Abstract
We study cross-modal alignment between independently pretrained vision (DINOv2) and language (all-MiniLM-L6-v2) encoders using the functional map framework from computational geometry, which represents correspondence between representation manifolds as a compact linear operator between graph Laplacian eigenbases. While the framework underperforms Procrustes alignment and relative representations for cross-modal retrieval across all supervision budgets, it reveals a structural property of multimodal representations. We find that the Laplacian eigenvalue spectra of the two encoders are quantitatively similar (normalized spectral distance 0.043), indicating that independently trained models develop manifolds of comparable intrinsic complexity. However, the functional map exhibits near-zero diagonal dominance (mean below 0.05) and large orthogonality error (70.15), showing that the eigenvector bases are effectively unaligned. We term this decoupling the spectral complexity--orientation gap