Age Subspaces in 3D Face Representations: Readability, Predictive Dependence, and Transferability

Understanding age-related face representations requires distinguishing whether age information is linearly readable, whether a fitted predictor relies on the identified directions, and whether those directions transfer across independently trained representations. We investigate these questions in 3DMM-derived shape representations using correlation-ranked PCA directions, controlled direction removal, and cross-run comparisons. Correlation-ranked PCA directions retain age-predictive performance with fewer dimensions than variance-ranked PCA directions. Under the evaluated removal protocol, removing the top ten correlation-ranked directions reduces the fixed predictor's $R^2$ from 0.588 to approximately 0.16, whereas dimension-matched random removal reduces $R^2$ by only 0.017. Across training runs, the discovered subspaces exhibit overlap close to the random baseline in native coordinates, and directly transferring these directions across runs produces limited removal effects. These findings establish predictive dependence within the measured representations without implying complete age-information removal or intrinsic semantic differences across models. We further introduce Age Subspace Learning (ASL), a PCA-based decomposition with identity supervision, for age-robust face representation. Together, the results distinguish age readability, predictor dependence, and direct transferability, clarifying the interpretation and scope of age-subspace analysis.