, a LogisticRegression classifier is trained to predict the open_status of a problem. The model uses a balanced class weight to handle potential label imbalances, and performance is evaluated using a confusion matrix to visualize predictive accuracy across categories.

Landscape Visualization and Similarity Detection

The final stage of the pipeline involves visualizing the problem landscape by reducing high-dimensional embeddings into two dimensions using UMAP (or PCA). This spatial mapping, combined with K-Means clustering, allows for the identification of related problem clusters. Furthermore, by computing a full similarity matrix across the dataset, the system can identify near-duplicate or highly related problem statements, providing a robust method for corpus-wide analysis.