A Hierarchy-Aware Video-Language Model Evaluation and Hyperbolic Baseline for Surgery

Surgical vision-language foundation models typically adopt educational materials, such as surgical lecture videos, to transfer surgical knowledge encoded in language into visual representations. These knowledge are multi-dimensional and hierarchical: fine-grained action cues appear in narration, mid-level key steps are summarized in subsection headings, and global procedural context, such as patient history and surgical strategy, is described in abstract texts. Prior work largely collapses these heterogeneous signals into a single flat embedding space, implicitly assuming independence across hierarchy levels. However, this is suboptimal because it ignores cross-level semantic containment, e.g., actions belong to steps, steps compose phases, weakens long-range dependency modeling. To this end, we propose a hyperbolic surgical video-language pre-training framework that explicitly preserves the hierarchical structure by mitigating structural false negatives induced by procedural context and enforcing semantic consistency between parent phases and their constituent child steps. Extensive experiments on multiple surgical benchmarks show consistent gains in zero- and few-shot phase recognition across procedures and institutions.

We introduce SurgAtlas, the largest surgical video-language dataset to date, comprising 15,291 videos (2,391 hours) spanning 18 surgical specialties and over 5,000 procedure types, sourced entirely from publicly available YouTube content. SurgAtlas is also the first surgical video-language dataset to include open surgery at scale, with 6,182 open procedure videos alongside over 9,000 minimally invasive recordings, and the first to establish standardized benchmarks for open-surgery video understanding. We additionally provide an expert-validated subset with verified visual question-answer pairs across diverse open and minimally invasive procedures, serving as a clinically grounded benchmark for surgical reasoning. Compared with existing surgical video-language datasets, SurgAtlas provides one of the most diverse annotation schemas, combining segment-level captions, step- and phase-level descriptions, video-level surgical descriptions, and reasoning-oriented question-answer pairs organized within a hierarchical taxonomy. These annotations are constructed through an automated multi-tier pipeline with LLM-based enrichment and a staged VQA generation framework with explicit groundedness verification. The scale and diversity of SurgAtlas enable training surgical foundation models with broad procedural coverage: we finetune Qwen3-VL-8B through a two-stage captioning-then-instruction pipeline and achieve competitive or state-of-the-art results on multiple established surgical benchmarks, including phase recognition, triplet detection, and reasoning question answering. More broadly, SurgAtlas provides a large native public video corpus that can support future large-scale pretraining of multimodal surgical AI systems and contribute to the development of next-generation foundation models for surgery. Dataset publicly available at https://huggingface.co/datasets/filbel/SurgAtlas

Whether a hyperbolic representation model uses its geometry cannot be inferred from curvature alone: what matters is the dimensionless operating point $\sqrt{c}ρ$ and whether the radial and cone mechanisms are operational there. We develop necessary-condition diagnostics and audit three published hyperbolic vision-language families -- MERU, HyCoCLIP, and PHyCLIP -- across released checkpoints and matched interventions. All converged checkpoints remain near-Euclidean ($H(u)\approx1$; none reaches $\sqrt{c}ρ>1$), and releasing the curvature floor changes $c$ and norms without leaving this regime or substantially degrading downstream performance. Entailment cones are inactive or saturated, and graded traversal fails under controlled readouts, including the models' native distance metrics. External parent-child ordering shows no shuffle-controlled pair-specific radial signal at quantified sensitivity; the only surviving pair-specific signal, a statistically detectable but small residual on the GRIT box-to-full-caption relation, remains non-operative under the evaluated readouts. Taxonomy correlations show no detectable norm contribution beyond cosine, and coarse-retrieval gains co-vary with box/compositional supervision without establishing an active radial mechanism. Gradient diagnostics expose a low-curvature, wide-cone shortcut in the entailment objective. A closed-form aperture identity places the saturation edge at $\sqrt{c}ρ\le2K$: with the floor released, all trained relation-level parent means lie at or below this edge, leaving the parent cones fully or nearly saturated. Entailment-off runs pass the edge and continue contracting. The shortcut is the dominant accelerator of collapse, not its sole cause. These audited formulations do not show an operative radial/cone mechanism under our diagnostics. We distill the audit into a five-number geometry report for hierarchy claims.