Convergence of stochastic gradient descent for learning linear neural networks
Why the algorithm behind AI training actually works mathematically
Researchers proved that stochastic gradient descent—the algorithm used to train virtually all modern neural networks—reliably converges to good solutions, even in simplified deep learning models. The proof works without requiring unrealistic assumptions like perfectly clean data, and holds for both fixed and adaptive learning rates.
SGD is used billions of times daily to train everything from language models to image recognition systems, yet engineers have lacked mathematical proof it actually works. This result provides that foundation, validating the theoretical soundness of a procedure that already works in practice and potentially guiding how to set learning rates and other training parameters more reliably.