Same Score, Same Capabilities? Regularizing Factorized Representations for Transfer

Similar scores need not imply equally reusable components. We ask whether the selection readout should match the representation interface used downstream. A population construction shows that identical full-representation validation, transfer and spectra can conceal different component utility. FACTOR-MAE controls separate weight-decay strength from same-strength dependence regularization. Utility-Constrained Regularization Selection (UCRS) screens strength, then maximizes backbone transfer subject to unique-code non-decrease. Separate selection and evaluation cohorts test whether this constraint improves downstream component reuse. Exchanging code and trunk guards reverses preference across student targets, with a 0.250-point interaction. A second, prediction-preserving interface intervention yields reciprocal preferences in both ViT-Ti and ResNet18, with interactions 0.313/0.312 points. These results support matching the selection readout to the consumer's interface, rather than simply adding a probe. Unique-only tradeoffs and retained student losses delimit the benefit: UCRS is neither student-optimal nor a guarantee of loss-free reuse. The anonymized code, data registry and experiment records are available at https://anonymous.4open.science/r/ID20229.