Hyperbolic parallel-transport steering outperforms Euclidean concept control
measured in 1 paperBriglia et al. introduce HyCon, which steers concepts in HyCoCLIP's pretrained Lorentz-model hyperbolic embedding space rather than the flat Euclidean CLIP space used by prior methods [briglia-etal-2026-hycon] Entailment-cone membership tests on MS-COCO captions confirm the reused geometry holds, with at least 93.33% (up to about 100%) of single/multi-concept captions falling within their expected Frechet-mean cone intersections [briglia-etal-2026-hycon] The method computes a concept direction between Frechet means and parallel-transports it along the geodesic to each query point before applying it, unlike flat additive steering that reuses one global direction [briglia-etal-2026-hycon] Across four safety benchmarks and four text-to-image backbones (SDXL, SD3, SD3.5, FLUX.1), HyCon substantially cuts unsafe-content generation while preserving quality (e.g. SD3.5/P4D NudeNet 42.4 to 5.96) [briglia-etal-2026-hycon] A direct ablation against a Euclidean refusal-vector baseline (same extraction, no transport) shows parallel transport itself is the source of the improvement [briglia-etal-2026-hycon]