Multi-Submanifold Structure in Latent Spaces of Large Language Models: A Topological and Geometric Analysis Across Architectures and Datasets

This deposit contains the complete reproducible analysis pipeline, experimental results, and research paper for a topological and geometric study of latent representation spaces in large language models.

Contents:
- latent_topology_notebook.ipynb — Jupyter notebook with the full analysis pipeline (Google Colab GPU-ready)
- generate_notebook.py — Python script that generates the notebook
- paper_latent_topology.pdf — Research paper (28 pages)
- paper_latent_topology.tex — LaTeX source
- latent_topology_results/ — All experimental outputs: 22 figures (PNG), 3 interactive 3D plots (HTML), 4 data tables (CSV), intermediate data (PKL), and automated reports (MD)
- README.md — Project documentation

The study analyzes four transformer models (Qwen2.5-0.5B, Qwen2.5-1.5B, GPT-2-124M, Phi-2-2.7B) across three cognitively distinct prompt datasets (knowledge, reasoning, language), totaling 12 configurations. Methods include persistent homology (Ripser), graph community detection (Louvain, Leiden), density-based clustering (HDBSCAN), intrinsic dimension estimation (TwoNN, MLE), bridge node detection, and perplexity probing.

All prompts are in Brazilian Portuguese (PT-BR). The pipeline is designed to run end-to-end on Google Colab Pro with GPU access.