Surgical procedures follow a phase-to-step hierarchy, yet the video-language models used to recognize them are evaluated with flat per-level metrics that ignore cross-level coherence and error structure. In this paper we make two contributions to address this problem, (i) we introduce SurgHiBench, the first hierarchy-aware evaluation suite for surgical video understanding, with three tasks measuring recognition, consistency, and severity across granularity levels.

We evaluate a general-purpose CLIP model, a Euclidean surgical model, and, as second contribution: (ii) HyperSurg, a new hyperbolic model that enforces phase-step containment via entailment cones, across four (existing) datasets spanning three procedure types. The suite reveals that two models with the same accuracy can produce predictions of very different error severity, ranging from sibling confusions within the correct phase to unrelated cross-phase predictions.

Hyperbolic geometry shifts predictions toward the correct procedural neighborhood, and these gains scale with the tree-likeness of each dataset's annotation hierarchy, providing a principled indicator when hierarchy-aware geometry helps.