Contrastive Geometric Transfer: Efficient Sentence Embeddings via Hyperbolic Projection with 24× Compression

Contrastive Geometric Transfer (CGT) is a framework for compressing sentence embeddings by projecting them from Euclidean to hyperbolic space (Lorentz model). KEY RESULTS - CGT-32: Achieves 97.4% of SBERT-base performance (ρ=0.812 vs 0.834) with 24× compression (768d → 32d)- CGT-128: Matches MiniLM-384d performance (ρ=0.819 vs 0.820) with 3× fewer dimensions- Efficiency: Reduces vector database costs by up to 95% and enables 25× faster similarity search PRACTICAL IMPACT Scale | SBERT-768d | CGT-32d | Savings------------|------------|----------|--------1M docs | 3.07 GB | 128 MB | 24×1B docs | 3.07 TB | 128 GB | 24× CONTENTS - toy-psi-slm/ - Python package with CGT implementation- tutorial_completo_full_knowledge.ipynb - Complete tutorial notebook- benchmark_exhaustive.ipynb - Reproducible benchmark experiments - cgt_arxiv_v3.pdf - ArXiv paper- exhaustive_benchmark_results.json - Raw experimental results METHOD CGT learns a neural projection from pre-trained SBERT embeddings to the Lorentz manifold using:- MSE loss for similarity alignment- Margin-based ranking loss for ordinal consistency- Exponential map projection with manifold correction CITATION @software{reis2025cgt, author = {Reis, Éric Hayda}, title = {Contrastive Geometric Transfer: Efficient Sentence Embeddings via Hyperbolic Projection}, year = {2025}, url = {https://github.com/gokuhayda/toy-psi-slm}}