GAHIB: graph attention VAE with a hyperbolic information bottleneck for biologically structured single-cell representations.

Current single-cell RNA-sequencing (scRNA-seq) variational autoencoders (VAEs) usually emphasise local cell graph structure, hyperbolic latent geometry, or bottleneck compression separately, yet these biases are rarely evaluated together in one evidence-gated representation model. We present GAHIB (graph attention VAE with a hyperbolic information bottleneck), which combines a graph-attention encoder, a 2D information bottleneck, and a Lorentz-hyperbolic geometry loss. Because the main clustering benchmark uses Leiden-derived proxy labels rather than definitive biological ground truth, we evaluate the model in two tiers: a broad 53-dataset proxy-label benchmark for method characterisation, and curated-label and marker analyses on annotated systems for biological interpretation. Across the proxy benchmark, GAHIB shows a balanced aggregate profile across clustering, projection-quality, and latent-structure metrics, while important comparisons remain mixed: scVI is statistically close to NMI/ARI, and scDHMap remains competitive on DRE-UMAP. On curated-label systems, the biological signal remains context-dependent; muscle atlas analyses support lineage-aligned structure with marker enrichment, whereas the fine T-cell immune-subtype task favors scVI. Sensitivity, seed-stability, a bounded count-dropout pilot, and cost analyses indicate practical runtime under the tested settings; however, the dropout evidence is limited to named pilot systems, and complete manually curated provenance remains an explicit limitation. Together, the results position GAHIB as a complementary, geometrically aware, single-cell representation rather than a drop-in clustering replacement.