Sufficient is better than optimal for training neural networks.

The array of neural network training techniques that invoke optimization but rely on ad hoc modification for validity suggests that optimization-based training is misguided. Shortcomings of optimization-based training are brought to strong relief by overfitting, where naive optimization produces spurious outcomes. Here, we introduce simmering, a physics-based method that trains neural networks to generate "good enough" weights and biases, paradoxically outperforming leading optimization-based approaches. Instead of optimizing, simmering systematically samples non-optimal weights and biases to generate an ensemble that provides sufficient representations of the underlying phenomenon. Simmering corrects neural networks that are overfit by optimization, and produces more generalizable predictions if deployed from the outset compared to other overfitting mitigation methods. Our results question optimization as a paradigm for training transformers, and feedforward and convolutional neural networks. We leverage information-geometric arguments to point to the existence of classes of sufficient-training algorithms that do not take optimization as their starting point.