Twin-Boot: Uncertainty-Aware Optimization via Online Two-Sample Bootstrapping

Standard gradient descent methods yield point estimates with no measure of confidence. This limitation is acute in overparameterized and low-data regimes, where models have many parameters relative to available data and can easily overfit. Bootstrapping is a classical statistical framework for uncertainty estimation based on resampling, but naively applying it to deep learning is impractical: it requires training many replicas, produces post-hoc estimates that cannot guide learning, and implicitly assumes comparable optima across runs - an assumption that fails in non-convex landscapes. We introduce Twin-Bootstrap Gradient Descent (Twin-Boot), a resampling-based training procedure that integrates uncertainty estimation into optimization. Two identical models are trained in parallel on independent bootstrap samples, and a periodic mean-reset keeps both trajectories in the same basin so that their divergence reflects local (within-basin) uncertainty. During training, we use this estimate to sample weights in an adaptive, data-driven way, providing regularization that favors flatter solutions. In deep neural networks and complex high-dimensional inverse problems, the approach improves calibration and generalization and yields interpretable uncertainty maps.