Cross-regularization: Adaptive Model Complexity through Validation Gradients

Model regularization requires extensive manual tuning to balance complexity against overfitting. Cross-regularization resolves this tradeoff by directly adapting regularization parameters through validation gradients during training. The method splits parameter optimization - training data guides feature learning while validation data shapes complexity controls - converging provably to cross-validation optima. When implemented through noise injection in neural networks, this approach reveals striking patterns: unexpectedly high noise tolerance and architecture-specific regularization that emerges organically during training. Beyond complexity control, the framework integrates seamlessly with data augmentation, uncertainty calibration and growing datasets while maintaining single-run efficiency through a simple gradient-based approach.

Geometric-Aware Variational Inference: Robust and Adaptive Regularization with Directional Weight Uncertainty

Deep neural networks require principled uncertainty quantification, yet existing variational inference methods often employ isotropic Gaussian approximations in weight space that poorly match the network's inherent geometry. We address this mismatch by introducing Concentration-Adapted Perturbations (CAP), a variational framework that models weight uncertainties directly on the unit hypersphere using von Mises-Fisher distributions. Building on recent work in radial-directional posterior decompositions and spherical weight constraints, CAP provides the first complete theoretical framework connecting directional statistics to practical noise regularization in neural networks. Our key contribution is an analytical derivation linking vMF concentration parameters to activation noise variance, enabling each layer to learn its optimal uncertainty level through a novel closed-form KL divergence regularizer. In experiments on CIFAR-10, CAP significantly improves model calibration - reducing Expected Calibration Error by 5.6x - while providing interpretable layer-wise uncertainty profiles. CAP requires minimal computational overhead and integrates seamlessly into standard architectures, offering a theoretically grounded yet practical approach to uncertainty quantification in deep learning.

World Models as Reference Trajectories for Rapid Motor Adaptation

Deploying learned control policies in real-world environments poses a fundamental challenge. When system dynamics change unexpectedly, performance degrades until models are retrained on new data. We introduce Reflexive World Models (RWM), a dual control framework that uses world model predictions as implicit reference trajectories for rapid adaptation. Our method separates the control problem into long-term reward maximization through reinforcement learning and robust motor execution through rapid latent control. This dual architecture achieves significantly faster adaptation with low online computational cost compared to model-based RL baselines, while maintaining near-optimal performance. The approach combines the benefits of flexible policy learning through reinforcement learning with rapid error correction capabilities, providing a principled approach to maintaining performance in high-dimensional continuous control tasks under varying dynamics.