GSSR: Graph-Spectral Control of Text-Induced Logit Updates for 3D Part Segmentation

Meaning-preserving prompts for the same 3D part can produce different pointwise masks. We measure the graph-frequency structure of paraphrase-induced logit changes and find that normalized Dirichlet energy adds modest held-out predictive value for soft-mask disagreement across two fusion heads. We then test a selective placement of a standard graph filter: GSSR filters the final query-dependent logit residual while leaving the query-independent base unfiltered. For the same frozen fields and filter, residual-only and full-logit filtering act identically on prompt-pair logit differences; the placement question is whether preserving the base benefits segmentation. In a PTv3-based controlled model, GSSR lowers soft disagreement ($100e_{\mathrm{soft}}$) from $3.20$ to $2.25$ and raises worst-prompt mIoU from $44.60$ to $48.80$ relative to the unfiltered Direct control. Its primary 3DCoMPaT-Coarse mIoU is $51.17$ versus $47.80$ (five-seed means). Frozen and retrained placement controls show higher observed region and boundary scores than full-logit filtering; a second fusion head replicates the Direct/GSSR direction. These findings support selective filter placement in the tested model family.