Twin: Tuning Learning Rate and Weight Decay of Deep Homogeneous Classifiers without Validation

We introduce Tune without Validation (Twin), a simple and effective pipeline for tuning learning rate and weight decay of homogeneous classifiers without validation sets, eliminating the need to hold out data and avoiding the two-step process. Twin leverages the margin-maximization dynamics of homogeneous networks and an empirical scaling law that links training and test losses across hyper-parameter configurations. This mathematical modeling yields a regime-dependent, validation-free selection rule: in the non-separable regime, training loss is monotonic in test loss and therefore predictive of generalization, whereas in the separable regime, the parameters' norm becomes a reliable indicator of generalization due to margin maximization. Across 37 dataset-architecture configurations for image classification, we demonstrate that Twin achieves a mean absolute error of 1.28% compared to an Oracle baseline that selects HPs using test accuracy. We demonstrate Twin's benefits in scenarios where validation data is scarce, such as small-data regimes, or difficult and costly to collect, as in medical imaging. Code available at https://github.com/lorenzobrigato/twin.