ExpTest: Loss-Curve Hypothesis Testing for Autonomous Learning-Rate Selection in Deep Neural Networks

Hyperparameter tuning remains a significant challenge in the training of deep neural networks (DNNs), requiring manual search or time-intensive grid searches that increase resource costs and limit the accessibility of machine learning. The global initial learning rate is among the most consequential of these hyperparameters. Adaptive and scheduling-based methods manage the learning rate during training but still require manual selection of an initial global value; learning-rate-free alternatives remove this selection at the cost of performance or stability on non-convex problems. We present ExpTest, an autonomous learning-rate controller that treats the training loss curve as an online signal and performs sequential statistical tests on theoretically motivated windows to detect convergent behavior and trigger learning-rate reductions. The framework combines a covariance-based initial learning-rate estimate, curvature-motivated window sizing, and two-phase test-driven decay, drawing on the approximately exponential decay behavior predicted under linearized network dynamics. We provide a mathematical motivation for ExpTest and evaluate it on regression, classification, forecasting, and natural-language tasks across fully-connected, convolutional, transformer-based, and pretrained architectures. Across these tasks, ExpTest achieves competitive performance relative to hand-tuned SGD-based baselines and recent learning-rate-free methods, without manual initial learning-rate selection or predefined scheduling.