Source-Optimal Training is Transfer-Suboptimal

We prove a fundamental misalignment in transfer learning: the source regularization that minimizes source risk almost never coincides with the regularization maximizing transfer benefit. Through sharp phase boundaries for L2-SP ridge regression, we characterize the transfer-optimal source penalty $τ_0^*$ and show it diverges predictably from task-optimal values, requiring stronger regularization in high-SNR regimes and weaker regularization in low-SNR regimes. Additionally, in isotropic settings the decision to transfer is remarkably independent of target sample size and noise, depending only on task alignment and source characteristics. CIFAR-10 and MNIST experiments confirm this counterintuitive pattern persists in non-linear networks.

Orthogonal Gradient Descent Improves Neural Calibration

We provide evidence that orthogonalizing gradients during training improves model calibration without sacrificing accuracy. On CIFAR-10 with 10% labeled data, $\perp$Grad matches SGD in accuracy but yields consistently improved calibration metrics such as lower test loss, reduced softmax overconfidence, and higher predictive entropy. These benefits persist under input corruption (CIFAR-10C) and extended training, where $\perp$Grad models degrade more gracefully than SGD-trained counterparts. $\perp$Grad is optimizer-agnostic, incurs minimal overhead, and works well with post-hoc calibration techniques like temperature scaling. Theoretically, we prove convergence of a simplified version of $\perp$Grad under mild assumptions and characterize its stationary points in positive homogeneous networks: $\perp$Grad converges to solutions where further loss reduction requires confidence scaling rather than decision boundary improvement.